94s combos

94s: the 4 combos

For 94s, the nine and the four must share a suit. With 4 suits and one way to pair them in each, the count is 4.

The 4 holdings of 94s are listed below, higher card first. Nothing is left out and nothing appears twice.

• 9♠4♠
• 9♥4♥
• 9♦4♦
• 9♣4♣

How cards you can see change the count

Combos shrink when cards are visible. The rows below give the 94s count left after one known card of each rank, from the ace down to the two.

A nine or a four 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 94s that are still possible after a board pair of each rank.

Pairing nines or fours on the board cuts 94s to 2 combos. Every other paired board leaves the full 4.

A worked example

Walk through it once. Your hole cards: a nine and a two. Your opponent's possible hands: 1,225. Of those, 94s 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 94s?

The ranking puts 94s at number 123 out of 169, below the middle of the ranking. Its equity against a random hand is 43.86%, with a tie counted as half a win.

A range that runs from the top of the ranking down to 94s is 926 combos, 69.83% of all two-card hands, and 922 of them rank above 94s itself.

94s against ranges of hands

Here is how 94s fares against five ranges that run from the top of the ranking down. It scores 23.21% against the top 5 percent (60 combos), 29.76% against the top 10 percent (130 combos), 32.66% against the top 20 percent (264 combos), 33.78% against the top 30 percent (386 combos) and 35.57% against the top 50 percent (658 combos).

94s 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 94s in your hand, an average of 126.00 are left. That is 4.00 combos fewer than the 130 an opponent has before you look.

Hands next to 94s

Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. 94s has 39.80% equity against T5o, the hand ranked number 122: it wins 38.82% of boards, ties 1.97% and loses 59.21%. It is the underdog in that matchup. 94s has 55.79% equity against 75s, the hand ranked number 124: it wins 54.31% of boards, ties 2.96% and loses 42.73%. It is the favorite in that matchup.

94o is 3 times as many combos but 3.19 points weaker against a random hand, and 94o is the offsuit twin, number 140 of 169 with 40.67% equity.

Questions about 94s combos

How many combos of 94s are there?

4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 94s about 1 time in 331.5.

How many 94s combos are left if I hold a nine?

3 combos of 94s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.

Is 94s stronger than 94o?

Yes, by 3.19 points: 94s has 43.86% equity against a random hand and ranks number 123, while 94o has 40.67% and ranks number 140. 94o has 12 combos to 94s's 4.

How this was computed

All 1,326 two-card holdings were grouped into classes, and the 94s 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.