Calculating your outs in Texas Hold’em

What are the chances? How do you calculate your chances of winning with one card to come?

In a community card poker game like Texas Hold’em, you’ll occasionally find yourself in a situation where the betting has completed, but not all the cards are dealt. The players’ hole cards are turned over and everyone can see what each person needs to draw on the river to win the pot. So how do you work out the chances for each hand?

The first step is to count how many known cards there are and how many unknown (unseen) cards there are.

• Known cards are your own hand, the community cards, plus any other exposed cards revealed for any reason — for instance, if the betting is complete and the cards are “on their backs”
• Unknown cards are the rest of the deck, and any folded cards.

Other players’ folded cards are unknown because they were randomly dealt and you haven’t seen them. You might be able to make an educated guess, given how those players were betting.

The number of known cards plus unknown cards is always 52 if you’re playing with a standard deck, while a Royal Hold’em hand calculation will revolve around a 20-card deck.

The cards in that pool of unknown cards that’ll win the hand for you are your outs.

Let’s look at a common situation:

    

The above four cards have been revealed. You’re all-in with a 3 of Clubs and 4 of Clubs, and you see that your opponent is currently winning with a 7 of Hearts and 7 of Diamonds.

You can see eight cards. Of the 44 unknown cards, nine are clubs and three others are 2s (you can’t count the 2 of clubs twice, and you already counted it with the clubs), so you have 12 outs to win. Even though many of the cards left don’t improve your opponent’s holding or change the outcome, all the rest are considered to be outs for your opponent because they don’t help your hand.

If you had two higher clubs than your opponent’s pair of 7s, such as the Queen and the 9, then you’d have nine clubs, three non-club Jacks, PLUS the three Queens and three 9s which make a pair for you. That comes to a total of 18 outs, and in a situation where there are only two players, that means it’s an 18 out of 44 chance to win, which is almost 41%

Interestingly, the hand that is currently winning is sometimes not the favorite to win the hand — especially when three or more hands are involved in the race.

   

For example, on the above board, where three players are all-in with the following holdings:

• A) J of Clubs, 10 of Clubs
• B) 9 of Spades, 5 of Spades
• C) Ace of Diamonds, 4 of Diamonds

There are 42 unknown cards, regardless of how many players were dealt in and have folded.

• A) wins with any one of: nine clubs, two Queens, two Jacks, two 10s, and two 7s, making 17 outs (40.5%).
• B) wins with any one of: nine spades, two remaining 9s, and the two remaining 5s that are not clubs, making 13 outs (31%).
• C) has the remaining cards that don’t improve an opponent, which is just 12 of them, for 28.6% and the lowest chance to win of the three!