88 vs AQs: preflop equity

The exact count puts 88 at 52.60% and AQs at 47.40% when the two hands see all five board cards.

88

52.60%

Wins 52.40%, ties 0.39%

AQs

47.40%

Wins 47.21%, ties 0.39%

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

88 against AQs: the numbers

Exact preflop results for 88 against AQs, in percent
HandWinsTiesLosesEquity
8852.3990.39247.20952.595
AQs47.2090.39252.39947.405

One side is a pocket pair, the other is a suited hand. One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.

With only 5.20 points between them, the board decides this matchup far more than the cards in hand. About 0.39% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.

By strength against a random hand, 88 holds place 7 of 169 and AQs holds place 10.

Boards behind the percentages: 41,095,296 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
8821,534,000161,00019,401,000
AQs19,401,000161,00021,534,000

The total is exact: 24 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.

88 against AQs read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
881.1091.9082.1180.901
AQs0.9012.1181.9081.109

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

Low rainbow flops (nine high or lower) are the best for 88 (77.24%); rainbow flops topped by a ten or better are the worst (46.66%). 88 is the favorite overall but falls behind on rainbow flops topped by a ten or better.

88 against AQs by flop texture, in percent
FlopShare of flops88 winsTiesAQs wins88 equity
Rainbow, ten or higher24.59546.5900.14853.26246.664
Rainbow, nine or lower6.31476.8150.85122.33477.240
Two-tone46.54550.5020.26949.22950.637
Monotone5.21250.4642.37847.15851.653
Paired17.33457.4230.30542.27257.575

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

Each hand has a baseline against a random hand: 69.16% for 88, 66.21% for AQs. Here the change is -16.56 and -18.81 points.

88 and AQs here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
88, all flops52.59569.163-16.5680.76045
88, rainbow, ten or higher46.66469.163-22.4990.67470
88, rainbow, nine or lower77.24069.163+8.0771.11678
88, two-tone50.63769.163-18.5260.73214
88, monotone51.65369.163-17.5100.74683
88, paired57.57569.163-11.5880.83245
AQs, all flops47.40566.209-18.8040.71599
AQs, rainbow, ten or higher53.33666.209-12.8730.80557
AQs, rainbow, nine or lower22.76066.209-43.4490.34376
AQs, two-tone49.36366.209-16.8460.74556
AQs, monotone48.34766.209-17.8620.73022
AQs, paired42.42566.209-23.7840.64077

Does a shared suit matter?

Does suit overlap move the numbers? 88 has 52.78% when the hands share a suit and 52.41% when they do not. 88 does better with a shared suit, by 0.37 points.

88 against AQs by suit overlap, in percent
DealsSpecific dealsShare of deals88 winsTiesAQs wins88 equity
Share a suit1250.0052.5580.43647.00652.776
No shared suit1250.0052.2400.34847.41252.414

How often this matchup comes up

You will meet this exact matchup 0.0030% of the time in a random heads-up deal: 48 of 1,624,350, counting either seat order.

A worked example

Put $100 each into a $200 pot and deal every board once: 88 averages $105.20 back, ahead of its $100 by $5.20, while AQs averages $94.80, short of its $100 by $5.20.

Out of 1,000 deals you should see around 524 outright wins for 88, 472 for AQs, and 4 split pots.

The same matchup from the other side

AQs versus 88 is this same page seen from the other hand: 47.40% for AQs, 52.60% for 88.

Try 8s8h against AdQd 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 24 specific 88 against AQs 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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