77 vs 97s: preflop equity

Averaged over every possible board, 77 is ahead of 97s by 23.56 points of equity, 61.78% to 38.22%.

77

61.78%

Wins 60.59%, ties 2.37%

97s

38.22%

Wins 37.04%, ties 2.37%

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

77 against 97s: the numbers

Exact preflop results for 77 against 97s, in percent
HandWinsTiesLosesEquity
7760.5902.37137.03961.775
97s37.0392.37160.59038.225

The first hand is a pocket pair; the second is a suited hand. The pair already holds one of the other hand's ranks, and that overlap cuts down the cards the other hand can pair with.

The lead is steady rather than large, and the flop still has plenty of say in who wins. Ties are 2.37% of the outcomes here; each tied board gives both hands half the pot.

In the ranking of all 169 starting hands, 77 is number 9 and 97s is number 94.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
7712,450,000487,0007,611,000
97s7,611,000487,00012,450,000

Exact total: 12 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.

77 against 97s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
771.6161.6502.7000.619
97s0.6192.7001.6501.616

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

If you know the kind of flop that came, the numbers shift: 77 holds 67.08% on paired flops and 52.28% on low rainbow flops (nine high or lower). 77 stays ahead on all five textures.

77 against 97s by flop texture, in percent
FlopShare of flops77 winsTies97s wins77 equity
Rainbow, ten or higher25.78663.6091.82134.57064.520
Rainbow, nine or lower4.99549.6975.16245.14152.278
Two-tone46.23658.4702.17739.35359.558
Monotone5.15257.2893.00839.70358.793
Paired17.83165.7272.70531.56867.079

Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.

Compared with a random hand

A random hand would give 77 66.24% and 97s 49.12%. Against each other the change is -4.46 points for 77 and -10.90 for 97s.

77 and 97s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
77, all flops61.77566.236-4.4610.93265
77, rainbow, ten or higher64.52066.236-1.7160.97409
77, rainbow, nine or lower52.27866.236-13.9580.78927
77, two-tone59.55866.236-6.6780.89918
77, monotone58.79366.236-7.4430.88763
77, paired67.07966.236+0.8431.01273
97s, all flops38.22549.118-10.8930.77823
97s, rainbow, ten or higher35.48049.118-13.6380.72234
97s, rainbow, nine or lower47.72249.118-1.3960.97158
97s, two-tone40.44249.118-8.6760.82336
97s, monotone41.20749.118-7.9110.83894
97s, paired32.92149.118-16.1970.67024

Does a shared suit matter?

A shared suit is impossible for this matchup, so 77's 61.78% is the answer for every suit pattern.

77 against 97s by suit overlap, in percent
DealsSpecific dealsShare of deals77 winsTies97s wins77 equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0060.5902.37137.03961.775

How often this matchup comes up

This page stands for 12 specific-card matchups (0.0007% of 1,624,350 ordered deals), or 24 once you count the seats both ways (0.0015%).

A worked example

Try it with money: two players each put in $100 and the whole board runs out every possible way. 77 averages $123.56 from the $200, up $23.56; 97s averages $76.44, down $23.56.

A thousand deals look like this: 77 takes 606, 97s takes 370, 24 are ties.

The same matchup from the other side

The mirror image, 97s against 77, is 38.22% to 61.78%, and its address redirects to this page.

7s7h against 9d7d is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.

How this was computed

This is an exact count with no sampling. For the 12 ways to deal one 77 and one 97s without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.

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

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