Gambler’s Fallacy And Why It Matters In Business - FourWeekMBA

I can't actually find it in the curriculum, so just wanted to clarify

Hello /CompetitiveHS!
Since I had some extra time, I've decided to start a new series. Or, at least, hopefully a series - depending on what the response will be to this first piece.
As the title suggests, the series would tackle cognitive biases, and how they affect Hearthstone players. I choose probably the most obvious one as my first example - gambler's fallacy. If you want to see more, I'll just paste the introduction below. Or you can get straight to the article here.
The human brain is a wonderful thing. Sometimes, when presented with two choices, which are the same, just worded differently, it will assume that one option is better than the other. Other times, when you don’t have enough information, it will fill the gaps itself (often incorrectly). It looks for correlations, even if there aren’t any. Or leads you to situations in which something just FEELS right, even though it’s really not.
Believe it or not, but cognitive biases aren’t something rare. To put it simply, they’re common flaws in logic. Person’s own, subjective interpretation of reality. Of course, after you really start thinking about them, you realize that they make no sense. But what’s important is that they affect everyone – like you and me – in our daily lives.
In this series, I will cover some of the common cognitive biases that can affect Hearthstone players in particular. How do they work? Why do they happen? Are there any situations in which they actually make sense? Identifying them and realizing what they are is a big step in terms of becoming a better player. Plus some of them are just interesting to read about.
In the first part, I will talk about probably the most common fallacy tied to randomness – gambler’s fallacy. When playing Hearthstone, or any other card game, a fair bit of chance is involved, and understanding gambler’s fallacy can make you look very differently at every random roll. I will also give some examples of situations in which gambler’s fallacy… actually works.
Click here to read to the full article.
I really hope that you like it. And for those of you wondering, I'll be back with the best decks compilation post-nerfs on... Wednesday, probably. Day 1 stuff.
If you have any questions or suggestions, be sure to leave a comment. And if you want to be up to date with my articles, you can follow me on the Twitter @StonekeepHS. You can also follow @HS Top Decks for the latest news, articles and deck guides!

I chose to post here, because my post got removed after I posted it on unpopularopinion
I mean a low IQ probably would affect your ability to make decisions that are right since it affects our ability to understand and apply our knowledge as well as think critically about things, but a higher than average IQ would not necessarily make you a better leader or decision maker.
I formed this thought after reading through The Intelligence Trap by David Robson. Overall the book talks about why talented, knowledgeable, or intelligent people would fail to make the right decision and often end up being stupid.
Their are many reasons why intelligent people can be stupid. But the main reason is that IQ typically doesn't measure many of the skills, temperaments, and cognitive abilities required for good leadership or decision making, including the ability to avoid cognitive biases in thinking. IQ isn't a holistic measure of intelligence or ability.
Also, intelligent people often fall prey to certain traps. According to book by David Robson, their are three types of mentalities that "trap" intelligent people or educated people.

• We may lack the necessary tacit knowledge and counterfactual thinking that are essential for executing a plan and preempting the consequences of you actions
• We may suffer from dysrationalia, motivated reasoning, and the bias blind spot, which allow us to rationalize and perpetuate our mistakes, without recognizing the flaws in our own thinking. This results in our building "logic-tight compartments" around our beliefs without considering available evidence
• We may place too much confidence in our own judgement, thanks to earned dogmatism, so that we no longer perceive our limitations and overreach our abilities
• Thanks to our expertise, we may employ entrenched automatic behaviors that render us oblivious to the obvious warning signs that disaster i looming, and more susceptible to bias

And one more that I'll add

• We often fall prey to cognitive biases, such as the outcome bias and the gamblers fallacy

Also, it's possible that having a mental illness would have a effect on your decision making (although it does no necessarily affect your leadership capability). Example include when a person in the manic phase of their bipolar acting impulsively or a person with Schizophrenia doing things based on their delusions and hallucinations.

Hello guys! Yoyotje here.
Lately there is going a lot around about the new Censure Summoning Method. The idea of using Grey/Daily Tokens to test how lucky your RNG is before you do an Atlantis 10x pull. As a student psychology I recognized some cognitive thinking errors with this idea. I’ve been wanting to say this for a while now but I was always to hesitant about being wrong myself. I also coded a E&P Simulator (Code shown below the post) to get myself some data to prove or disprove. Let’s begin with the begin.
What is the Censure Summoning Method? The Censure Summoning Method has 4 steps you have to go through for you to get ‘good pulls’. I did not come up with this method myself and all credit goes to the original author of whom I do not know his/her name. The original author posted this which has more information about the method: https://docs.google.com/document/d/1A9x3CO1UFEXD20KSdg8tpcbFaTFrSX9cEwhvKKjYYqg/edit.
Step 1: Use a Grey/Daily token and get a 3 star hero or a troop. If you get an 1 or 2 star hero you STOP. Step 2: Use a Grey/Daily token. If you get a 2 or 3 star troop or a 3 star hero proceed to step 3. If you get a 1 star troop repeat step 2(repeat max 2 times). Anything else you STOP. Step 3: Use a single Atlantis Summon with either 100 Atlantis coins or 350 gems. If you get a season 1 3* hero you STOP! Anything else you proceed to step 4. Step 4: Do a 10x Atlantis Summon. Don’t exceed two 10x Summons
The idea behind this method is to recognize when you are on a lucky streak and take advantage of it. On top of that there a few more pros for the method. It limits the amount you spend massively and it helps with your mental state by getting less frustrated.
Why does this not work?
The cognitive thinking error that is made here is known as the Gambler Fallacy. The Gambler Fallacy thinking error states that people think that events in the past affect the events in the present.
An example: if I flip a coin 10 times and it lands 10 times in a row on heads, what is the chance it will be tails on the next throw? There are people who would say it would be a big chance because we already got 10 heads and it has to even out, right? This is where the error comes in, on the 11th throw it will still be a 50/50 whether its heads or tails, negating anything that happened before that.
This is exactly what happens with this method. If I got five 3* troops in a row from the Daily Summon Portal and I go to the Atlantis portal, the chance that I will get an featured hero is still 1,3%. This percentage will not change, no matter what happened before it. That being said, you can’t know for sure when you triggered an ‘lucky streak’ because there is no way to predict what your next summon will be.
An important note is that I stated all of this information on the idea that the odds in the summoning portals are actually true. In a lot of countries its obligated by law to state the odds of any loot box that can be bought by minors that could cost in real currency. Following this we can assume the percentages in the summoning portals are correct and there are no other systems in play.
Why do people believe it works?
A lot of people seem to believe this is a working method to get good summons. There are a lot of YouTube videos out there who claim that it works and actually show a good 10x pull while using the Censure Summoning Method. The big question that has to be asked here, it is a good 10x pull BECAUSE the method was used or is it just a coincidence? The thing that’s in play here is the conformation bias. People tend to acknowledge any evidence that supports their claim while ignoring any evidence that could disprove it.
I have used the method myself as well and my pulls were least to say pretty bad. I could still make the same mistake with the conformation bias only looking at my one 10x pull. We simple do not have enough reliable data to actually test if it works. That is why I coded a E&P Simulator. In this simulator I did 10,000 summons with the method and 10,000 summons without the method. I calculated if there are any significant difference between the summons and there is not a single significant difference to be found. I will link the code here below so you can check it out. In the code I will explain as much as I can. I also will explain why I ‘only’ did 10,000 summons each and what flaws could potentially be in the code. It’s still a good pointer into the direction that this method is just a superstition with not a single scientifically proven background.
TL:DR
In conclusion: The Censure Summoning Method does not work to get better summons. People tend to make mistakes like the Gambler Fallacy and the confirmation Bias. The method has pros in the sense of spending less money and getting less frustrated. With a sample size of 10,000 summons there is no significant difference to be found by using the method or not using it.
Link to the code: https://repl.it/@yoyotje/EandP-Summon-Simulator#main.py

I'd like to show an example on biases I've encountered while having fun drawing TA charts during the lockdown. In some cases like Indonesia's COVID19 curve for example, Technical Analysis (TA) and a properly done predictive analytics model do converge, as In they gave out the same results, so I choose to display my model in TA style for the lulz.
Cognitive biases that were encountered : confirmation bias, continued influence effect, curse of knowledge,Dunning–Kruger effect,Hindsight bias
Social biases : Authority bias, halo effect, asymetric insight, shared information bias.
My tendency and this sub is to criticize the general Indonesian population on the usually news article related silly believes, behaviours and practices (curse of knowledge) ,(Naive Realism). Which ironically is also very heavy in here. /indonesia have a youngish mid-up tech minded demographic, with many that study/work in engineering/IT. So redditors have been accustomed to think/assume they are smarter then the average population(they use more logical reasoning)
but as I will show this comes with biases as well.
As an example last month this sub voted for Singapore's SUTD Machine Learning SIR model as the COVID19 prediction model they believe the most.
https://www.reddit.com/indonesia/comments/gedg4s/which_covid19_epidemic_model_on_indonesia_do_you/
(Sadly my funny & cool looking charts only came at number 3 on that vote)
That model even though it has shown zero predictive value triggered all the cognitive&social biases for /indonesia demographic
- came from singapore (ultimate attribution error)
- from a reputable university (Authority bias)
- by a charismatic professor and grad student working with MIT and other top world institutions. (halo effect)
- Use all the right hot trigger words, machine learning, SIR, etc. (confirmation bias, shared information bias)
It made headline news in Indonesia's media. As I've pointed out it is silliness trying to use a base deterministic SIR model underneath non linear kernels in neural networks to try to predict a non stationary time series. Their model which was continuously updated on new infection data, predicted April 19 as the peak using May's data, up to May 15th. Here is a screenshot before they "internalized" the model.
https://ibb.co/8MnP4xM
Needless to say this diverged so hard from reality and the model have been "internalized" which is corporate speak for our model sucks so bad that we are ashamed to publish it.
https://ddi.sutd.edu.sg/
As compared to my tinfoil prediction that have been very accurate so far, track record here :
https://www.reddit.com/indonesia/comments/guogj8/covid19_megathread_part_2/ft937wg?utm_source=share&utm_medium=web2x
and don't forget my psuedo sciency meme laden TA chart
https://www.reddit.com/indonesia/comments/gnvtgl/new_indicators_indonesia_covid19_daily_infection/
https://www.reddit.com/indonesia/comments/gtw82n/clarifying_what_i_think_on_the_covid19_epidemic/
However because i wear a tinfoil hat and draws TA chart+memes ppl think I'm an OP warnet or something, even a few redditors think they can do better.
Dunning–Kruger effect,Hard–easy effect
https://www.reddit.com/indonesia/comments/guogj8/covid19_megathread_part_2/ft9mw14?utm_source=share&utm_medium=web2x
(Baader–Meinhof phenomenon, Gambler's fallacy)
https://www.reddit.com/indonesia/comments/guogj8/covid19_megathread_part_2/ftcpcua?utm_source=share&utm_medium=web2x
And even after proven wrong, they refuse to acknowledge any merit in my model / prediction so far because it is so meme ladden and doesn't fit into their world view (Semmelweis reflex)
If I had presented my model in a more sane and structured way, called it machine learning, neural nets, genetic algorithm, etc... it probably would have won over many redditors, but alas where's the fun in that and I still have lot's of time to fill in this pandemic.
Edit 1 : Thanks for the award kind stranger.
As a reward, you get the special Safe & Social Award icon on your submission. Very dapper.
Want to say thanks to your mysterious benefactor? Reply to this message. You will find out their username if they choose to reply back.
This post was meant to raise awareness in the importance of psychology&social sciences for techie redditors. Don't repeat my experience here :
https://www.reddit.com/indonesia/comments/gze24v/why_you_can_be_intellectual_but_still_be_very/ftfy180?utm_source=share&utm_medium=web2x

Muslim (203) narrated from Anas (may Allaah be pleased with him) that a man said: “O Messenger of Allaah, where is my father?” He said: “In Hell.” When he turned away he called him back and said: “My father and your father are in Hell.”
Al-Nawawi (may Allaah have mercy on him) said:
This shows that whoever dies in a state of kufr will be in Hell. And being related to one who is close to Allaah will not avail him anything. It also shows that whoever died during the fatrah (the interval between the Prophethood of ‘Eesa (peace be upon him) and that of Muhammad (peace and blessings of Allaah be upon him)) and was the follower of the way of the Arabs at that time, which was idol worship, will also be among the people of Hell. There is no excuse for the call not reaching them, because the call of Ibraaheem and other Prophets (peace be upon them) had reached these people.
Look at this pitiful excuse by nawawi. Islam didn't exist prior to Muhammad and yet they are in hell. How is this not contradicted by the hadith that there are some people that would be spared hell because they died before puberty, the interval between Jesus and Muhammad etc, and those who never heard of Islam today? The excuse given is that there were remnants of Islam at the time of muhammads parents and that they should of known idolatry was wrong, and because they didn't they'll be in hell forever. Bear in mind ibraheem existed thousands of years ago, and no prophet after him went to the Arabs until Muhammad. The message was corrupt beyond recognition, so how were they to know?
Ahh the good old fitrah response, see I don't buy that crap, because we humans have innate biases that prevent us from being rational. Social psychologists have identified over a dozen cognitive issues that lead us astray and cause us to make serious errors in judgement. Confirmation bias: Our tendency is to agree with people who agree with us. We love to read or hear things that confirm what we already believe to be true.
In group bias: A throwback to our tribal roots, we innately trust and believe people in our in-group, while being fearful, suspicious and possibly even disdainful of other people.
Gamblers fallacy: We erroneously put weight on past events to predict future ones.
Status quo bias: We tend to be apprehensive of change, which sometimes cause us to make choices and decisions that will keep things the same or at least be the least disruptive.
Bandwagon effect: We love to go with the flow of the crowd and we feel safety in numbers. A groupthink mentality can cause us to hold ideas that are very popular but possibly not true. It's a part of our desire to fit in and be a part of a group. You may be familiar with the saying, "a billion Chinese can't be wrong," but they absolutely can be.
These are just a few of the most recognized biases. And yet Islam dosent acknowledge any of these. Only black and whites, no shades of greys. It's either you believe or you don't so it's hell for you. This clearly isn't, if a god did exist, a message he would write since if he created us he would know how fucked up our brain is. It really is damning information. We know now that we humans are complex creatures with biases and yet we are punished if we don't make the right 'obvious' decision. It beggars belief.

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Mutually affecting Titans ever overreaching
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Settle for distraction Athene’s teaching
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Covertly campaigned defiling my name
Creations Instigate destruction
Erupts surreptitious instruction
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Military missionary hold prostrate to vaccinate
Chaotic Kronos ordered time consumed
Stow stoked fumes subsidies gave the gods room
Whilst land of the fraud is home to the knave
Babylon of living nonexistent through the golden age
Cassandra of this stage ilk ignores inklings of alarmed sage
Chicken little forebodes sky is falling
Rope a dope fades rationalisation
Brittle doth be fragile ye recalling
Loquacious news needs slews feigned of disambiguation
Mendacious or fallacious contagious be implications
Butterfly flapped wing doth not move a thing
But a gnat perhaps who's too GAD to fly
Financing is how but where is the why
Important that all patriots patronize conquesting troops
Dodge ye head stoop as pooping eagle swoops
Most dismissive uninspired missive
Perceptually far too derisive
Guiding hand not apparent visual
Missing cash flows continual residual bottom lines
Pinnochio hopes to know Which ideal conjures growth sublime
Dendrites potentially stimulate spine
Titanic torrents mist venetian blinds
Decidedly distort bilked disincline
Writhe in through chasm in awe open wide
Formless figures summon uniform pride
Dismiss discontent conveyors subside
Tributaries dispersed springs knowledge trees freeze molten ore
Splintering sparks displaced thick dark coruscate tangible floor
Cumulus clouds of primordial dust
Question our senses in sun god we trust
Sifted silts produce thunderbolts of Zeus
Oval elliptical orbits the folds tidal tendency
Blue sphere girds spoken word breathed clay Boulder Forge Company
Quality moulding is job number one
Caste mass producing consumes many sons
My duty to ensure we always run
Figured would be a piece of cake more at work than give and take
Thought this would be my big break but not knowing literally
Apprenticed construction now I maintain
Composite skill same commissioning game
Swim or wallow in Uranus disdain
I made the trade not for reward nor deemed security
Only gospel guarantee is confidence in mastery
Tasked to sit in a chair contemplate stare
Crosswords in wait for a breakdown repair
I study craves of machines which behave
Rhythmic clang links chain react percussional power set free
Insatiable harmony piques morbid curiosity
Beast belly bowel bubbles belch smelt death
To quota of product do I owe breath
Economic cauldron of corrosion
We operate Vesuvius ungodly hours breathing brine
Facilitate yon amplidyne oxygenate lavas shine
Steering eather into three cyclops cells
Myopically they motion for me when cycles in chaos my sirens knell
Lion hearted as Hephaestus take knee before crucibles hearth
Examine vitals symptoms prognosis deduce further impart
Volt amps transcend times root of three powers
Frequently electrons ebb in order
Arc bath gives rise to hot molten showers
May bring flowers demonstrate my will in accord rewards her
Athena is truth incarnate dream she is a movement
Immaculate perfection possessed no
need for improvement in her coveralls
Wert she to eaten apple I befall
Sand disseminates beneath hourglass curves she manipulates
How could I anticipate
Rapt hints had she to intimate
Roots hypotenuse squares summed pendulum
Enlightened visions profound pit this plum
On que she hooks her thunderbolts so ample in restriction
Destabilized my volts despite my amping up conviction
Magnetisms repulsive attraction
Bipolar feedback generates action
Machining floral dissatisfaction
Narcissus is spring can't this robot tool be taught anything
Recommence imaging thine vault undermined after fault
Intuit as her nuclear annihilates tumult
June accusations forced violation
Vulnerable to invalidation
Confrontations repudiation consents allegation
Placate June”s wells breached swell fore July conflagration
Use wu wei to vacate situation
But weightless behemoth ate all greenbacks
Can’t manage exit not even a crack
Inward forays shunned malfunction unknown overgrown morass
Cult of quantity all students get a pass coach seat class
God’s walled over all access to egress
Those who cannot do are experts at best
Past practise succeeds failures teach what needs
Viridescent pools dilate grey eyed dubious stressed madness
Feeling she was slighted by my passage through her nucleus
Disinterested I had disinterred
Down period Kondratieff winter
Intrinsic tragedy all fairy tales end inherently
Gave me what I wished for in a way I was not hoping for
Destiny permits paths forbade
How shallow wilt thou will wade
PCB cesspools black bile pitches glue
Smoldering sand dune trenches shore magmas excess residue
Admit this time smashing cymbals whilst cyclops wert drumming too
Keep the fantasy alive in my head
Earthquake take other route instead
Always say they never saw it coming
They did In Herculaneum still their brains steamed in their skulls
Summer solstice solace lulls lava ladles plentiful
Cumulative studies validations
Inseminate process degradation
Trying not to mention my invention
Bending toward normalcy absorption emits diffraction
Inverted perceptions withdraw inflections from emptiness
Perplexing she rejects ram intellect
Anecdotal evidence cached respect
Zip plans to stockpile cognizance combined
Designed secret punishment to circumvent I resigned
Recollect for instance cognitive lessons in dissonance
Logic accepts one view perceived of two
Pit of mine stomach whence knot always knew
Treasonous betrayed lion taming shrew
Spite cleaved interface continued dutiful onward pace
Humiliations goal wert to replace cheers with disgrace
Orchestrations untold meticulous
Malevolence is still in existence
Narrative streams unfold conspicuous
Childish bliss unscrupulous epidemic Narcissus
Invasive species multiplied since Zeus supplied his sun’s abyss
Affect change rather than effect ere cause
Gaslight obfuscates reasonable laws
Tall tales half truths edged lies by omission
Unwary reprehense motive intents of recognition
Splitting of the faculty augments a new reality
Fight freeze or flee options only three
Trials choose middle choice typically
Stockholm syndrome captors figured friendlies
Volunteer for brunt of blame acquiesced toxic shame domain
Raging stirs steroid cortisol adrenaline cocktail brain
Idealize devalue sudden discard
Benevolent dictatorship abstained
Without the faintest regret or regard
Figured she was playing me but never thought she'd try so hard
Had a little influence pummeling blacksmith into bard
Feeling flashback symptoms PTSD
Reflux acid regurgitates anxiously
Facilities shut down my apogee
Estranged entanglement is indiscriminate vicinity
Projection deflects inspection detects proffered rejection
Upon reflection I/O failed connection
Reverse detail switched doppler direction
Attacked mine tranquility enacted thine stability
Great relationships determined by good portability
Amor Fati defeat of agony
Heroic transitions affirmation
Chinks of crevasse evasive to bypass
Labyrinth strings web of deceit light and dark unlikely meet
Shadows reconnection Schadenfreude revels surrection
Maze ambled afore trapped in Minotaur
Disintegrating reintegration
Unfurled divest individuation
Emergence of self under siege August surfacing intrigues
Sun god aims retribution penetrating air dilution
Perpetrating vengeful execution
Cyclop's blindsided coming attraction
Apollo's exaction vents extraction
Redress reclaimed door discharged from mine chore
Concussions cavitations roar gaff retrieved my staff from shore
Gangplank fastened transit for deck from wreck
Embodied under mass gravitation
Nothingness consistent contradiction
In retrospect ahead investigate that Which is suspect
Chastened flaming embers titillate orange September moon
Hastened retreat not an instant too soon
Burgeoning three wave prosperity shewn
Wave five trait mimics Echo past monsoon
Perpetually parallel dramas punctual insane
Aphrodite's inception purged migraine foam seethed fire in vain
Twain hath liquidity trickled down drain
Consult oracle ogle tangent plane
Bow to stern brood tempestuous coxswain
Demurrage fee aptly sought to regain lay of way terrain
Masked my gnashing lion waves stumble as they spread before me
Mountain rubble crumbles bloodied red sea
Locusts cannibalistic commotion
Uncanny notion overt devotion
Fixed betwixt twin scorpions stings subtle by a hares degree
One longs to age as seas submit one hole subliminally
Desire loves desire more than that desired
Overtime I find wanting displeasing
Fuel to fire Aphrodite’s teasing
Symptomatically nymphomaniac releasing
Random cosmos berth patterned beyond cyclic perimeter
Doth not feel momentum ye be the tide
Volume reduced ambient limiter
Futile to resist flow fatal to ride
Impressed by the strung rope ladder of unquestioned good status
Doctors orders therapeutic regressive Hedonism
Bureaucracy forced parentalism
Founding fathers Titan nepotism
The health preventative catechism
Give only to take away to give again another day
Rewards gods some token compensation
Anyone here not get paid besides me
Red light starboard wax eared crew rendezvous
Bounded by my sacrifice to irresponsibility
None of the other prize winning
players gamble here but me
Battened down fear gauge groups psychopathy
Ever since world went into bankruptcy
Call for Panic Zeus black masked his swan song
Yarn for youthful innocence gone stick slip traction moves this throng
Tread borderline separating time providing till from when
Uneven Titans tip unbalanced ships
Dualities tune unity in trine
One thing I did learn when within confine
Whom hath desire for nothing believes doth not need anything
Misinterpretation required missing zero still a thing
Axons bemoan sequence of no return
Feeling slight injustice step forward commandeer ambition
Venus akin to mine headache just better known rendition
Under spotlight favorite position
Internally propelled by externals
Take this Autumnal equinox swear on the cross tis vernal
All the gods explicitly sing chants how lucky I must be
Bring Mordor back to toss this precious ring
Prospect she fertilized inferring seed
Open union upon Which we agreed
Karma conflates heavens gates contrived in Pandemonium
Green shoots elate consummate concerns inspire Pavlovian
Theories cosigned conspiracies maligned
Impermanence ineffably refined
Ignorance binds energy disinclined
Universal conception pride of self
love contraception
Trying to be pliable but find it reprehensible
All dispensable Great Complacent Sea
Sizing words wisely rids ostensible
Lies the only guise now found comprehensible
Prophylactic allude to didactic
Though whilst I work at chore she’s Ares whore
I snagged them embarrassingly naked afore gods before
Yellen Helen neither nor wert worth war
Bowl of wrath judgement ignored poor decor
Titans empathizing with swimming clothes
In her throws she extolled excitement being extra exposed
Far be it from she to assume joint responsibility
Exponential debt credits game theory
On that we agree tis rigged currency
Opportunistic imperialists
Propaganda grasshoppers enlist ants backbone socialist
Can't remember when gathered last had a say any matter
Other nations forfeit right to do it
Export of inflation needs conduit
Concert donates borders New World Order
Blockchain came about when drunk bartender could not reach the spout
Yahweh will control all money now they have it figured out
Waiting for my minute to be clever
Stamp my name on the gods minds forever
My switchblade really needs to cut them off
No clue what the gods know only that they need to run the show Narcissistic parasites charisma lands entitlement
Vampires nourish roots to stunt encouragement
Protocol enticing invitation
Condemnation staged cooperation
Intolerable acts left no coercive tea leaves intact
Coven of bag passing Witches gave chase across red waters
Need another nine stitches sons twixt daughters
Waiting in the balance moment of force
Hatch guillotine MRI triggered source
Soaked up dripped Wyrmwood postulated solvent tasted good
Full equilibrium half ballast set assail for malice
Octobers placid benign chilled chalice
Brain scan photocell senses light all is well
If instead bulb shows dead off with thee head
Also as a godsend bonus honed mom’s splendid jury throne
Captive chaperone audience fettered judgement chains inlaid
Skipping to a Witch hunt after masquerade
Topside upper deck on the promenade
Propellor fashion later ohm made blade
Behooved turtle jail sac tail flailed back satyromaniac
Passionate parade personifying Nature of tirade
Horney gimp hind quarters brace graced limp
Llama spitting image of Obama
Clinton's dole out cigars contribute scars
All guests in attendance dressed as promised change we forget lest
Salubrious familiar strangers grooving Harvey Danger
Politically free redundancy
Reagan closed asylums threw away key
Identity hath no cost found when lost
Consolidations vibrate quantized sinusoidal noise
Pullback hull triangulate alow by my device and Echo
Feel lonely frost amongst the other masks
Survival is appeasing to their tasks
Remember November elect Semper
Meaning faithful to all members not just only archaic
On the way to office run your head
through photovoltaic
Vanishing quickly old liquidity
Seven plagues capsized immortality
The line hath paid out to the bitter end
Too big to sail exhale replications glorification
Night zeniths elevation nadirs sun's regeneration

Source: https://www.scientificamerican.com/article/momentum-isnt-magic-vindicating-the-hot-hand-with-the-mathematics-of-streaks/

It’s NCAA basketball tournament season, known for its magical moments and the “March Madness” it can produce. Many fans remember Stephen Curry’s superhuman 2008 performance where he led underdog Davidson College to victory while nearly outscoring the entire determined Gonzaga team by himself in the second half. Was Curry’s magic merely a product of his skill, the match-ups and random luck, or was there something special within him that day?
Nearly every basketball player, coach or fan believes that some shooters have an uncanny tendency to experience the hot hand—also referred to as being “on fire,” “in the zone,” “in rhythm” or “unconscious.” The idea is that on occasion these players enter into a special state in which their ability to make shots is noticeably better than usual. When people see a streak, like Craig Hodges hitting 19 3-pointers in a row, or other exceptional performances, they typically attribute it to the hot hand.
The hot hand makes intuitive sense. For instance, you can probably recall a situation, in sports or otherwise, in which you felt like you had momentum on your side—your body was in sync, your mind was focused and you were in a confident mood. In these moments of flowsuccess feels inevitable, and effortless.
However, if you go to the NCAA’s website, you’ll read that this intuition is incorrect—the hot hand does not exist. Belief in the hot hand is just a delusion that occurs because we as humans have a predisposition to see patterns in randomness; we see streakiness even though shooting data are essentially random. Indeed, this view has been held for the past 30 years among scientists who study judgment and decision-making. Even Nobel Prize winner Daniel Kahneman affirmed this consensus: “The hot hand is a massive and widespread cognitive illusion.”
Nevertheless, recent work has uncovered critical flaws in the research which underlies this consensus. In fact, these flaws are sufficient to not only invalidate the most compelling evidence against the hot hand, but even to vindicate the belief in streakiness.

 

RESEARCH MADE IT THE ‘HOT HAND FALLACY’
In the landmark 1985 paper “The hot hand in basketball: On the misperception of random sequences,” psychologists Thomas Gilovich, Robert Vallone and Amos Tversky (GVT, for short) found that when studying basketball shooting data, the sequences of makes and misses are indistinguishable from the sequences of heads and tails one would expect to see from flipping a coin repeatedly.
Just as a gambler will get an occasional streak when flipping a coin, a basketball player will produce an occasional streak when shooting the ball. GVT concluded that the hot hand is a “cognitive illusion”; people’s tendency to detect patterns in randomness, to see perfectly typical streaks as atypical, led them to believe in an illusory hot hand.
GVT’s conclusion that the hot hand doesn’t exist was initially dismissed out of hand by practitioners; legendary Boston Celtics coach Red Auerbach famously said: “Who is this guy? So he makes a study. I couldn’t care less.” The academic response was no less critical, but Tversky and Gilovich successfully defended their work, while uncovering critical flaws in the studies that challenged it. While there remained some isolated skepticism, GVT’s result was accepted as the scientific consensus, and the “hot hand fallacy” was born.
Importantly, GVT found that professional practitioners (players and coaches) not only were victims of the fallacy, but that their belief in the hot hand was stubbornly fixed. The power of GVT’s result had a profound influence on how psychologists and economists think about decision-making in domains where information arrives over time. As GVT’s result was extrapolated into areas outside of basketball, the hot hand fallacy became a cultural meme. From financial investing to video gaming, the notion that momentum could exist in human performance came to be viewed as incorrect by default.
The pedantic “No, actually” commentators were given a license to throw cold water on the hot hand believers.

 

TAKING ANOTHER LOOK AT THE PROBABILITIES
In what turns out to be an ironic twist, we’ve recently found this consensus view rests on a subtle—but crucial—misconception regarding the behavior of random sequences. In GVT’s critical test of hot hand shooting conducted on the Cornell University basketball team, they examined whether players shot better when on a streak of hits than when on a streak of misses. In this intuitive test, players’ field goal percentages were not markedly greater after streaks of makes than after streaks of misses.
GVT made the implicit assumption that the pattern they observed from the Cornell shooters is what you would expect to see if each player’s sequence of 100 shot outcomes were determined by coin flips. That is, the percentage of heads should be similar for the flips that follow streaks of heads, and the flips that follow streaks of misses.
Our surprising finding is that this appealing intuition is incorrect. For example, imagine flipping a coin 100 times and then collecting all the flips in which the preceding three flips are heads. While one would intuitively expect that the percentage of heads on these flips would be 50 percent, instead, it’s less.
Here’s why.
Suppose a researcher looks at the data from a sequence of 100 coin flips, collects all the flips for which the previous three flips are heads and inspects one of these flips. To visualize this, imagine the researcher taking these collected flips, putting them in a bucket and choosing one at random. The chance the chosen flip is a heads—equal to the percentage of heads in the bucket—we claim is less than 50 percent.
To see this, let’s say the researcher happens to choose flip 42 from the bucket. Now it’s true that if the researcher were to inspect flip 42 before examining the sequence, then the chance of it being heads would be exactly 50/50, as we intuitively expect. But the researcher looked at the sequence first, and collected flip 42 because it was one of the flips for which the previous three flips were heads. Why does this make it more likely that flip 42 would be tails rather than a heads?
If flip 42 were heads, then flips 39, 40, 41 and 42 would be HHHH. This would mean that flip 43 would also follow three heads, and the researcher could have chosen flip 43 rather than flip 42 (but didn’t). If flip 42 were tails, then flips 39 through 42 would be HHHT, and the researcher would be restricted from choosing flip 43 (or 44, or 45). This implies that in the world in which flip 42 is tails (HHHT) flip 42 is more likely to be chosen as there are (on average) fewer eligible flips in the sequence from which to choose than in the world in which flip 42 is heads (HHHH).
This reasoning holds for any flip the researcher might choose from the bucket (unless it happens to be the final flip of the sequence). The world HHHT, in which the researcher has fewer eligible flips besides the chosen flip, restricts his choice more than world HHHH, and makes him more likely to choose the flip that he chose. This makes world HHHT more likely, and consequentially makes tails more likely than heads on the chosen flip.
In other words, selecting which part of the data to analyze based on information regarding where streaks are located within the data, restricts your choice, and changes the odds.
The complete proof can be found in our working paper that’s available online. Our reasoning here applies what’s known as the principle of restricted choice, which comes up in the card game bridge, and is the intuition behind the formal mathematical procedure for updating beliefs based on new information, Bayesian inference. In another one of our working papers, which links our result to various probability puzzles and statistical biases, we found that the simplest version of our problem is nearly equivalent to the famous Monty Hall problem, which stumped the eminent mathematician Paul Erds and many other smart people.
We observed a similar phenomenon; smart people were convinced that the bias we found couldn’t be true, which led to interesting email exchanges and spirited posts to internet forums (TwoPlusTwo, Reddit, StackExchange) and the comment sections of academic blogs (Gelman, Lipton&Regan, Kahan, Landsburg, Novella, Rey Biel), newspapers (Wall Street Journal, The New York Times) and online magazines (Slate and NYMag).

 

THE HOT HAND RISES AGAIN
With this counterintuitive new finding in mind, let’s now go back to the GVT data. GVT divided shots into those that followed streaks of three (or more) makes, and streaks of three (or more) misses, and compared field goal percentages across these categories. Because of the surprising bias we discovered, their finding of only a negligibly higher field goal percentage for shots following a streak of makes (three percentage points), was, if you do the calculation, actually 11 percentage points higher than one would expect from a coin flip!
An 11 percentage point relative boost in shooting when on a hit-streak is not negligible. In fact, it is roughly equal to the difference in field goal percentage between the average and the very best 3-point shooter in the NBA. Thus, in contrast with what was originally found, GVT’s data reveal a substantial, and statistically significant, hot hand effect.
Importantly, this evidence in support of hot hand shooting is not unique. Indeed, in recent research we’ve found that this effect replicates in the NBA’s Three Point contest, as well in other controlled studies. Evidence from other researchers using free throw and game data corroborates this. Further, there’s a good chance the hot hand is more substantial than we estimate due to another subtle statistical issue called “measurement error,” which we discuss in the appendix of our paper.
Thus, surprisingly, these recent discoveries show that the practitioners were actually right all along. It’s OK to believe in the hot hand. While perhaps you shouldn’t get too carried away, you can believe in the magic and mystery of momentum in basketball and life in general, while still maintaining your intellectual respectability.

Edit: Formatting; emphasis my own.

If you spam folder the M1 emailers, you might have missed this good article:
https://www.m1finance.com/blog/cognitive-biases-in-investing/
It's worth reading the whole article, but the gist is everyone has cognitive bias and self-awareness is the weapon against it. Some that will have a negative impact on your investing decisions:

• Confirmation bias: You only believe evidence that supports your investment decisions, nevermind the facts.
  
• Reactive devaluation bias: You are less likely to credit advice from people you don't like. For example, if you despise senior citizens, you won't listen to any advice from Warren Buffett.
  
• Loss aversion: You are afraid of losing, even if giving something up (like selling a stock that loses -4% per year) will get you something much better (a stock that gains 18% per year).
  
• Dunning-Krueger Effect (the article calls this the "Lake Woebegon effect"): Dumb people think they are smart, average investors think they are the next Gordon Gekko, stock pickers think they can beat the market, etc.
  
• Optimism bias: "This is fine." The belief that positive outcomes are more likely than they actually are.
  
• FOMO: Fear of missing out bias. You gotta jump on the hottest tip, or you'll miss out. Bandwagoneering.
  
• Gambler's fallacy (aka Sunk Cost Fallacy): The belief that you are due to win and that a loser can't keep losing, buying more when it's down will win you more when it goes back up, and that your luck has to change for the better -- a bit of the optimism bias in that as well.
  

The article makes the point that the list above is not exhaustive, and indeed, I'm surprised they left out a bias that I think is extremely common for investors:

• Anchoring bias: You believe that something that has won before HAS TO win again. Getting stuck on an old fact or belief and ignoring new data.

I found this awesome information about 7 cognitive biases, which play a significant role in our life:
1. Confirmation Bias. This occurs when you warp data to fit or support your existing beliefs or expectations. The effects are often found in religion, politics, and even science.
Why does that matter? Because an inability to look outside of your existing belief systems will vastly limit your ability to grow and improve, both in business and in life. We need to consider more possibilities, and be more open to alternatives.
2. Loss Aversion. Also known as the endowment effect, loss aversion is a principle in behavioral economics whereby someone will work harder to keep something than they will to acquire it in the first place. This is also closely related to the sunk cost fallacy, where one is inclined to pump more resources into something based solely on the resources already expended.
If you need an example, being hesitant to fire a bad employee is a common one. You might think, "Well, I've already put so much time into training them, paying them, insuring them, and their performance isn't really THAT bad...I should see if I can salvage this."
Don't make this mistake. When time or money is gone, it's gone, and you need to consider the future without attachment to the past. Speaking of past and future...
3. Gambler's Fallacy. The human brain has difficulty understanding probability and large numbers, so you are naturally inclined to believe that past events can somehow change or impact future probabilities.
For example, there are many people who try to analyze the past performance of the stock market in order to pick future stocks that should be winners, usually with terrible results (there's a reason why very few money managers outperform the S&P 500). This is a product of the Gambler's Fallacy, and it can get you, your clients, and your businesses into a great deal of trouble.
How does this hold you back? In most cases, past events don't change the future unless you let them, so you need to take great care when attempting to learn from the past. It's fine to look to the past for insights, but don't fall into the "past performance dictates future performance" trap.
4. Availability Cascade. Just because you hear something frequently does not make it true, though the brain sure likes to believe otherwise. For example:
You don't use just 10 percent of your brains (you actually use 100 percent). Gum doesn't take seven years to digest (it doesn't digest at all; it just passes right through in about the same time as everything else). Bats aren't blind (they see quite well, and have amazing hearing to boot). Surprised? Bad information seems to spread as fast, if not faster, than the truth, so you need to fact-check frequently before you make decisions based on bad information. If you notice something coming up again and again, dig into the facts and determine for yourself what is or isn't true.
5. Framing Effect. This one is fascinating, and I take advantage of it regularly as a marketer. In a nutshell, how something is framed, positively or negatively, has an enormous impact on how the information is processed...even if the information is fundamentally identical.
For example, let's say you've been diagnosed with a terminal illness, and two different doctors come to tell you what happens next:

• Doctor A: "With proper treatment, you have an 80 percent chance of a full recovery."
• Doctor B: "There's a 20 percent chance that you'll die after being treated for this illness."

Which doctor would you want to work with? Even though both are exactly the same, most people will pick Doctor A, because an 80 percent chance of recovery sounds way better than a 20 percent chance of death.
It's important to carefully consider how you present information in all walks of life, because your method of presentation can make or break the outcome.
6. Bandwagon Effect. Just because many people believe something doesn't make it true...though it does make it much easier for the brain to accept. In many ways, humans behave like herd animals, blindly accepting whatever they encounter as long as there seems to be some social proof.
One of my favorite quotes is attributed to Mark Twain, and says:
"Whenever you find yourself on the side of the majority, it is time to pause and reflect."
It's important not to allow the beliefs of others to sway you without careful thought and research on your part. Don't accept things at face value.
7. Dunning-Kruger Effect. Last but not least, this cognitive bias is at play behind arrogance and egotism. People have a psychological tendency to assess their abilities as much greater than they really are.
How do you conquer this? I personally have a four-step approach:

• Keep a journal
• Meditate
• Pause before you act
• Self-analyze As you go through this process, you'll find yourself better equipped to assess your skills without bias. I've written a more detailed blog post about self-awareness, if you want to check it out.

To Hell with this piece of shit - Hearthstone.
i have had fucking had enough of this shit.
​
This post is a kind warning to everyone out there.
If you want to have a great life with happiness, productivity, mental focus, girlfriend, health, etc, don't play this game.
For those active players, Consider quitting this game.
For those have just started, Don't continue playing. Quit immediately
For those who are thinking whether to start on this game, Don't. Do not start playing this game.
​
This game is cancerous and toxic.
Playing this game isn't fun.
It Causes cold sweats, anxiety problems, low self esteem, mood swings, Bipolar disorder, breakdown of relationships, loss of focus, Rage, Frustration, tilt, anger, your time wasted, sleep & Life disrupted and health deterioration, & MONEY WASTED
Ruins your social life, causes physical and mental health deterioration, and makes you sad.
[ TLDR : This Game Causes all kinds of problems,
But most importantly it causes your Time wasted, your Health affected, and you don't feel happy playing it. ]
​
My playing experience in Hearthstone :
I started out as a purely casual HS gamer. I didn't started playing this game with a free2play mindset. Initially, I didn't mind spending a small sum of cash on this game. I only purchased packs on sale, like the welcome bundle, or when there was special promotions like special bundles,
However, after playing for a little while, after repeatedly losing and losing, I became frustrated, and then i became obssessed with climbing the standard ladder. i wanted to reach legend. I started dumping loads of money and time into the game. After an extremely tiring climb, i reached rank 5. I mustered my strength and continue climbing. With extreme effort and time spent ( i wouldn't even use the word invested), my rank kept fluctuating up and down (5,4,3,2,1,2,3,4,3,2,1, etc. you can imagine.). I wanted to reach legend just once, just for the cardback. I wanted to give up multiple times, but i felt that if i give up, i'll be wasting all my time and effort thus far. I continued to push on. And then I finally reached legend. I just wanted the cardback. I've got it. I was satisfied. But I wasn't happy. I was extremely exhausted. I only wanted to reach legend once. Never again am I going to grind the climb with my effort and time again.
It's not worth it. This game is not worth it.
Thereafter, my lifetime Hearthstone goal is to just reach rank 5 every month(for the rewards), and to just do daily quests everyday. That's it. I felt that this mindset and goal is good.
But on several occasions when I decide to play a few more games, I only experience tilt, anger, and frustration.
​
I am a decent player with decent plays with decent decks. I use tier one decks and I always change it up a little bit(swap a few cards) according to the meta i've seen and i'm facing.
I used to spam one deck for many consecutive plays but now I rotate decks every 1 ~ 2 plays.
There are countless occasions and examples of bloody stupid unfairness and unluckiness and rage inducing cases, but I won't write all. I am sure many of you have experienced it yourself. I'll give a few examples. These examples are that either i've seen from instagram or youtube videos, or played/experienced myself
- made good plays, secures control of the board, for sure to win next turn, but losing to unlucky opponent's topdecks (e.g. soulfire, leeroy),
- Losing to opponent's highroll and good draws
- arcane missiles/cinderstorm to all land on face but never the desired target.
- not rolling a taunt totem in several consecutive chances from "Primal Talisman" card
- keep encountering vargoth priests. changes to odd rogue, encounters odd warrior. changes to togwaggle druid, encounters odd paladin but didn't draw spreading plague. Always queueing to unfavourable matchups.
- always unlucky, opponent always lucky
- 2x silver hand recruit & 1 Frostwolf warlord. Deadly shot twice, twice landed on both silver hand recruits.
- includes skulking geist and mojomaster to counter mechathun decks. when playing against mechathun decks, didn't draw geist or mojomaster.
- saronite taskmaster and leeroy to counter vargoth priest's resurrect pool. Opponent's spellstone resurrects 4 minions - none of which are saronite's free agent or leeroy's whelps.
Builds a Deck to counter predictable, broken meta decks, but rng still favours the broken deck and not favour the counter ? $@#%!#!
​
we could queue a favourable deck in a favourable matchup, make no mistakes playing but lose to lousy Rng at the last instant due to pure unluckiness. It feels like the win we worked hard for has been stolen, and the effort and time wasted.
Plays 20 - 30 min games, several close games, some blatant sure win games but gets the win robbed off by bad luck/rng
Perhaps game can be balanced by having odds favour the player with unfavourable position, and not favouring the player with already favourable board?
Losing is not fun. Experiencing losing streaks is not fun.
Stupid game feels like it's never fair and feels stupid and rigged.
Not to mention connectivity/disconnection issues and problems, opponent's bad behaviour by roping and making extremely slow moves, as well as the numerous BUGS present in this game
​
This game has only caused frustration. no fun. I feel that playing the game everyday only makes me feel exhausted.
​
This game is not all skill. Probably 90% luck, 10% skill.
Stop learning all the useless, pointless hearthstone interactions, combos and OTKs.
Start learning a game of pure intellect and skill such as International Chess.
Learn Chess moves, Chess openings, defences, endgames, etc. It is much more fruitful
​
Unfortunately i lost, the Game & Team 5 won though. (Notice i said Team 5, and not Blizzard. I like blizzard games, except HS. Fuck HS.)
i have spent approximately 1.2k USD on this game,
and it took countless hours for me to realise i don't like this game. Countless hours lost.
(Actually Hate this game)
Should have spent the money on charity or at a casino or to invest in myself instead of this game.
Should have spent the time more wisely.
​

1. I have been wanting to write this post for a very long time.

time and time again i felt i have reached my limit, but have always given the game another chance.
This time i have hit my tipping point.

1. i QUIT this piece of fuckshit.

​
Now that i am done with this fuckshit, i feel like a huge load of my shoulders, so much more at ease and free.
​
This game is exploitative, harmful, and damaging to all aspects of your life, health, financial, social, etc.
other threads and links :https://www.reddit.com/hearthstone/comments/4rto3z/i_have_fucking_had_it/https://www.reddit.com/hearthstonecirclejerk/comments/43z3oe/fuck_hearthstone_and_fuck_you/https://www.pcgamer.com/behind-the-addictive-psychology-and-seductive-art-of-loot-boxes/https://www.gamesradar.com/chasing-hearthstones-legend-rank-only-cost-my-soul-what-life-is-like-when-youre-consumed-by-cards/https://www.polygon.com/2017/12/12/16763594/hearthstone-expensive-expansions-costhttps://www.reddit.com/CompetitiveHS/comments/8kls25/cognitive_biases_in_hearthstone_gamblers_fallacy_1/https://www.hearthstonetopdecks.com/cognitive-biases-in-hearthstone-gamblers-fallacy-1/https://www.extremetech.com/gaming/277317-study-loot-boxes-are-psychologically-akin-to-gambling
​
Updates :
https://www.pcgamer.com/lifecoach-on-quitting-hearthstone-you-dont-get-rewarded-you-get-punched-in-the-face/ the best players of the world can only play at 1% better than an average player, then it's a pure gamble(RNG) and it really has nothing to do with competitiveness at all. you don't get rewarded, you get punched in the face". https://www.youtube.com/watch?v=EsmKkKbZkH8 Lifecoach quits hearthstone
https://www.reddit.com/hearthstone/comments/bdb6fe/hafu_has_quit_hearthstone/
https://www.twitch.tv/savjz/clip/FurryAgreeableLegJKanStyle Savjz quits hearthstone
https://www.youtube.com/watch?v=IeDndj92lec&t=1s Disguised toast loses his mind !

I'm determined to prove that Joe's rolling still obeys the laws of thermodynamics and that, over all history, his rolls are evenly distributed like all other dice rolling in existence (especially given that everyone changes dice all the time). As I'm sure we're all aware, it is physically impossible for one person's overall roll statistics to deviate very far from a flat distribution (check "roll automatically" on this simulator for one die).
Our perception of Joe's poor rolling seems, at times, CLEARLY CURSED! But in reality it is the result of a delightful combination of Confirmation Bias and The Gambler's Fallacy: every time he rolls poorly, we're even more convinced, and every time he rolls poorly multiple times in a row we're even more convinced! (Long streaks of low rolls are perfectly normal, and a long streak never means that a high roll is "due") And the times he rolls well, we sit back on Disconfirmation Bias (technically just a form of confirmation bias I guess), where we ignore evidence to the contrary of our prejudiced belief. (Here are some other interesting cognitive biases encountered in gaming but they're not all related to just dice rolling)
If I had the time I'd like to write a tensorflow AI algorithm to "listen" to all of Joe's rolls and create a master list of throw results, but there would be a lot of difficulties and problems with that, among them the fact that not all the results are announced out loud, and speech-to-text is still not completely accurate. And since the purpose is statistical, no data is better than wrong data, so a few mis"heard" results would skew the analysis.
So we're stuck with someone manually writing down every roll they heard ;p Can we crowdsource this? Like certain people can claim episodes and put the results in a master google docs spreadsheet...
I'm not really kidding! X-)

Hi, I will be discussing a topic today that has not been talked about on the sub: 6 cognitive biases that are holding you back from analyzing units fairly and building better "off-meta" squads. I have a background in competitive Pokemon and Hearthstone and similar articles have been written for those games so I figured that it would be worthwhile to make an article about this topic with relation to Brave Frontier. I am simply interested in this area and am not a professional in psychology (at least not yet) so I will be taking all definitions from Wikipedia. This article was largely inspired by an article about Magic: The Gathering. Whenever I mention a point about choosing whether to summon for a unit, I am not targeting players who have the resources to pull for any and all units, but rather the players who have limited resources and need to make informed decisions on whether a given unit is worth summoning for.
A cognitive bias is a systematic error in thinking that affects the decisions and judgments that people make. This can lead to poor judgment and biased thinking. As such, these biases can affect how we judge and analyse units and squads in Brave Frontier. The cognitive biases I am covering are also largely applicable outside of Brave Frontier so I hope this will be a worthwhile read for the whole community.

1. Distinction Bias

The tendency to view two options as more distinctive when evaluating them simultaneously than when evaluating them separately.
When 2 subjects are compared side by side, they are often considered more dissimilar than they actually are. Distinction bias can magnify small differences between 2 similar units and can even be decisive factor in whether a player pulls for a unit.
For example, a player with Krantz as his main mitigator will probably be very satisfied with Krantz, but when a Stein rateup gate is released, he might be prompted to compare Krantz and Stein side by side and point out that Stein has important buffs on his SP options such as BC fill when attacked and status ailment negation, which makes Stein a much more attractive mitigator that he should pull for, and hence overrate Stein by comparing him to Krantz and listing out buffs that Stein has but Krantz does not. In actuality, a player with Krantz alone will most likely not require Stein as they accomplish very similar roles (2 turn mitigation, burst healing, etc.) and Krantz has his own unique buffs and traits such as BC/HC droprate, stats from his extra skill and cheap BB costs that make him a good mitigator in his own right.
We can compensate for this by reminding ourselves to evaluate a unit on its own. When juxtaposing a unit with another similar unit, take into consideration that distinction bias exists and avoid blowing up small differences in their kits which would otherwise be unnoticeable if not compared simultaneously.

2. Conservatism Bias

The tendency to revise one's belief insufficiently when presented with new evidence.
This is a problem that many of us do not realize. It is easier to hold on to an old belief and simply tweak it slightly (or not at all) when new information is released which disputes that original notion.
For a long time, the community believed that using Double Avant leads for Frontier Hunter were the best for getting the highest damage numbers, even when UBB-ing. However, after alternative setups that were not using Avants were discovered (some by yours truly), many players refused to believe that it was possible, because Avant's leader skill provided so much damage.
By having a more open mind towards opinions or strategies that have merit but contradict what we know, we can learn better and faster by being more accepting of the fact that sometimes, our view of the metagame and the best squads and units available might not be the most optimal.

3. Selective Perception

The tendency to allow our expectations to influence perception.
We tend to see what we want or expect to see and overlook stimuli which contradicts our beliefs or expectations.
When we build squads for any sort of content in Brave Frontier, we are hoping that they work out well. As such, we tend to focus on evidence that confirms that they are great squads, while dismissing information that point out their flaws.
I have two friends who were discussing Endless FG squads a while back, and both of them created squads that each had their unique characteristics. However, the discussion became heated when they began criticizing each other's squads and pinpointing how the squad that the other theorized would fail to reach stage 300. Neither person wanted the other to be nitpicking the flaws of the squad that they took time to theorize.
As much as we like our expectations to be affirmed, we should be aware that we are looking through rose-tinted glasses very often, and take those glasses off to seriously consider the blind spots or shortcomings.

4. Anchoring Bias

The tendency to rely too heavily on the first piece of information offered when making decisions.
When new unit information is released, players tend to over-rely on the first unit analysis post or video that they see as those will usually be their main reference points.
While it is fine to agree with what is covered in unit analysis threads/videos and use the information to help you decide whether to pull for a unit, what content the unit excels in and what SP builds to go for, they should not be the be-all and end-all of information.
It is a good practice to forge your own opinions on a new unit first, before reading the unit analysis posts or videos. You might find something new that others have not considered which you might not have realized if you relied solely on those outlets for unit analysis.

5. Availability Cascade

A self-reinforcing process in which a collective belief gains increasing plausibility through its rising repetition in public discourse.
We are constantly relying on the Internet for information on just about anything. We rely on this subreddit for much of our information on Brave Frontier. The problem arises when the original information is incorrect or has loopholes that have not been addressed but continues to spread, with more players that receive this erroneous information simply repeating and spreading it, hence "validating" it and making the information difficult to challenge.
Such was the case for Ciara's supposed lack of viability in FH or FG1 squads. When OE Ciara was released, a few players were quick to pick up on the fact that Ciara's buffs were delayed due to her animation which killed her use in 0 ms delay squads. Some players began saying that Ciara was unusable for nuke squads, and this information quickly spread.
I decided to do some testing for UBB nuke squads utilizing Ciara and found that with appropriate ms delay timings, she could activate her buffs for the entire squad and squad damage was decent. D3monicUnicorn made a post about utilizing Ciara in an autobattle nuke squad for FH and FG1. So were they all wrong? Or were we wrong?
The most likely answer is that the players who originally labelled Ciara as garbage for any kind of nuke squad (not only for 0 ms) did not explore or entertain the concept of non 0 ms sequences, and more people just repeated the original sentiment.
Common knowledge might not always be correct. When your findings contradict the popular opinion, you are not always going against a horde of players, it might very well be the opinion from a few players that were repeated over and over.

6. Gambler's Fallacy

The tendency to believe that the onset of a certain random event is less likely to happen following an event or a series of events.
This last one does not pertain to unit analysis or squadbuilding but I figured I would cover it anyway.
Sometimes we love gacha, and sometimes we hate gacha. But one very common sentiment that players experience when summoning is the urge to summon 1 more time after a series of failed summons, hoping that the probability of them pulling the unit they want in the subsequent summon will be higher than the last because they had failed to pull the unit. As we all know, each summon gacha is an independent event (assuming gates with x10 rates are at x10 rates already) so past summons have no bearing on future summons.
On this note, perhaps x10 rateup summon gates were designed to prey on the gambler's fallacy, but that is another post for another day.

Closing Thoughts

While Brave Frontier is mostly a PvE game with few "competitive" events, we can still be better informed players by being aware of these cognitive biases that affect our knowledge and game sense. They are also good to know as they all have real life applications. Hopefully this article was helpful to you in some way. I would appreciate conducive discussion regarding the points that I raised and any other related topics. Cheers!

Currently, I am interested in a few different topics, but am kind of having a hard time finding literature or even the proper vocabulary to describe what I would like to study. The best way I can think about putting it is the development and cognition behind causal reasoning, particularly maladaptive biases related to causal reasoning. For example, many people have trouble and extrapolate incorrect/illogical patterns from everyday observation and behavior, like in the cases of the gambler's fallacy or the post hoc fallacy. I am interested in seeing if these errors in reasoning are evolutionarily advantageous and how so, if they have an effect on criminal activity and antisocial tendencies among other facets of psychopathology, and whether there are neural correlates which can reliably predict where these kinds of errors might come from.
Related topics would include Life History Theory and Temporal Discounting, Reasoning Fallacies and Biases - mostly evolutionary and cognitive psychology paradigms.
Thanks for reading and for your help! It will help me a lot in finding doctoral advisors (:

Probabilities are subject to a lot of cognitive biases such as the Gambler's Fallacy, so it's hard to develop the correct intuition about how they work.
Your win rate is certainly related to how fast you'll climb from Rank 5 to Legend, but it's not exactly the right quantity to be examining.
The correct quantity to look at is the chances that ANY contiguous subset of your win/loss history has 25 more wins than losses. When that occurs, you've hit legend. It doesn't matter if you lost 1000 games in a row at Rank 5 and then went 50-25 (unlikely example, obviously). As you play more and more games, the number of contiguous subsets goes through [[Wild Growth]] and the chances that one of them will contain 25 more wins than losses goes towards 100%.
I made a matlab script to simulate 10,000 runs to legend from rank 5 and ran it with different win rates. I recorded the number of games to legend and then looked at percentiles of the distribution. The results look like this:

Win Rate	10%	25%	50%	75%	90%
45.0%	930	2,419	5,557	10,804	17,930
47.5%	300	620	1,316	2,520	4,088
50.0%	170	278	492	857	1,341
52.5%	120	173	267	412	602
55.0%	92	125	180	257	357
57.5%	77	100	134	183	243
60.0%	65	82	107	140	178

The code is here:

p = .6; %Change as needed nRuns = 1e5; gamesToLegend = NaN(nRuns,1); for i = 1:nRuns stars = NaN(1e6,1); winLoss = NaN(1e6,1); terminated = false; j = 1; stars(1) = 0; while ~terminated winLoss(j) = rand(1) < p; if winLoss(j) stars(j+1) = stars(j) + 1; if stars(j+1) == 25 terminated = true; end else if stars(j) == 0 stars(j+1) = 0; else stars(j+1) = stars(j) - 1; end end j = j + 1; end gamesToLegend(i) = j; end disp(prctile(gamesToLegend,[10 25 50 75 90])) 

I don't want to make this post super long, but the effects will be even more prominent below rank 5 where you get bonus stars. In that case, it is even more valuable to go 6 wins then 4 losses than to go win-loss-win-loss-win-loss-win-loss-win-win.
tl;dr Your luck with getting lots of your wins in a short period is a big factor for hitting legend, often as important as your overall win rate.

It's that time again when the FFBraveExvius subreddit explodes with posts and speculation regarding the enigmatic and ever elusive "solution" to the Enchanted Maze. It's because I find myself often at times lost in deep thought thinking about random topics of interest in the morning that something came to mind this morning when I saw the surge in EM posts. Many people before have tried to crack the code and there are a wealth of theories out there on the subject, but I think it's a lot simpler than people think or make it out to be. It's because of this that I'd like to propose my own theory.
First, I need to explain a little bit of the "why" in order to explain the "how" of my theory. I recently read Leonard mlodinow's The Drunkard's Walk. The book is an exceedingly interesting and delightful read about how randomness drives our lives, and how cognitive biases and our egos lead us into the logical trap that we are capable of predicting and controlling the outcomes of an otherwise chaotic and random world.
The book is named after a mathematical model called the "random walk", a type of random/stochastic process, that is used to approximate the outcome of a series of seemingly random occurrences.
While I believe this would be a potentially good method to use to try to sort out the insanity of the enchanted maze, the level of knowledge needed to make sense of any. stochastic processes is a little above my head at the moment. That being said, I think there is something that's a little simpler that can be used to develop a strategy for successful completion of the maze. The book also went in to great detail about the gamblers fallacy (hotstreak/dueness fallacies), but also went into great detail about the Law of Large Numbers.
In the case of the EM I think the Law of Large Numbers can be successfully applied. LLN says that as the number of identically distributed, randomly generated variables increases, their sample mean (average) approaches their theoretical mean. However, this depends on one condition, that the desired outcome being tested remain the same.
The enchanted maze has a 162 individual paths from start to finish. People have reported repeatedly, on this and other forums, that they achieve the highest level of success by simply going through the middle door every time. For me, my preferred path from start to finish is mid->mid->left->right->right. While I imagine that there plenty of people with competing methods and theories, the common thread between all of them is that the player is traveling the same path every time.
To put it simply...pick a path...run the maze as many times as possible...the more you run the EM on the same path the desired rate of success will move closer to the theoretical rate of success
--end thought--

In behavioral, the curriculum talks about gamblers fallacy which I think relates somewhat to the concept of mean reversion, basically saying that premise is a cognitive bias, yet in the equity section on statistical arbitrage, trying to exploit the potential for mean reversion is an active equity management strategy. Can someone tell me why this isn't a conflict?

Introduction
We’ve all experienced it: you sim 6 nodes to get a shard and none drop. Or you buy a 120 energy refill and try 15 times to get a purple bit and get none of them. And it always seems to happen at the worst time, such as when you only need one more item. It’s infuriating, and it makes it seem like the game is bugged, or even nefariously programmed against your interests.
The CG developers have denied any sort of manipulation of the odds. And when I look at numbers over a long time I believe them. So what’s really going on here? A combination of phenomena: random numbers are weird; probability is hard to understand; and people’s perceptions are colored by biases they often don’t realize they even have.
I hope the following helps some of you understand what’s going on here. Please don’t view this as me lecturing from on high, incidentally, because I’ve fallen prey to all of these things myself.
Random Numbers are Weird
People do not understand random numbers. In fact, people are so bad at understanding them that humans cannot generate truly random numbers. (Try it yourself: attempt to come up with a list of 10 random numbers between 1 and 10. You will find that after the first couple, you will be thinking about what number should come next. You will be influenced by what the previous numbers were. The results will not be random. In particular, humans will tend to “distribute” the numbers to something that seems random, fearing that duplicates are not “random enough”. As an example, I just used a computer to randomly generated these numbers: 1, 1, 2, 4, 3, 3, 4, 5, 8, 4, 3, 1. No human would generate a sequence like this because there are so many duplicated numbers, and all but 1 is 5 or below, so it seems “unrandom”.)
A major confusion comes in the form of believing that if a random chance has a particular value that this means you should always, or usually, get the stated percentage. So if there’s 1/3 chance of a shard dropping from a hard mission, simming it 3 times should always or usually give 1 shard.
The truth is that random numbers are unpredictable and do not tend to follow consistent patterns (see the example 10 numbers above). Long stretches of uneven results are not only normal, they are expected. In the case of a 1/3 chance of a shard and 3 hard missions, the chances of getting exactly 1 shard are actually less than 50%. More than 50% of the time, you will get some other value (0, 2 or 3). Streaks are also entirely normal with random numbers. This is what makes people think that there are bugs, or the game is cheating against them. Here’s an example. Yesterday I decided to keep track of enemies in GW/Arena when Old Daka was on the team to see how often enemies self-revived. The nominal odds of this are 10%. At one point, I experienced a streak where there were 7 self-revives out of 25 kills in only 5 games. That’s 28%, almost triple the expected number! But then later on, I had another streak where there were only 2 self-revives out of 43 kills, which is less than half the expected value. These streaks are entirely normal.
People Do Not Understand Probabilities
One of the reasons why games like this exist, and why lotteries and casinos make a fortune, is that probability is hard to understand. People tend to make assumptions about odds that are false. They also tend to believe they have a better chance at a good outcome than they do.
Lotteries are an easy example. Have you ever noticed that the Powerball numbers always seem to be random, unrelated numbers? For example, they are usually something like 5, 17, 32, 39, 61 and 70. When is the last time you saw a lottery where the winning numbers were 1, 2, 3, 4, 5 and 6? If this ever happened, it would make the news, people would scream and claim that the game was rigged. In reality though, that result is just as likely as any other. Think about how many times you have seen lottery numbers and how you probably never have seen a regular pattern like that (or 1, 3, 5, 7, 9, 11, etc.) That gives you an idea of just how unlikely it is that you will ever strike it rich.
People also again expect to see odds “even out” over time, which doesn’t always happen. Each random occurrence is independent of the others, and the cosmos is not keeping track. While over a long time the average will tend to converge to the probability rate, this is because the numbers get very large so differences become less important in percentage terms. It doesn’t mean that after a long stretch of misses on a sim that you are “due” to get shard drops. This is called the Gambler’s Fallacy, and has made many people walk out of a casino with their pockets empty and a sour look on their faces.
Let’s think about those hard missions again. You have probably simmed a hard mission 3 times and gotten 0 shards and felt frustrated. And then said to yourself: “How come I get 0 so often and never seem to get 3? I should be getting 3 sometimes to offset all these 0s!” I’ve been there. Would you be surprised to learn that, if the chance is really 1/3, the odds of getting a 0 result are 8 times higher than getting a 3 result? That’s how the math works out. In fact, with a 1/3 chance, you should get 0/3 almost 30% of the time. That’s why it happens so often.
(Full odds assuming 1/3 chance: 0/3 result 8/27 times; 1/3 result 12/27; 2/3 result 6/27; 3/3 result 1/27).
What about double-simming two hard nodes, so 6 tries? Assuming 1/3 chance, you should get 6/6 only 1 out of 729 tries. The game’s only been open for something like 45 days, so if 6/6 has never happened to you, that’s why: the odds say it shouldn’t. But the odds of getting 0/6 are only 1 in 11, or 64x as often as a 6/6 result. So you should have had this happen, on average, at least once every two weeks. That’s why it seems like the game isn’t being fair.. it’s just the math not being fair.
Now this assumes a 1/3 chance of a drop. If it is lower, as I suspect, things get even worse. If the odds are 1/4 to get a drop, then your chances of going 0/3 increase from 32% to 43%. Your odds of going 3/3 decrease from 3.7% all the way to 1.6%.
If the odds of a purple item dropping are 15%, then if you sim 15 times, you should go 0/15 8.7% of the time, or about once every 12 refills. If you refill 3 times per day, you should EXPECT to get 0/15 every few days.
Confirmation Bias
This is a scientific term that describes the tendency of people to assign more weight to outcomes that match their preconceived notions than outcomes that contradict them. Simply put, when something happens that matches what we expect, we notice it and tend to use it to confirm our beliefs. When something happens that doesn’t match what we expect, we tend to either not notice it, or disregard it as being “atypical” or otherwise not relevant.
For example, I’ve read several comments over the last few days that “drop rates have been reduced since the update”. This is possible, but I doubt it. I don’t notice any difference. But if you are convinced that this is the case, you will tend to notice cold streaks much more than hot streaks and believe that this is proof that your theory is correct. This isn’t malicious, it’s just how most people work.
This sort of thing also leads to superstitions that get passed around, usually when something happens out of coincidence but a person finds a pattern that they believe explains it. For example, yesterday I saw someone say that if he is having a cold streak trying to farm a purple gear item, he goes and does something else and then comes back and has better luck. No programmer would write code that works in this way, so this is purely psychological. (It’s actually good advice, but not because it actually works, but rather because it encourages you to cool down rather than getting aggravated, so you view things more clearly.)
Another example: when I was having trouble getting Dooku shards someone suggested to me that I not do Dooku first but rather some other character I cared less about, and come back and do Dooku later, because he had better luck this way. I tried it, and it made no difference at all. Again, I highly doubt the developers bothered to tweak the odds based on what order you sim missions. It’s just a cognitive bias he developed because he had better luck doing Dooku later in the day a couple of times.
“Red Light Syndrome”
We tend to notice things more when they are unusual, when they are annoying, and when they happen at what seems like a bad time. Ever tried to drive somewhere and you hit every red light? Ever noticed that this always seems to happen when you are running late or in a hurry? Of course the traffic lights don’t know anything about your schedule. You just NOTICE the red lights more when you hit a lot of them, and especially when you are in a hurry. I’ve actually tried to look at this phenomenon and noticed that sometimes I actually hit all the green lights. But I have to pay attention to notice them. When I hit all the red lights I need no effort to notice it.
This happens in games as well. You notice the 0/6 because it irritates you; you notice the 4/6 much less because it’s a good outcome (and also because you “expect it” since you are “overdue” from having so many 0/6 results).
I have in the past remarked that I never seem to get 3/3 from hard missions. Yesterday I paid close attention and it happened to me 3 times, on different characters. But I probably would have glossed over it if I hadn’t deliberately been paying attention.
The “in a hurry” part comes in with a game when you are trying to get that last shard or item drop. You have 79/80 shards and you sim 10 times and get 0 drops. Clearly the game must be deliberately torturing you by lowering the odds! It’s not true. I’ve actually examined this and found no difference in drop rates as I approach an unlock point. It just SEEMS this way because you are paying much more attention to shard #80 than, say, shard #17.
So, no, the game is not trying to prevent you from getting that character you want. You are just noticing every failed attempt because it's important to you.
The same thing happens when you are running low on a resource. Say you only have enough energy for 4 tries at something.. you'll notice if you fail at those 4 much more than 4 tries first thing after a refresh.

I've been working past mocks and putting together notes by topic based on CFAI's answer guidelines. I have BF typed up so far, I'm in the process of writing up PWM and Instl and can share those later if you guys find this helpful. These were typed up quickly, so let me know if you find any errors.
I'm not an authority or expert on this, but to get full credit, written responses must relate to the client's specific situation and explain why they exhibit a particular bias or will take a certain action. Mark Meldrum has a great video on his YouTube channel: https://www.youtube.com/watch?v=vL_gRk1wFX0
The guidelines prefer Bayesian language, especially for Conservatism and Representativeness biases.
Read the question carefully - they may specifically ask you to identify and explain a cognitive bias while the client exhibits both cognitive and emotional.
Advisor Actions:
Moderate/educate cognitive biases, especially when client has high SLR
Adapt to emotional biases especially when client has low SLR
Conservatism
What: slow to update old views when presented with new information
How it affects client: Client overweights base information A, underweights new information B
Representativeness
What: overweighting new information based on prior experience (base rate neglect), or assumes small samples are representative (sample size neglect)
How it affects client: Client underweights base information A, overweights new information B
· Optimistic ABC stock will perform well because CEO was at a success company before
Confirmation Bias
What: seek out and overweights info supporting beliefs, ignores contradicting info
How it affects client: Client placed greater weight on A which confirms views, ignored information B which was contradictory
Regret Aversion
What: avoid pain of regret from poor investment outcome
· holding losers fearing they may appreciate
· or, buying into rising market (FOMO)
· or, hold onto winners
How it affects client: Client buys equities in rising market (FOMO)
· or Client refuses to sell loser fearing it will appreciate
· or Client will not sell ABC stock because it has appreciated, fears missing out on further appreciation
Self-Attribution
· What: take credit for success, assign blame for failure
· How it affects client: Client assigned blame for A, took credit for B.
Bounded Rationality
· What: using heuristics to arrive at acceptable, not optimal, decisions; maximizes expected wealth subject to safety constraint
· How it affects client: Client not making optimal choice/satisficing, which is not optimal because did not research A; or, Client applying heuristic to XYZ choice, not optimal but meets needs
Availability
What: selecting choice that is easily recallable; resonance; narrow range of experience
How it affects client: Client is familiar with A, option B is less known; or, A is impactful to client; or, client has always used A; client selects investment based on advertising
Conclusion: Client likely to select A
Loss Aversion
What: disposition effect, sell winners early and hold losers too long
How it affects client: Client feels more impact from loss than a gain of equal size
Conclusion: Client will sell winner ABC; or client will hold loser XYZ
Mental Accounting
What: treating one sum of money differently based on mental account it’s assigned to
· does not consider money fungible
· assigns different goals to different sums of money
· Behavioral Portfolio Theory – inconsistent with Mean Variance Framework
How it affects client:
· Client considers principal and income separately
· Layers investments based on importance, holds riskless assets and highly speculative assets
· Does not consider covariance of returns between different assets
Framing
What: answer question differently based on how it’s presented
How it affects client: Client will select option whose risk metrics focus on safety (80% change no loss) over identical investment whose metrics focus on risk (20% chance of loss)
Conclusion: Client selects ABC (fund presented more positively)
Endowment
What: valuing an owned asset more than its true value
How it affects client: emotional tie to ABC stock; believing their company worth significant premium to peers
Illusion of Control
What: believe you have control over uncontrollable situation
How it affects client: Client believes their actions at work influence stock price
Gambler’s Fallacy
What: expecting reversion to mean in the short-run
How it affects client: Client has forecast for above-average interest rates because they are currently lower than average
Naïve Diversification
What: equally weighting investment across number of choices
How it affects client: Client equally weights his capital across all G-7 country bonds
Overconfidence
What: irrational belief in skill, ability
How it affects client:
· sets narrow range for forecast
· maintains forecast as new information emerges
· fails to include other factors
· Believes he is expert investor
· Excessing trading and underperformance
Comparing Biases w/ Traditional Finance
· Mental Accounting: Client classifies wealth by source: current income, currently-owned assets, PV future income
o REM doesn’t use mental accounts, money is fungible
· Self-Control: client spends all salary and most of bonus on current consumption, pursues short-term satisfaction, hurts long-term financial security
o REM: use self-control in reaching long-term goals; achieves optimal consumption plan that maximizes expected utility over life