Suppose someone offers you a bet that they can flip a coin ten times so that their heads fall in all attempts. He will let you touch the coin, so you will find that it is a regular coin. What odds would you offer him? 100: 1? 1000: 1? You can offer 1000: 1, and it still pays off.
Now imagine that your friend already flips the coin nine times. And the head fell every time. What would be your last bet?
The Principle of Gambler's Fallacy
Many players think that previous attempts at an event (coin flip, roulette spin, etc.) affect the next roll. It does not. As for the coin example, the head fell 9 times does not mean anything for the tenth flip!
For the tenth attempt, the chances are again 50 to 50, as in the first attempt. The coin has no memory, so the probability remains the same. You can even replace coins, and it won't change anything.
If we look at how to calculate probability, we will see it even more clearly. For one coin flip, the chances are 50-50 that the head or tails will fall - so the odds are 2: 1 (paying twice the bet). The odds of 5 times in a row are calculated - 2 x 2 x 2 x 2 x 2 = 32, and as you can see in each flip, the probability is still only 2.
How Gambler's Fallacy Affects a Game
This mistake plays a considerable role in gambling. Many people who play tend to look at previous games and develop a past-based strategy.
For example, if they find that black struck on roulette many times in a row, they will probably start betting on red. Because they feel like the red must fall now. If they lose many rounds in a row, many players will begin doubling bets because they assume there is some kind of balance.
This is the basis of the Martingale system, in which the player doubles the bets after each spin lost. This system may work in the short term, but in the end, the house edge, the betting limits, or the player's bankroll will attack. A player who bets based on this belief can find himself in serious trouble.
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