99 vs 76s: preflop equity

Counting every board, the equity split is 80.21% for 99 and 19.79% for 76s, so 99 leads by 60.42 points.

99

80.21%

Wins 79.90%, ties 0.62%

76s

19.79%

Wins 19.48%, ties 0.62%

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

99 against 76s: the numbers

Exact preflop results for 99 against 76s, in percent
HandWinsTiesLosesEquity
9979.8980.61619.48680.206
76s19.4860.61679.89819.794

99 is a pocket pair and 76s is a suited hand. A pair against two lower cards is a lopsided matchup: the pair is ahead and the other hand has no overcard to catch.

That is a heavy lead: 76s needs the board to help it on most runouts and still falls behind far more often than not. Of every 100 boards, about 0.62 are split pots, and the equity figures already include them.

The hand ranking puts 99 at 6 and 76s at 115 out of 169 starting hands.

Boards behind the percentages: 41,095,296 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
9932,834,000253,0008,008,000
76s8,008,000253,00032,834,000

24 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, rounded to the nearest thousand.

99 against 76s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
994.0521.2525.1320.247
76s0.2475.1321.2524.052

In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.

Who is ahead on which flops

The flop changes the picture. 99 does best on rainbow flops topped by a ten or better, at 84.62%, and worst on low rainbow flops (nine high or lower), at 68.33%. 99 stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

99 against 76s by flop texture, in percent
FlopShare of flops99 winsTies76s wins99 equity
Rainbow, ten or higher25.84484.4390.35115.21084.615
Rainbow, nine or lower5.06568.1200.42031.46068.330
Two-tone46.54578.2050.34221.45378.376
Monotone5.21273.3072.44824.24574.531
Paired17.33483.0981.25015.65283.723

A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.

Compared with a random hand

Against one random hand instead, 99 holds 72.06% and 76s holds 45.37%. Facing each other changes that by +8.15 points for 99 and -25.58 points for 76s.

99 and 76s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
99, all flops80.20672.057+8.1491.11309
99, rainbow, ten or higher84.61572.057+12.5581.17428
99, rainbow, nine or lower68.33072.057-3.7270.94828
99, two-tone78.37672.057+6.3191.08769
99, monotone74.53172.057+2.4741.03433
99, paired83.72372.057+11.6661.16190
76s, all flops19.79445.372-25.5780.43626
76s, rainbow, ten or higher15.38545.372-29.9870.33909
76s, rainbow, nine or lower31.67045.372-13.7020.69801
76s, two-tone21.62445.372-23.7480.47659
76s, monotone25.46945.372-19.9030.56134
76s, paired16.27745.372-29.0950.35875

Does a shared suit matter?

Split by suits, the deals give 99 80.76% when the hands overlap in a suit and 79.65% when they do not. 99 does better with a shared suit, by 1.11 points.

99 against 76s by suit overlap, in percent
DealsSpecific dealsShare of deals99 winsTies76s wins99 equity
Share a suit1250.0080.4340.65818.90880.763
No shared suit1250.0079.3630.57320.06479.649

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 24 are 99 in one seat and 76s in the other (0.0015%); with the seats swapped too, 48 (0.0030%).

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average 99 takes back $160.42 of it, which is $60.42 more than it put in, and 76s takes back $39.58, $60.42 less than it put in.

Per 1,000 deals: 99 wins about 799, 76s wins about 195, and about 6 end in a split pot.

The same matchup from the other side

The reversed view, 76s against 99, shows 19.79% for 76s and 80.21% for 99. It is the same count, so it redirects here.

Open the calculator with 9s9h against 7d6d already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.

How this was computed

Method: exact enumeration. The 24 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.

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

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