Practical Poker Math

3. Odds in Texas Hold’em
Among the 16 cards in the deck with a rank of Jack or better
there are 120 possible combinations calculated as Comb(16, 2):
(16 * 15) = 120
(1 * 2)
This number includes 24 possible pair combinations. There
are 120 – 24 = 96 combinations that WILL contain 2
unpaired cards above the rank of Ten.
Another way is to multiply the probability of the first card by
the probability of the second. In this case, after the first card
is dealt, there are only 12 cards left that will not pair the first
card:
(16 * 12) / (1 * 2) = 96 (WILLs)
Total Possibilities = 1,326
– WILLs = 96
WILLNOTs = 1,230
WILLNOTs (1,230) : WILLs (96)
1,230 : 96
Reduce
1,230 / 96 : 96 / 96
12.8 : 1
The probability of 2 unpaired Big Cards in the hole is
WILLs
* 100 = Probability as %
Total Possibilities
96
1,326
* 100 = 7.2%
On average you will be dealt 2 unpaired Big Cards once in
13.8 hands or roughly 7.2% of the time.
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