How do you calculate the odds of something occurring if you have two bites at the cherry? For example you have a four flush in hold’em with two cards to come.
The most accurate method is simulating the situation on a computer and running it many thousands of times. Mathematically it can be done as follows:
Probability of winning =
1 – the probability of not making it the first time x probability of not making it the second
You hit the flush about 1 in 3. Thus you win 1 – 2/3 x 2/3 = 5/9.