# How do probabilities balance the odds?

Let's consider a simple roulette game, where one may either get red or black. Since the probabiblity P of an event A, P(A) is defined as the relative frequency at which the event occurs, if we get red , say 3 times in a row, it is very likely that the next random pick will be black.

My question is, does this mean that the probability of Black increases as more reds occur? consider a person that only joins the roulette game when several reds have occured before he joins and bets on black, will he never have a high probability of winning?

PeroK
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Let's consider a simple roulette game, where one may either get red or black. Since the probabiblity P of an event A, P(A) is defined as the relative frequency at which the event occurs, if we get red , say 3 times in a row, it is very likely that the next random pick will be black.

My question is, does this mean that the probability of Black increases as more reds occur? consider a person that only joins the roulette game when several reds have occured before he joins and bets on black, will he never have a high probability of winning?

If you get 3 reds in a row, it makes no difference to the probability that the next roll is red or black. It's the same roulette table with the same odds every time.

Yours is a common misconception about the "law of averages". Imagine tossing a coin until you get, say, 4 heads in a row and then taking that coin and making a bet based on the false assumption that the next throw is likely to be tails. What if you toss the coin straight away or leave it a day? - or put it in a drawer for a year? - how would that coin remember that it had 4 heads in a row and ought to come up tails next time?

Stephen Tashi