98s vs 97s: preflop equity

Counting every board, the equity split is 64.65% for 98s and 35.35% for 97s, so 98s leads by 29.30 points.

98s

64.65%

Wins 55.21%, ties 18.90%

97s

35.35%

Wins 25.89%, ties 18.90%

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

98s against 97s: the numbers

Exact preflop results for 98s against 97s, in percent
HandWinsTiesLosesEquity
98s55.20618.89725.89764.654
97s25.89718.89755.20635.346

The matchup is suited hands on both sides, 98s against 97s. The two hands share a rank, and the one with the better other card dominates: it wins most kicker battles when that shared rank hits.

The lead is steady rather than large, and the flop still has plenty of say in who wins. Of every 100 boards, about 18.90 are split pots, and the equity figures already include them.

Place 83 of 169 belongs to 98s and place 94 belongs to 97s in the ranking against a random hand.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
98s11,344,0003,883,0005,321,000
97s5,321,0003,883,00011,344,000

The total is exact: 12 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and rounded to the nearest thousand.

98s against 97s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
98s1.8291.8113.8610.547
97s0.5473.8611.8111.829

The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.

Who is ahead on which flops

The flop changes the picture. 98s does best on rainbow flops topped by a ten or better, at 67.51%, and worst on paired flops, at 60.00%. 98s stays ahead on all five textures.

98s against 97s by flop texture, in percent
FlopShare of flops98s winsTies97s wins98s equity
Rainbow, ten or higher25.84457.96819.09122.94167.514
Rainbow, nine or lower5.06564.2154.89030.89566.660
Two-tone46.54357.57614.91827.50665.035
Monotone5.21553.78613.66732.54760.619
Paired17.33342.51634.95822.52659.995

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

Start from the random-hand figures, 50.80% for 98s and 49.12% for 97s. This opponent changes them by +13.85 and -13.77 points.

98s and 97s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
98s, all flops64.65450.801+13.8531.27269
98s, rainbow, ten or higher67.51450.801+16.7131.32899
98s, rainbow, nine or lower66.66050.801+15.8591.31218
98s, two-tone65.03550.801+14.2341.28019
98s, monotone60.61950.801+9.8181.19326
98s, paired59.99550.801+9.1941.18098
97s, all flops35.34649.118-13.7720.71961
97s, rainbow, ten or higher32.48649.118-16.6320.66139
97s, rainbow, nine or lower33.34049.118-15.7780.67877
97s, two-tone34.96549.118-14.1530.71186
97s, monotone39.38149.118-9.7370.80176
97s, paired40.00549.118-9.1130.81447

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.

98s against 97s by suit overlap, in percent
DealsSpecific dealsShare of deals98s winsTies97s wins98s equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0055.20618.89725.89764.654

How often this matchup comes up

Counting specific cards, 98s against 97s appears in 12 of the 1,624,350 ordered heads-up deals (0.0007%), and in 24 when the seats are swapped too (0.0015%).

A worked example

With $100 from each side, the $200 pot is split on average as $129.30 for 98s and $70.70 for 97s; the first side gains $29.30 per all-in and the second gives up $29.30.

Run 1,000 deals and the tally comes out near 552 for 98s, 259 for 97s and 189 ties.

The same matchup from the other side

97s versus 98s is this same page seen from the other hand: 35.35% for 97s, 64.65% for 98s.

Open the calculator with 9s8s against 9h7h 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

This is an exact count with no sampling. For the 12 ways to deal one 98s 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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