In your simplified example, once you see that the 3.125% *did* happen, then the chance that the 1.5625% *does not* happen is exactly 50%. In other words, if you had a (very long) video tape of roulette spins and selected all the times that five successive spins were black, then you would see that in (approximately) half of those times the sixth spin was again black, and in the other half it was red.

If you want to understand the math behind that, check the chapter on “conditional probability” in your favorite textbook. For discrete variables it’s not hard at all, involving only multiplication and division, and it will give you a definite edge on “the man” and all other laymen that rely on their intuitive-but-wrong generalizations of simple probability of one event to the case of series of independent events. ]]>

Little Roulette Info, there are 38 spaces, 18 red and 18 black.

So the odds of Hitting red or black is 47.37%

The payout for hitting red or black is 100%

So the man who bet $100 on red won his $100 back and an extra $100

I don’t gamble and I don’t condone it, but I do agree with the man’s theory. If you look at the chances of each individual spin, yes it’s 47.37% chance of red or black.

But if you look at a series of spins, it’s a little different. For simplification purpose pretend there is no Green 0 and 00 and only red and black.

So for a series of four spins to all be black is a 6.25% chance

A series of five spins to all be black is a 3.125% chance

A series of six spins to all be black is 1.5625% chance

and so on.

So what the man was doing was waiting and watching for the 3.125% chance to happen, becuase it’s only a matter of time before it does.

When he saw that the 3.125% chance did happen, he bet money that the 1.5625% chance WOULD NOT happen.

Had he LOST his money and the 1.5625% chance DID happen, then he would probably double up his bet on black and bet $200. Becuase now he has there is a 0.78125% chance that any 7 spins will come out all red.

It’s true that in theory if the wheel spins infinite number of times, eventually you will have really long streaks of nothing but one color. But it’s still a safer bet than walking in blind.

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