Chapter 16, Problem 80E

In head-to-head, 7-card stud poker you make your hand by selecting your 5 best cards from the 2 in your hand and 3 from the 5 common cards showing on the table (the “board”). Suppose you are holding $A♠$, $2♠$, in your hand and $Q♠$, K ♥, $3♠$, 7♦ are showing on the board (this is called a “flush draw”)—if the last card (“river” card) is a spade you will have an ace high flush and a guaranteed win. Assume that your opponent has a decent hand and if you don't get the spade on the river card you will lose the hand.

a. Suppose there is $\$100$ in the pot and your opponent moves “all-in” with a $\$50$ bet. Should you call the bet or fold? Explain.

b. Suppose there is $\$100$ in the pot and your opponent moves “all-in” with a $\$20$ bet. Should you call the bet or fold? Explain.