Practical Poker Math

3. Odds in Texas Hold’em
Starting Hand Hand to Flop Odds
Pocket Pair Boat 101.1 : 1
Pocket Pair Quads 407.3 : 1
Pocket Pair Set or Better 7.3 : 1
Pocket Pair 2 Pair 5.19 : 1
Pocket Pair >>> Set Only
To find the odds of flopping a Set and a Set only we need to
find the number of possible Flops that will include one of
the cards to make the Set and no Pair.
First find the number of 2-card combinations possible from
the remaining unseen 50 cards minus the 2 cards that will
make the Set — Comb(48, 2):
(48 * 47) = 1,128
(1 * 2)
There are 1,128 2-card combinations that do not include the
2 cards either one of which will make the Set. From this
number subtract all of the possible 2-card combinations in
the deck that are Pairs (78) minus the 6 Pairs that come from
the rank of the hole cards (72):
1,128 – 72 = 1,056
Multiply this number (1,056) by the number of remaining
cards that WILL make the Set (2) and you will have the
number of possible 3-card Flops that will make the Set and
the Set only:
1,056 * 2 = 2,112
72