32s combos

32s: the 4 combos

For 32s, the three and the two must share a suit. With 4 suits and one way to pair them in each, the count is 4.

The 4 holdings of 32s are listed below, higher card first. Nothing is left out and nothing appears twice.

• 3♠2♠
• 3♥2♥
• 3♦2♦
• 3♣2♣

How cards you can see change the count

Combos shrink when cards are visible. The rows below give the 32s count left after one known card of each rank, from the ace down to the two.

A three or a two 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 32s that are still possible after a board pair of each rank.

Pairing threes or twos on the board cuts 32s to 2 combos. Every other paired board leaves the full 4.

A worked example

Walk through it once. Your hole cards: a three and a four. Your opponent's possible hands: 1,225. Of those, 32s 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 32s?

The ranking puts 32s at number 163 out of 169, among the 30 weakest classes. Its equity against a random hand is 35.98%, with a tie counted as half a win.

A range that runs from the top of the ranking down to 32s is 1,254 combos, 94.57% of all two-card hands, and 1,250 of them rank above 32s itself.

32s against ranges of hands

Here is how 32s fares against five ranges that run from the top of the ranking down. It scores 21.62% against the top 5 percent (60 combos), 29.07% against the top 10 percent (130 combos), 32.36% against the top 20 percent (264 combos), 33.13% against the top 30 percent (386 combos) and 34.16% against the top 50 percent (658 combos).

32s 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 32s in your hand, an average of 130.00 are left. That is no loss at all: 32s blocks none of those hands.

Hands next to 32s

Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. 32s has 39.59% equity against 63o, the hand ranked number 162: it wins 27.15% of boards, ties 24.89% and loses 47.96%. It is the underdog in that matchup. 32s has 48.18% equity against 43o, the hand ranked number 164: it wins 25.68% of boards, ties 44.99% and loses 29.33%. It is the underdog in that matchup.

32o is 3 times as many combos but 3.68 points weaker against a random hand, and 32o is the offsuit twin, number 169 of 169 with 32.30% equity.

Questions about 32s combos

How many combos of 32s are there?

4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 32s about 1 time in 331.5.

How many 32s combos are left if I hold a three?

3 combos of 32s remain out of 4. With a four as your other card, an opponent has it about 1 time in 408.

Is 32s stronger than 32o?

Yes, by 3.68 points: 32s has 35.98% equity against a random hand and ranks number 163, while 32o has 32.30% and ranks number 169. 32o has 12 combos to 32s's 4.

How this was computed

All 1,326 two-card holdings were grouped into classes, and the 32s group was counted. The blocker rows drop each combo containing a visible card; the board-pair rows do it for a visible pair.

Exact matchups, counted over all 1,712,304 boards, supply the rank and equity. A tie counts as half, and ranges are weighted by the combos that remain.

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