K9s vs 76s: preflop equity

If K9s and 76s get all the chips in before the flop, K9s owns 61.57% of the pot in the long run and 76s owns 38.43%.

K9s

61.57%

Wins 61.24%, ties 0.67%

76s

38.43%

Wins 38.09%, ties 0.67%

Equity counts a tie as half a win. Exact over every board.

K9s against 76s: the numbers

Exact preflop results for K9s against 76s, in percent
HandWinsTiesLosesEquity
K9s61.2350.66838.09761.569
76s38.0970.66861.23538.431

Two suited hands meet here: K9s against 76s. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.

A 23.14 point lead is real, and 76s still takes about 381 of every 1,000 deals outright. Ties are 0.67% of the outcomes here; each tied board gives both hands half the pot.

K9s ranks number 29 of 169 starting hands, and 76s ranks number 115, by equity against a random hand.

Boards behind the percentages: 27,396,864 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
K9s16,776,000183,00010,437,000
76s10,437,000183,00016,776,000

Exact total: 16 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.

K9s against 76s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
K9s1.6021.6332.6250.624
76s0.6242.6251.6331.602

The final column gives the least the pot must offer for each unit called for a call to break even at this equity.

Who is ahead on which flops

Rainbow flops topped by a ten or better are the best for K9s (65.68%); low rainbow flops (nine high or lower) are the worst (43.58%). The lead reverses on low rainbow flops (nine high or lower): there 76s is the favorite even though K9s is ahead overall.

K9s against 76s by flop texture, in percent
FlopShare of flopsK9s winsTies76s winsK9s equity
Rainbow, ten or higher25.22065.5300.30634.16465.683
Rainbow, nine or lower5.68943.3630.43756.20043.582
Two-tone46.72760.6600.30739.03360.813
Monotone5.27357.1773.46139.36258.908
Paired17.09163.6681.40834.92464.372

Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.

Compared with a random hand

The table below sets each hand against its own random-hand baseline: a change of +1.58 points for K9s, from 59.99%, and -6.94 for 76s, from 45.37%.

K9s and 76s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
K9s, all flops61.56959.988+1.5811.02636
K9s, rainbow, ten or higher65.68359.988+5.6951.09494
K9s, rainbow, nine or lower43.58259.988-16.4060.72651
K9s, two-tone60.81359.988+0.8251.01375
K9s, monotone58.90859.988-1.0800.98200
K9s, paired64.37259.988+4.3841.07308
76s, all flops38.43145.372-6.9410.84702
76s, rainbow, ten or higher34.31745.372-11.0550.75635
76s, rainbow, nine or lower56.41845.372+11.0461.24345
76s, two-tone39.18745.372-6.1850.86368
76s, monotone41.09245.372-4.2800.90567
76s, paired35.62845.372-9.7440.78524

Does a shared suit matter?

Does suit overlap move the numbers? K9s has 63.78% when the hands share a suit and 60.83% when they do not. K9s does better with a shared suit, by 2.95 points.

K9s against 76s by suit overlap, in percent
DealsSpecific dealsShare of dealsK9s winsTies76s winsK9s equity
Share a suit425.0063.4060.75235.84263.782
No shared suit1275.0060.5110.64038.84960.831

How often this matchup comes up

Exactly 16 specific deals fit this matchup in one seat order, which is 0.0010% of 1,624,350; both orders together give 32, or 0.0020%.

A worked example

A $100 all-in from each player makes a $200 pot, and the exact equity says K9s gets $123.14 of it on average and 76s gets $76.86.

A thousand deals look like this: K9s takes 612, 76s takes 381, 7 are ties.

The same matchup from the other side

One page covers both views. From 76s' side the equity is 38.43%, and from K9s' side it is 61.57%.

Try Ks9s against 7h6h in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.

How this was computed

We counted every case. Each suit pattern of the 16 specific K9s against 76s deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.

Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.

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