Texas Hold'em Poker Starting Hands

When comparing two starting hands, the heads-up probability describes the likelihood of one hand beating the other, assuming that neither hand will fold, and there will be a showdown. This situation occurs quite often in no limit hold'em and tournament play.

An exhaustive analysis of all heads-up match ups in Texas Hold'em poker is made, which required evaluating each possible board for each distinct head-to-head match up, or 169 (number of non-equivalent starting hands out of the 1,326 combinations of choosing 2 cards from 52 cards, assuming that, for example, and are all the same) * 1,225 (number of combinations of choosing 2 cards from a deck of 50 cards) * 1,712,304 (number of combinations of choosing 5 cards from a deck of 48 cards) ≈ 354 billion possibilities. Some techniques are used to avoid redundant calculations.

For example, suppose you are holding pocket aces and you are playing heads-up against another player holding a random hand.

 

What is your odds of winning at the showdown if no one folds?!

As illustrated below, in this scenario, you will win 84.93% of the time, lose 14.53% and split the pot 0.54% of the time.

Chances Against a Random Hand
Win: %
Tie: %
Loss: %

What is the strongest hand against your pocket aces?!

Another pocket pair like pocket kings?! As you can find in the Heads-up Probability Table, pocket kings wins only 17.09% of the time if it has the same suits as your aces and 18.55% of the time if the suits are different from the suits of your aces. It's interesting that pocket kings is even weaker than pocket threes (33) which has 18.68% chance of winning against pocket aces.

Suited connectors?! Yes, but not Jack-Ten though. Surprisingly, ignoring the case when your opponent is also holding pocket aces - which results splitting the pot %95.65 of the time -, the strongest hand against pocket aces is 56 suited (where suits are different from the suits of the aces).

Lowest Chance of Winning Against
Win: %
Tie: %
Loss: %

What is the weakest hand against your pocket aces?!

Likewise, it's also counter intuitive that the weakest hand against pocket aces, is A9-off-suit (where 9 has the same suit as one of the aces). Pocket aces wins 93.37% of the time against such hand. AK-off-suit (where king has a suit of one of the aces), is also one of the worst hands against pocket aces. It loses 92.80% of the time against pocket aces.

Highest Chance of Winning Against
Win: %
Tie: %
Loss: %

Give it a try!

See the head-to-head probabilities for your favourite hands here.

↩ Back to blog archive