How do probabilities balance the odds?

[DarkFalz]

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 occurred before he joins and bets on black, will he never have a high probability of winning?

 

[PeroK]

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 occurred 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]

Since the probabiblity P of an event A, P(A) is defined as the relative frequency at which the event occurs

That is not the mathematical definition of probability. The probability of an event can't be directly related to actual frequency of the event except by statements that tell about the probability of an actual frequency.