42s combos

42s: the 4 combos

There is one four-two pairing per suit, and a suited hand counts each suit once, so 42s is 4 combos.

All 4 ways to hold 42s are shown here, one tile each. Counting them is how a range gets its size.

• 4♠2♠
• 4♥2♥
• 4♦2♦
• 4♣2♣

How cards you can see change the count

Every card you can see is a card nobody else can hold. The table shows how many of the 4 combos of 42s are still possible when you hold one card of each rank, and the same count applies when that card is on the board.

Only two ranks change the count: a four or a two leaves 3 combos, 25% fewer. Any card of a different rank leaves all 4 combos in play.

When the board is paired

How does a paired board change the count? For 42s, the rows below show the combos left after the board pairs each rank in turn.

A board pair of fours or twos leaves 2 combos of 42s; a pair of any other rank leaves all 4.

A worked example

Worked example: your cards are a four and a three, so 1,225 two-card hands remain for your opponent. Of those, 3 are 42s, a 0.24% chance (about 1 in 408). With two cards that do not touch 42s, it would be 4 combos and 0.33%.

How strong is 42s?

42s holds rank 158 among the 169 classes, among the 30 weakest classes. Against a random hand it has 36.83% equity: wins in full, ties as half, every board counted.

1,198 combos rank above 42s, and with its own 4 the running total is 1,202, 90.65% of the 1,326 hands.

42s against ranges of hands

Take the strongest hands in rank order and ask how 42s does against them. The answers, with live combos as weights: 22.00% against the top 5 percent (60 combos), 29.43% against the top 10 percent (130 combos), 32.76% against the top 20 percent (264 combos), 33.71% against the top 30 percent (386 combos) and 34.81% against the top 50 percent (658 combos).

42s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.

Your cards matter to the opponent's range too: with 42s, 130.00 of the 130 top-10-percent combos survive on average. That is no loss at all: 42s blocks none of those hands.

Hands next to 42s

Two quick matchups show where 42s stands among its neighbours. 42s has 43.36% equity against 83o, the hand ranked number 157: it wins 40.92% of boards, ties 4.89% and loses 54.19%. It is the underdog in that matchup. 42s has 36.60% equity against 82o, the hand ranked number 159: it wins 30.14% of boards, ties 12.92% and loses 56.94%. It is the underdog in that matchup.

Next to 42s sits 42o, its offsuit twin: rank 168, 12 combos, 33.20% equity against a random hand. 42o is 3 times as many combos but 3.63 points weaker against a random hand.

Questions about 42s combos

How many combos of 42s are there?

4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 42s about 1 time in 331.5.

How many 42s combos are left if I hold a four?

3 combos of 42s remain out of 4. With a three as your other card, an opponent has it about 1 time in 408.

Is 42s stronger than 42o?

Yes, by 3.63 points: 42s has 36.83% equity against a random hand and ranks number 158, while 42o has 33.20% and ranks number 168. 42o has 12 combos to 42s's 4.

How this was computed

We counted from the deck itself: 1,326 possible two-card hands, each placed in one of 169 classes. A table row then deletes the combos that need a card known to be elsewhere, and the survivors are tallied.

Equity comes from an exact table of preflop matchups, every one of the 1,712,304 boards counted. A tie is half a win, and each hand in a range is weighted by the combos your cards leave.

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