Binomial distribution with changing success rate

[poker_n00b]

Searched the internets, couldn't find anything.

I am kind of trying to quantify the "running bad concept".

Let's say I lose one 70/30 flip, one 80/20 flip and one 50/50 flip. The success rate of winning, p(winning), changes in all three examples.

How can I calculate the probability of losing those 3 flips?

Note:

I want to exclude the amount of money or chips put it, because it has a bias. For example, I may lose 10 times AA vs 72o for 10$, but win 72o vs AA for 1 million. The amount of money you end up having is in no way representative of how you are running. I may be wrong on this one.