Some Heads Up Stats

Just somes stats I want to keep around,

There are a total of 1326 starting hands in Texas Holdem poker, this is calculated by taking 1 of the original 52 card deck and then one of the remaining 51 cards:
(1/52)*(1/51) = 1326 combinations.

If we leave aside the different combinations of suits then these can be reduced to 169 distinct starting hands. 13 of these are pairs, 78 are suited unpaired cards and the remaining 78 are unsuited unpaired cards.

The cards that you are dealt affect the probability of your opponent having the same holding. For example if you are dealt an Ace before the flop there are only 3 remaining aces in the deck – the chances of an opponent holding an ace has been reduced by 25%.

The table below shows the odds of being dealt specific strength holdings before the flop.

A-A (220/1 or 0.45%)
A-K (81.9/1 or 1.1%)
A-A, K-K, Q-Q or 10-10 (54.3/1 or 1.8%)
Any Pocket Pair (16:1 or 6.25%)
Any 2 Cards Jack or Higher (10.1/1 or 9.05%)

The relative strength of pre-flop hands in heads-up poker can be calculated by assuming that your opponent has a random holding. That is to say that the chances your hand will win a showdown if all the chips went in to the middle immediately can be ranked in terms of your holding compared to the whole range of your opponent’s possible cards.

The table below gives the pre-flop odds of selected head-up poker hands
A-A, wins 84.93% of the time.
K-K, wins 82.12% of the time
Q-Q, wins 79.63% of the time.
J-J, wins, 77.15% of the time
A-K (suited), wins 64.47% of the time
K-Q (not suited), wins 60.43% of the time.
J-10 (suited) wins 56.15% of the time
K-4 (not suited) wins 50.23% of the time
Hands below K-4 off suit are not favorite before the flop… the very worst hand 2-3 (not suited) wins only 29.24% of the time.