Gambler's Fallacy
The biggest gambling myth is that an event that has not happened recently becomes overdue and more likely to occur. This is known as the “gambler’s fallacy.” Thousands of gamblers have devised betting systems that attempt to exploit the gambler’s fallacy by betting the opposite way of recent outcomes. For example, waiting for three reds in roulette and then betting on black. Hucksters sell “guaranteed” get-rich-quick betting systems that are ultimately based on the gambler’s fallacy. None of them work. If you don’t believe me here is what some other sources say on the topic:
A common gamblers’ fallacy called “the
doctrine of the maturity of the chances” (or “Monte Carlo fallacy”)
falsely assumes that each play in a game of chance is not independent of
the others and that a series of outcomes of one sort should be balanced
in the short run by other possibilities.
A number of “systems” have been invented by gamblers based largely on this fallacy; casino operators are happy to encourage the use of such systems and to exploit any gambler’s neglect of the strict rules of probability and independent plays. — Encyclopedia Britannica (look under “gambling”)
No betting system can convert a subfair game into a profitable enterprise... — Probability and Measure (second edition, page 94) by Patrick Billingsley
The number of ‘guaranteed’ betting
systems, the proliferation of myths and fallacies concerning such
systems, and the countless people believing, propagating, venerating,
protecting, and swearing by such systems are legion. Betting systems
constitute one of the oldest delusions of gambling history.
Betting systems votaries are spiritually akin to the proponents of perpetual motion machines, butting their heads against the second law of thermodynamics. — The Theory of Gambling and Statistical Logic (page 53) by Richard A. Epstein
Vegas Click also has a good expose of the gambler’s fallacy.
The Martingale
Every week I receive two or three emails asking me about
the betting system by which a player doubles his/her bet after a loss.
This system is generally played with an even money game such as the
red/black bet in roulette or the pass/don’t pass bet in craps and is
known as the Martingale.
The idea is that by doubling your bet after a
loss, you would always win enough to cover all past losses plus one
unit. For example if a player starts at $1 and loses four bets in a row,
winning on the fifth, he will have lost $1+$2+$4+$8 = $15 on the four
losing bets and won $16 on the fifth bet.
The losses were covered and he had a profit of $1. The problem is that it is easier than you think to lose several bets in a row and run out of betting money after you’ve doubled it all away.
In order to prove this point I created a program that
simulated two systems, the Martingale and flat betting, and applied each
by betting on the pass line in craps (which has a 49.29% probability of
winning).
The Martingale bettor would always start with a $1 bet and start the session with $255 which is enough to cover 8 losses in a row. The flat bettor would bet $1 every time. The Martingale player would play for 100 bets, or until he couldn’t cover the amount of a bet. In that case he would stop playing and leave with the money he had left.
In the event his 100th bet was a loss, he would keep betting until he either won a bet or couldn’t cover the next bet. The person flat betting would play 100 bets every time. I repeated this experiment for 1,000,000 sessions for both systems and tabulated the results. The graph below shows the results:
As you can see, the flat bettor has a bell curve with a peak at a loss of $1, and never strays very far from that peak. Usually the Martingale bettor would show a profit represented by the bell curve on the far right, peaking at $51; however, on the far left we see those times when he couldn’t cover a bet and walked away with a substantial loss. That happened for 19.65% of the sessions. Many believers in the Martingale mistakenly believe that the many wins will more than cover the few losses.
In this experiment the average session loss for the flat
bettor was $1.12, but was $4.20 for the Martingale bettor. In both cases
the ratio of money lost to money won was very close to 7/495, which is
the house edge on the pass line bet in craps. This is not coincidental.
No matter what system is used in the long run, this ratio will always
approach the house edge.
To prove this point consider the Martingale player on the pass line in craps who only desires to win $1, starts with a bet of $1, and has a bankroll of $2,047 to cover as many as 10 consecutive losses. The table below shows all possible outcomes with each probability, expected bet, and return.
use link to see graphs they are way too large to post
https://wizardofodds.com/gambling/betting-systems/
Hot Forum Topics
