>Leland,
>
>>Hint: Each time you lose increases the odds that the next round will be a winner.
>
>Probability does not work that way. Each round is an independent event. One round does not affect the next. The odds on winning P(w)_n+1 or losing P(l)_n+1 any given event are the exact same as they were for the event before P(w)_n or losing P(l)_n

You are correct, each event is independent. On any flip of a coin there is a 50% change that it will be heads...

But, there is also the probablity of the repeating events... flip a coint once, you have a 50/50 chance it will be heads. Flip it again, there is a 50/50 change it will be heads. Let's say it was heads 3 times in a row, what is the probability that it will be heads a fourth time?

Sure, there is still a 50/50 chance of heads on that fourth flip? However, the chance of 4 heads in a row is alot lower than three heads and a tail.

It has something to do with standard deviation, and distribution, but I don't know much about those things.

BOb