The Gambler's Fallacy
In proper gambling there are no systems and no rules. Every toss of a coin, spin of the wheel or throw of the dice is a stand-alone item.
Many people believe in the false logic which says that a heads spin will follow ten tail spins. This is completely false. If I toss a coin and it comes down heads time after time, it will come down tails the next time.
What is actually happening is that each flip of the coin is a stand-alone individual event and is not connected to any other spins in any way. The law of averages says that after many flips, the coin will have come down as many times heads as tails and this was proved by a prisoner-of-war who spun a coin thousands of times and recorded the result of every flip.
The law of averages proved to be correct. He got as many heads as tails after all these flips, but he could not forecast the result of any one spin. Each time he flipped the coin into the air, it was like the first time. He may often have had ten or twenty heads in a row but it all evened out in the long run.
Test yourself. You are flipping a coin, and you are being quite honest. You have just flipped 8 heads in a row. Is your next flip more likely to be:
- heads and tails are equally likely
The correct answer is No 3, heads and tails are equally likely. Answer No 1 is an example of one version of the Gambler's Fallacy where you think that your luck will continue. Answer No 2 is an example of the opposite version of the Gambler's Fallacy where you think that your luck will change. A popular way to explain why answer No 3 is correct is the simple explanation, "the coin has no memory. It does not matter what the previous spins were. The coin always shows 50-50 odds."
And of course, this principle applies equally to the red/black or odds/even bets on the roulette wheel.