1. World Series of Poker Main Event 2005, Day 1, from cardplayer.com: *Date / Time:* 2005-07-08 01:23:00 With the board showing 10  9  5  Q , Chris "Jesus" Ferguson moves all in. Kalee Tan calls. Ferguson shows Q-Q for a set of queens, and Tan flips up J-8 for a queen high straight. Ferguson needs the board to pair in order to stay alive. The river is the 8 , no help to Ferguson, and he is eliminated on Day 1. Kalee Tan drags the pot with uncontrollably shaky hands as Ferguson heads to the rail. Q: What is the probability of flopping an open- end straight draw, given you have J-8? What about J-9 or J-T?

2. A: For J-8, you need the flop to be KQT or T9x or 976 or 765. Consider the case where x is T or 9 separately (x ≠ Q or 7!). So the probability is: P( KQT or TT9 or T99 or T9x or 976 or 765 ) = 4 x 4 x 4 + C(4,2) x 4 + C(4,2) x 4 + 4 x 4 x 34 + 4 x 4 x 4 + 4 x 4 x 4 C(50,3) = 4.0%, or 1 in 25. A: For J-9, you need KT7 or T8x or QTx or 876, so it’s P( KT7 or TT8 or T88 or QQT or QTT or T8x or QTx or 876) = 64 + [C(4,2) x 4] x 4 + [4 x 4 x 34] x 2 + 64 C(50,3) = 6.7%, or 1 in 15.

3. A: For J-T, you need: KQx, Q9x, 98x, AQ8, K97, Q87, KKQ, KQQ, QQ9, Q99, 998, or 988. So the probability is: 3 x [4 x 4 x 34] + 3 x [4 x 4 x 4] + 6 x [C(4,2) x 4] C(50,3) = 10.0%, or 1 in 10.