Gambling Fallacies

Availability error:

Availability Error is the tendency to focus only on good, unusual, or easily remembered experiences, forgetting the bad, common, or less available ones. Hearing that someone has won the lottery sticks in our mind more than hearing that someone has lost.

Favorable events:People believe something favorable to be more likely to happen than something unfavorable, even if the mathematical odds are the same
• California Lotto Jackpot: odds are approximately one in 18million.  If you have to drive ten miles to buy this ticket, you are three times more likely to be killed in an automobile accident on the way than to win the jackpot, yet many people would incorrectly think that winning this lottery would be more probable.
• Unusual events:  People overestimate the frequency of infrequent events and underestimate frequent ones. 
• Many people are more afraid of dying in an act of terrorism than they are of dying in an auto accident, despite the fact that they are MUCH more likely to die in an auto accident.
• Long shot: Overvaluing high gain, low probability wagers and undervaluing low gain, high probability wagers.
• Many people prefer to play the lotto (high gain, low probability) to a fair coin toss (low gain, high probability).

• Large chance:  Many people prefer a single large chance to many small chances, even if the odds are equal (unless the multiple chances have a different source, in which case they are preferred).

Conjunction errors:

Added conditions can make a case seem more probable, despite the fact that added conditions make it inherently less probable.

• Rolling a 6-sided die with 2R and 4G sides, many people incorrectly believe that the sequence GRGRRR is more likely than RGRRR.
• One experiment asked people to choose the more likely of the following two statementsâ and 85% of them chose the first! 
•  Linda is a bank teller and active in the feminist movement.
• Linda is a bank teller.
• Similarly, among the next two statements, the first was preferred by most people:
•  Borg will lose the first set but win the match.
• Borg will lose the first set.

 

Anchoring and adjustment errors:

• Initial estimates are skewed by unrelated facts or by recent examples
• Adjustment of skewed initial estimates tends to be inadequate.

Illusion of control:

Illusion of control results from overestimating the role of skill and underestimating the role of chance.

• Attributing wins to skill and losses to external events.

• Hindsight bias:  Evaluating decisions as good or bad depending on whether they led to a win or a loss. 

• Belief in Luck:  Luck is considered a quantity to conserve, independent of chance.

 

Mis-atribution of cause:

• Post hoc ergo propter hoc:
• For example, misattributing the regression to the mean effect:  after a person has an especially good performance on a test or in some other difficult situation, s/he will normally do less well the next timeâ otherwise the especially good performance would have been considered “normal” and a better performance would be required for you to call it “especially good.”  If you happen now to praise the person for her/his great performance, and the next time s/he goes back to normal (as you’d expect) then it is easy to misattribute the drop in performance to your having praised her/him.
• Be careful not to mistake “regression to the mean” for the Gambler’s fallacy.
• Confusing correlation with causation: assuming since two things are statistically correlated that one is the cause of the other.
• One famous case is the putative milk-cancer link.  Cancer is CORRELATED to milk consumption, but probably not CAUSED by drinking milk.  Rather the correlation is more likely because milk drinkers live longer than milk abstainers, and people who live longer are more likely to die of cancer than those who die young.
• Hot Handâ Patterns and Prediction:  (perhaps inspiring the Epaminondas system) Despite evidence of independence of trials, people try to predict the future based on past resultsâ they look for streaks and patterns.
• Evidence shows that there is no “ hot hand” in basketballâ at least no more than one would expect due to chance.
• Coin streaks: On average you should expect a streak of at least 8heads or 8tails whenever you flip a fair coin at least 500 times.  Yet, many would mistake the appearance of such a streak for proof that the coin is unfair.
• Limited sample:  overvaluing the significance of a limited sample.
• For example: “My two friends both won more money at slots than they spent, so I’ll be able to too.”
• Anthropomorphization: people attribute personality to various inanimate objects (e.g., dice).  Indeed some people literally believe that the dice have periods when they are hot or cold.  And others talk to the dice: “Baby needs some new shoes.”

 

Pseudo-Mathematical errors

• Gambler’s Fallacy: The belief that the dice, the coin, the roulette wheel, or whatever it is will make things “even out.”  That somehow the roulette ball knows about and will try to fix the fact that the last three numbers were all red, and so a black is “due.”  A variation of the Gambler’s Fallacy is the Monte Carlo fallacy:  “After successes, a failure is inevitable, and vice versa.”  Do not confuse this with the Law of Large Numbers.
• Confusing a specific rare event with any rare event: Every license plate is a miracle.  This is a pseudo-mathematical overcorrection of the unusual events availability error.
• The self-proclaimed lotto maven Gail Howard claims you should never pick the sequence of numbers 1-2-3-4-5-6, since the chances that they’d come up are tinyâ but she forgets that the chances of any sequence of numbers coming up are exactly as tiny as the chances for 1-2-3-4-5-6.
•   The probability of a multiple additive choice is underestimated; a multiplicative probability is overestimated.  (Like the conjunction fallacy)
• Successive events:  People consider successive independent events as additive rather than multiplicative.
• John A. Paulos claims to have heard a weatherman say “There is a 50% chance of rain on Saturday and a 50% chance of rain on Sundayâ so there is a 100% chance of rain over the weekend.”  One can’t help but wonder what that weatherman would make of a situation where the chances were 60% each day.
• Misestimation of large and small numbers: Most people do not have a good sense of how much a thousand is, compared to a hundred thousand, a million, or a billion.  For example, do you have any clue how big a building a thousand, a million, or a billion bricks would build?  Do you have any idea how long a line of a million people would be?  Or how long it would take to read all their names?
• If all of the losers of the California (1 in 18 million) lotto were to stand in line, they would reach approximately 6,800 miles, which is approximately the distance from Salt Lake City, Utah to Moscow, Russia.
• Quit while you are ahead each time and you'll never lose: (i.e., keep chasing your lost money until you recover it.)This belief is a hallmark of pathological gamblers.

 

Paranormal phenomena

Gamblers often try to use patently silly methods, like

• Psychic powers,
• Astrology,
• Numerology,
• Biorhythms and other cycles,
• Or "Luck."

A useful experiment to perform, if you are tempted to use one of these phenomena, is to look at ALL predictions made by these methods over the past year.  What percentage came true? I recently saw a collection of such predictions made in 1990 for the coming year of 1991â unfortunately not one single psychic nor astrologer in the collection made a correct prediction that year, not even the very highly-acclaimed Jeanne Dixon and Uri Geller.

Religion:

Some gamblers believe that God (or whatever they believe in) wants to make them rich: "I've been good all my life--He wants me to be happy."

It appears, however, that the overwhelming majority of these people lose--thus one cannot help but wonder if perhaps God wants them to use a different means to get rich (like hard work).