Assuming I have flipped 99 coins all tails, what is the chance of the 100th coin being heads?
Yes I know it's still 50%, but is there any other formula that could help explain the risk/probability of a heads/win if I only start playing after X amount of losses? I would like to know how much better 'chances' I have of a heads if I start playing after a certain amount of losses.
Best Answer
Let $X$ be the event that we throw $n$ tails in a run, and $Y$ the event we throw heads,
Using Bayes theorem we can write
$$P(Y|X) = \frac{P(X|Y)P(Y)}{P(X)} = \frac{\large(\frac12\large)^n\frac12}{\large(\frac12\large)^n} = \frac12$$
So it doesn't matter how many times we lose, the chance of a head remains the same.