K5o combos

K5o: the 12 combos

An offsuit hand pairs any king with any five of a different suit: 4 x 4 = 16 pairings, minus the 4 suited ones, leaves 12.

Here is every one of the 12 combos, written as the two cards you would see. Clubs, diamonds, hearts and spades each appear in the way the count above requires.

• K♠5♥
• K♠5♦
• K♠5♣
• K♥5♠
• K♥5♦
• K♥5♣
• K♦5♠
• K♦5♥
• K♦5♣
• K♣5♠
• K♣5♥
• K♣5♦

How cards you can see change the count

Seeing a card changes which hands are possible. Here is the count of K5o combos that remain after you hold, or the board shows, one card of each rank.

Holding a king or a five takes K5o from 12 combos down to 9, a cut of 25%. Any card of a different rank leaves all 12 combos in play.

When the board is paired

A paired board shows two cards of one rank, and those two cards cannot be in an opponent's hand either. The table shows the K5o combos left when the board holds a pair of each rank.

Kings or fives paired on the board leave 6 combos of K5o, and no other pair changes the count of 12.

A worked example

You hold a king and a two. Your opponent's hand is one of 1,225 equally likely two-card holdings. 9 of them are K5o, which is 0.73%, or about 1 in 136. If your two cards had nothing to do with K5o, the same hand would have 12 combos and a 0.98% chance, about 1 in 102.

How strong is K5o?

Measured against a random hand, K5o has 53.31% equity and the number 69 spot of 169, in the middle of the ranking. Wins count once and ties count half.

Together with all stronger classes, K5o covers 500 combos, which is 37.71% of the 1,326 starting hands.

K5o against ranges of hands

Against a range, equity is averaged over every hand in it, weighted by how many combos of each hand are still possible. K5o makes 26.17% against the top 5 percent (60 combos), 29.40% against the top 10 percent (130 combos), 32.78% against the top 20 percent (264 combos), 35.22% against the top 30 percent (386 combos) and 43.26% against the top 50 percent (658 combos).

K5o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.

Your own cards block part of an opponent's strong range. The top 10 percent holds 130 combos, and when you hold a combo of K5o an average of 121.00 of them stay possible. That is 9.00 combos fewer than the 130 an opponent has before you look.

Hands next to K5o

Compare K5o with the hand ranked just above it and the hand just below it. K5o has 58.79% equity against Q8o, the hand ranked number 68: it wins 58.45% of boards, ties 0.69% and loses 40.87%. It is the favorite in that matchup. K5o has 56.07% equity against J9o, the hand ranked number 70: it wins 55.73% of boards, ties 0.68% and loses 43.59%. It is the favorite in that matchup.

The suited twin of K5o is K5s, ranked number 54 with 55.79% equity against a random hand. K5o has 3 times as many combos as K5s and is 2.48 points weaker against a random hand.

Questions about K5o combos

How many combos of K5o are there?

12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt K5o about 1 time in 110.5.

How many K5o combos are left if I hold a king?

9 combos of K5o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.

Is K5o stronger than K5s?

No: K5o has 53.31% equity against a random hand and ranks number 69, while K5s has 55.79% and ranks number 54. K5s has 4 combos to K5o's 12.

How this was computed

The count starts from 1,326 two-card hands sorted into 169 classes. Removing the combos that use known cards gives each blocker and board-pair row, with nothing estimated.

Our preflop table counts every board (1,712,304 of them) for each pair of classes, so rank and equity here are exact. Ties are halves; ranges are weighted by live combos.

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