T2s combos

T2s: the 4 combos

There is one ten-two pairing per suit, and a suited hand counts each suit once, so T2s is 4 combos.

All 4 ways to hold T2s are shown here, one tile each. Counting them is how a range gets its size.

• 10♠2♠
• 10♥2♥
• 10♦2♦
• 10♣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 T2s 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 ten 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 T2s, the rows below show the combos left after the board pairs each rank in turn.

A board pair of tens or twos leaves 2 combos of T2s; a pair of any other rank leaves all 4.

A worked example

Worked example: your cards are a ten and a three, so 1,225 two-card hands remain for your opponent. Of those, 3 are T2s, a 0.24% chance (about 1 in 408). With two cards that do not touch T2s, it would be 4 combos and 0.33%.

How strong is T2s?

T2s holds rank 118 among the 169 classes, below the middle of the ranking. Against a random hand it has 44.84% equity: wins in full, ties as half, every board counted.

878 combos rank above T2s, and with its own 4 the running total is 882, 66.52% of the 1,326 hands.

T2s against ranges of hands

Take the strongest hands in rank order and ask how T2s does against them. The answers, with live combos as weights: 24.38% against the top 5 percent (60 combos), 29.27% against the top 10 percent (130 combos), 32.50% against the top 20 percent (264 combos), 33.97% against the top 30 percent (386 combos) and 35.30% against the top 50 percent (658 combos).

T2s 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 T2s, 123.00 of the 130 top-10-percent combos survive on average. That is 7.00 combos fewer than the 130 an opponent has before you look.

Hands next to T2s

Two quick matchups show where T2s stands among its neighbours. T2s has 56.38% equity against 87o, the hand ranked number 117: it wins 55.42% of boards, ties 1.93% and loses 42.66%. It is the favorite in that matchup. T2s has 56.50% equity against 85s, the hand ranked number 119: it wins 55.53% of boards, ties 1.93% and loses 42.53%. It is the favorite in that matchup.

Next to T2s sits T2o, its offsuit twin: rank 135, 12 combos, 41.67% equity against a random hand. T2o is 3 times as many combos but 3.17 points weaker against a random hand.

Questions about T2s combos

How many combos of T2s are there?

4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt T2s about 1 time in 331.5.

How many T2s combos are left if I hold a ten?

3 combos of T2s remain out of 4. With a three as your other card, an opponent has it about 1 time in 408.

Is T2s stronger than T2o?

Yes, by 3.17 points: T2s has 44.84% equity against a random hand and ranks number 118, while T2o has 41.67% and ranks number 135. T2o has 12 combos to T2s'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.