Q9s vs 97s: preflop equity

Over all 1,712,304 boards that can follow this deal, Q9s finishes with 69.64% of the pot and 97s with 30.36%.

Q9s

69.64%

Wins 67.59%, ties 4.09%

97s

30.36%

Wins 28.32%, ties 4.09%

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

Q9s against 97s: the numbers

Exact preflop results for Q9s against 97s, in percent
HandWinsTiesLosesEquity
Q9s67.5934.09328.31469.639
97s28.3144.09367.59330.361

Q9s meets 97s, and both are suited hands. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.

A lead of 39.28 points is large but not decisive: 97s still takes about 283 of every 1,000 deals. Of every 100 boards, about 4.09 are split pots, and the equity figures already include them.

Among the 169 starting hands, Q9s is number 43 and 97s is number 94 by strength against a random hand.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
Q9s13,889,000841,0005,818,000
97s5,818,000841,00013,889,000

The board total is exact, 12 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

Q9s against 97s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
Q9s2.2941.4793.5320.436
97s0.4363.5321.4792.294

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

Rainbow flops topped by a ten or better are the best for Q9s (74.84%); low rainbow flops (nine high or lower) are the worst (54.37%). Q9s stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

Q9s against 97s by flop texture, in percent
FlopShare of flopsQ9s winsTies97s winsQ9s equity
Rainbow, ten or higher25.25473.0853.50223.41374.836
Rainbow, nine or lower5.65452.4653.80443.73154.367
Two-tone46.54366.8233.23629.94168.441
Monotone5.21560.4025.48134.11763.142
Paired17.33468.7546.93424.31272.221

Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.

Compared with a random hand

Against one random hand instead, Q9s holds 57.66% and 97s holds 49.12%. Facing each other changes that by +11.98 points for Q9s and -18.76 points for 97s.

Q9s and 97s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
Q9s, all flops69.63957.664+11.9751.20767
Q9s, rainbow, ten or higher74.83657.664+17.1721.29779
Q9s, rainbow, nine or lower54.36757.664-3.2970.94282
Q9s, two-tone68.44157.664+10.7771.18689
Q9s, monotone63.14257.664+5.4781.09500
Q9s, paired72.22157.664+14.5571.25245
97s, all flops30.36149.118-18.7570.61812
97s, rainbow, ten or higher25.16449.118-23.9540.51232
97s, rainbow, nine or lower45.63349.118-3.4850.92905
97s, two-tone31.55949.118-17.5590.64251
97s, monotone36.85849.118-12.2600.75040
97s, paired27.77949.118-21.3390.56556

Does a shared suit matter?

There is no shared-suit case for this pair, since the cards they would need are already in the other hand. Every deal is a no-shared-suit deal.

Q9s against 97s by suit overlap, in percent
DealsSpecific dealsShare of dealsQ9s winsTies97s winsQ9s equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0067.5934.09328.31469.639

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. Q9s averages $139.28 from the $200, up $39.28; 97s averages $60.72, down $39.28.

Scaled to 1,000 deals, that is roughly 676 wins for Q9s, 283 for 97s and 41 chopped pots.

The same matchup from the other side

The reversed view, 97s against Q9s, shows 30.36% for 97s and 69.64% for Q9s. It is the same count, so it redirects here.

Try Qs9s against 9h7h 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

This is an exact count with no sampling. For the 12 ways to deal one Q9s 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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