43s combos

43s: the 4 combos

For 43s, the four and the three must share a suit. With 4 suits and one way to pair them in each, the count is 4.

The 4 holdings of 43s are listed below, higher card first. Nothing is left out and nothing appears twice.

• 4♠3♠
• 4♥3♥
• 4♦3♦
• 4♣3♣

How cards you can see change the count

Combos shrink when cards are visible. The rows below give the 43s count left after one known card of each rank, from the ace down to the two.

A four or a three you can see leaves 3 of 4, so 25% of the combos are gone. Any card of a different rank leaves all 4 combos in play.

When the board is paired

Now put two cards of the same rank on the board. This table counts the combos of 43s that are still possible after a board pair of each rank.

Pairing fours or threes on the board cuts 43s to 2 combos. Every other paired board leaves the full 4.

A worked example

Walk through it once. Your hole cards: a four and a two. Your opponent's possible hands: 1,225. Of those, 43s is 3, so the chance is 3 / 1,225 = 0.24%. With no blocking card it would be 4 / 1,225 = 0.33%.

How strong is 43s?

The ranking puts 43s at number 150 out of 169, among the 30 weakest classes. Its equity against a random hand is 38.64%, with a tie counted as half a win.

A range that runs from the top of the ranking down to 43s is 1,138 combos, 85.82% of all two-card hands, and 1,134 of them rank above 43s itself.

43s against ranges of hands

Here is how 43s fares against five ranges that run from the top of the ranking down. It scores 23.44% against the top 5 percent (60 combos), 30.76% against the top 10 percent (130 combos), 33.92% against the top 20 percent (264 combos), 34.73% against the top 30 percent (386 combos) and 36.43% against the top 50 percent (658 combos).

43s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.

The top 10 percent is 130 combos before you look at your cards. With 43s in your hand, an average of 130.00 are left. That is no loss at all: 43s blocks none of those hands.

Hands next to 43s

Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. 43s has 46.77% equity against 92o, the hand ranked number 149: it wins 45.20% of boards, ties 3.15% and loses 51.66%. It is the underdog in that matchup. 43s has 38.00% equity against 74o, the hand ranked number 151: it wins 28.78% of boards, ties 18.44% and loses 52.78%. It is the underdog in that matchup.

43o is 3 times as many combos but 3.50 points weaker against a random hand, and 43o is the offsuit twin, number 164 of 169 with 35.15% equity.

Questions about 43s combos

How many combos of 43s are there?

4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 43s about 1 time in 331.5.

How many 43s combos are left if I hold a four?

3 combos of 43s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.

Is 43s stronger than 43o?

Yes, by 3.50 points: 43s has 38.64% equity against a random hand and ranks number 150, while 43o has 35.15% and ranks number 164. 43o has 12 combos to 43s's 4.

How this was computed

Combos are counted by listing all 1,326 two-card hands in a 52-card deck and sorting each into its class. The known-card rows remove every combo that uses a card of that rank; the board-pair rows remove those that use either of two such cards.

Rank and equity read our table of all 169 by 169 preflop matchups, each counted over every one of the 1,712,304 boards. Ties count as half a win, and a range is weighted by its live combos.

Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.