AQs vs 98s: preflop equity

The exact count puts AQs at 61.85% and 98s at 38.15% when the two hands see all five board cards.

AQs

61.85%

Wins 61.62%, ties 0.48%

98s

38.15%

Wins 37.90%, ties 0.48%

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

AQs against 98s: the numbers

Exact preflop results for AQs against 98s, in percent
HandWinsTiesLosesEquity
AQs61.6160.47637.90861.854
98s37.9080.47661.61638.146

Two suited hands meet here: AQs against 98s. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.

The lead is steady rather than large, and the flop still has plenty of say in who wins. Ties are 0.48% of the outcomes here; each tied board gives both hands half the pot.

AQs ranks number 10 of 169 starting hands, and 98s ranks number 83, by equity against a random hand.

Boards behind the percentages: 27,396,864 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AQs16,881,000130,00010,386,000
98s10,386,000130,00016,881,000

Exact total: 16 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.

AQs against 98s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AQs1.6221.6232.6380.617
98s0.6172.6381.6231.622

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

Break the boards down by their first three cards and AQs is strongest on rainbow flops topped by a ten or better (67.48%) and weakest on low rainbow flops (nine high or lower) (40.57%). On low rainbow flops (nine high or lower) the numbers flip and 98s is the one ahead.

AQs against 98s by flop texture, in percent
FlopShare of flopsAQs winsTies98s winsAQs equity
Rainbow, ten or higher24.59567.4070.14932.44467.481
Rainbow, nine or lower6.31440.2300.68159.08940.571
Two-tone46.72761.0480.23438.71861.165
Monotone5.27357.5233.40039.07759.223
Paired17.09163.9960.62835.37664.310

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

How much does the opponent matter? Compared with its random-hand 66.21%, AQs changes by -4.36 points, and 98s, from 50.80%, by -12.65.

AQs and 98s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AQs, all flops61.85466.209-4.3550.93422
AQs, rainbow, ten or higher67.48166.209+1.2721.01921
AQs, rainbow, nine or lower40.57166.209-25.6380.61277
AQs, two-tone61.16566.209-5.0440.92382
AQs, monotone59.22366.209-6.9860.89449
AQs, paired64.31066.209-1.8990.97132
98s, all flops38.14650.801-12.6550.75089
98s, rainbow, ten or higher32.51950.801-18.2820.64013
98s, rainbow, nine or lower59.42950.801+8.6281.16984
98s, two-tone38.83550.801-11.9660.76445
98s, monotone40.77750.801-10.0240.80268
98s, paired35.69050.801-15.1110.70255

Does a shared suit matter?

Split by suits, the deals give AQs 64.06% when the hands overlap in a suit and 61.12% when they do not. AQs does better with a shared suit, by 2.94 points.

AQs against 98s by suit overlap, in percent
DealsSpecific dealsShare of dealsAQs winsTies98s winsAQs equity
Share a suit425.0063.7810.55335.66664.058
No shared suit1275.0060.8940.45038.65661.119

How often this matchup comes up

This page stands for 16 specific-card matchups (0.0010% of 1,624,350 ordered deals), or 32 once you count the seats both ways (0.0020%).

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average AQs takes back $123.70 of it, which is $23.70 more than it put in, and 98s takes back $76.30, $23.70 less than it put in.

Run 1,000 deals and the tally comes out near 616 for AQs, 379 for 98s and 5 ties.

The same matchup from the other side

One page covers both views. From 98s' side the equity is 38.15%, and from AQs' side it is 61.85%.

AsQs against 9h8h 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

Each figure is a complete count over boards. Take the 16 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.

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

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