Re: quick probability question
If I am understanding correctly, this is straightforward.
If you want, you can think of this as a direct application of Bayes Rule. Notation:
- V is a value hand
- T is a trash hand
- B is bet
- P is probability
Then at a certain point in the hand we know the following:
We seek P(V|B) and P(T|B).
Bayes rule tells us:
P(V|B) = [P(B|V)*P(V)] / [P(B|V)*P(V) + P(B|T)*P(T)]
= [(1.00)*(.70)] / [(1.00)*(.70) + (.50)*(.30)]]
Similarly, it is easy to see that P(T|B) = 15/85.
Thus, the ratio of value hands to trash hands given that he bets is 70/15.