65o combos

65o: the 12 combos

For 65o, there are 4 sixes and 4 fives, so 16 pairings, and the 4 that share a suit belong to the suited hand. That leaves 12.

The 12 holdings of 65o are listed below, higher card first. Nothing is left out and nothing appears twice.

• 6♠5♥
• 6♠5♦
• 6♠5♣
• 6♥5♠
• 6♥5♦
• 6♥5♣
• 6♦5♠
• 6♦5♥
• 6♦5♣
• 6♣5♠
• 6♣5♥
• 6♣5♦

How cards you can see change the count

Combos shrink when cards are visible. The rows below give the 65o count left after one known card of each rank, from the ace down to the two.

A six or a five you can see leaves 9 of 12, so 25% of the combos are gone. Any card of a different rank leaves all 12 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 65o that are still possible after a board pair of each rank.

Pairing sixes or fives on the board cuts 65o to 6 combos. Every other paired board leaves the full 12.

A worked example

Walk through it once. Your hole cards: a six and a two. Your opponent's possible hands: 1,225. Of those, 65o is 9, so the chance is 9 / 1,225 = 0.73%. With no blocking card it would be 12 / 1,225 = 0.98%.

How strong is 65o?

The ranking puts 65o at number 145 out of 169, among the 30 weakest classes. Its equity against a random hand is 39.94%, with a tie counted as half a win.

A range that runs from the top of the ranking down to 65o is 1,102 combos, 83.11% of all two-card hands, and 1,090 of them rank above 65o itself.

65o against ranges of hands

Here is how 65o fares against five ranges that run from the top of the ranking down. It scores 21.19% against the top 5 percent (60 combos), 29.02% against the top 10 percent (130 combos), 32.86% against the top 20 percent (264 combos), 34.19% against the top 30 percent (386 combos) and 35.68% against the top 50 percent (658 combos).

65o 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 65o in your hand, an average of 127.00 are left. That is 3.00 combos fewer than the 130 an opponent has before you look.

Hands next to 65o

Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. 65o has 45.05% equity against 93o, the hand ranked number 144: it wins 43.44% of boards, ties 3.23% and loses 53.33%. It is the underdog in that matchup. 65o has 60.54% equity against 53s, the hand ranked number 146: it wins 48.45% of boards, ties 24.20% and loses 27.36%. It is the favorite in that matchup.

65o has 3 times as many combos as 65s and is 3.19 points weaker against a random hand, and 65s is the suited twin, number 128 of 169 with 43.13% equity.

Questions about 65o combos

How many combos of 65o are there?

12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 65o about 1 time in 110.5.

How many 65o combos are left if I hold a six?

9 combos of 65o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.

Is 65o stronger than 65s?

No: 65o has 39.94% equity against a random hand and ranks number 145, while 65s has 43.13% and ranks number 128. 65s has 4 combos to 65o's 12.

How this was computed

All 1,326 two-card holdings were grouped into classes, and the 65o 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.