3/01/2015

Texas Hold'em Poker Probability - Pocket Pair vs. 2 Overcards(not suited, connected)

With continuing our previous discussion, say if you have pocket pair 77, the other player X has TJ (not suited).

1.Player X could get a 789TJ straight:

In case b, with a 7, but no TJ:
  b.1) 789yz: 2*4*4*C(28,2)  yz not in (7,8,9,T,J,Q)
Sum of (b.1) is 12,096, the probability is about 0.71%. 

In case c,
  c.1) 789Ty, 789Jy: 2*4*4*3*C(28,1)*2=5,376, the probability is about 0.31%. 

2.Player X could get a 89TJQ straight:

In case a, without 7,T,J, but 
  a.1) 89Qyz: 4*4*4*C(24,2)  yz not in (7,8,9,T,J,Q,K)
  a.2) 889Qy,899Qy,89QQy:  6*4*4*C(24,1)*3
  a.3) 8899Q,889QQ,899QQ: 6*6*4*3
Sum of (a.1,a.2,a.3) is 25,008, the probability is about 1.46%. 

In case b,
  b.1) 789Qy: 2*4*4*4*C(24,1)  y not in (7,8,9,T,J,Q,K)
Sum of (b.1) is 3,072, the probability is about 0.18%.

In case c,
  c.1) 789QT, 789QJ: 2*4*4*4*3*2=768, the probability is about 0.04%. 

3.Player X could get a 9TJQK straight:

In case a.
  a.1) 9QKyz: 4*4*4*C(24,2)  yz not in (7,9,T,J,Q,K,A)
  a.2) 99QKy,9QQKy 9QKKy:  6*4*4*C(24,1)*3
  a.3) 99QQK,99QKK,9QQKK: 6*6*4*3
Sum of (a.1,a.2,a.3) is 25,008, the probability is about 1.46%. 

In case b,
  b.1) 79QKy: 2*4*4*4*C(24,1)  y not in (7,9,T,J,Q,K,A)
Sum of (b.1) is 3,072, the probability is about 0.18%. 

In case c,
  c.1) 79QKT, 79QKJ: 2*4*4*4*3*2=768, the probability is about 0.04%. 

4.Player X could get a TJQKA straight:

In case a,
  a.1) QKAyz: 4*4*4*C(28,2)  yz not in (7,T,J,Q,K,A)
  a.2) QKAy,QKAy QKAy:  6*4*4*C(28,1)*3
  a.3) QQKKA,QQKAA,QKKAA: 6*6*4*3
Sum of (a.1,a.2,a.3) is 32,688, the probability is about 1.91%. 

In case b,
  b.1) 7QKAy: 2*4*4*4*C(28,1)  y not in (7,T,J,Q,K,A)
Sum of (b.1) is 3,584, the probability is about 0.21%. 

In case c,
  c.1) 7QKAT, 7QKAJ: 2*4*4*4*3*2=768, the probability is about 0.04%. 

The probability for player X to get a straight (without you getting a full house or 4-of-a-kind) is about 6.55%.  Your probability of winning is lowered to about 51.73%+q, anyway you could still win with a flush.


No comments :