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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,
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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?
Q: What is the probability of flopping an open-end straight draw, given you have J-8? What about J-9 or J-T? 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 + 4x4x4 + 4x4x4 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.
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.