Practical Poker Math

3. Odds in Texas Hold’em
the pocket. From the 12 ranks that do not include the rank
of the Pocket Pair there are 48 different 3-card combinations
that are Sets — Comb(4, 3):
(4 * 3 * 2) * 12 = 48
(1 * 2 * 3)
In all there are 2,256 + 48 = 2,304 possible 3-card Flops that
will make a Set or Full House when holding a Pocket Pair.
We now have all the numbers needed to calculate the odds of
flopping a Set or a Full House:
Total Possibilities = 19,600
– WILLs = 2,304
WILLNOTs = 17,296
Odds of Flopping a Set or Boat with a Pocket Pair
WILLNOTs : WILLs
17,296 : 2,304
Reduce
17,296 / 2,304 : 2,304 / 2,304
7.5 : 1
Pocket Pair >>> Full House
To flop a Full House with a Pair in the hole, the 3-card board
must contain 1 of the remaining 2 cards that make the Set
and any of the remaining 72 Pairs; or the Flop itself must be
a Set. Any of the 72 Pairs may combine with either of the 2
cards that will make the Set to make the Full House, which
means that there are:
72 * 2 = 144
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