AQo vs QTs: preflop equity

Averaged over every possible board, AQo is ahead of QTs by 37.10 points of equity, 68.55% to 31.45%.

AQo

68.55%

Wins 67.83%, ties 1.45%

QTs

31.45%

Wins 30.72%, ties 1.45%

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

AQo against QTs: the numbers

Exact preflop results for AQo against QTs, in percent
HandWinsTiesLosesEquity
AQo67.8261.44930.72568.550
QTs30.7251.44967.82631.450

The first hand is an offsuit hand; the second is a suited hand. 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.

AQo is the clear favorite, though QTs gets there on roughly one board in 3. Ties are 1.45% of the outcomes here; each tied board gives both hands half the pot.

For context, AQo sits at number 14 of 169 starting hands and QTs at number 34 when each is run against a random hand.

Boards behind the percentages: 61,642,944 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AQo41,810,000893,00018,940,000
QTs18,940,000893,00041,810,000

The board total is exact, 36 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

AQo against QTs read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AQo2.1801.4743.2550.459
QTs0.4593.2551.4742.180

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

By flop texture, AQo's equity runs from 64.17% on monotone flops up to 79.92% on low rainbow flops (nine high or lower). AQo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

AQo against QTs by flop texture, in percent
FlopShare of flopsAQo winsTiesQTs winsAQo equity
Rainbow, ten or higher23.17765.9121.29232.79666.558
Rainbow, nine or lower7.77179.3551.12419.52179.917
Two-tone46.52765.9681.17132.86166.553
Monotone5.19262.7482.83434.41864.165
Paired17.33371.7262.13526.13972.793

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

The table below sets each hand against its own random-hand baseline: a change of +4.12 points for AQo, from 64.43%, and -28.02 for QTs, from 59.47%.

AQo and QTs here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AQo, all flops68.55064.432+4.1181.06391
AQo, rainbow, ten or higher66.55864.432+2.1261.03300
AQo, rainbow, nine or lower79.91764.432+15.4851.24033
AQo, two-tone66.55364.432+2.1211.03292
AQo, monotone64.16564.432-0.2670.99586
AQo, paired72.79364.432+8.3611.12976
QTs, all flops31.45059.468-28.0180.52886
QTs, rainbow, ten or higher33.44259.468-26.0260.56235
QTs, rainbow, nine or lower20.08359.468-39.3850.33771
QTs, two-tone33.44759.468-26.0210.56244
QTs, monotone35.83559.468-23.6330.60259
QTs, paired27.20759.468-32.2610.45751

Does a shared suit matter?

The suit split reads 69.58% for AQo with a shared suit and 68.04% without one. AQo does better with a shared suit, by 1.54 points.

AQo against QTs by suit overlap, in percent
DealsSpecific dealsShare of dealsAQo winsTiesQTs winsAQo equity
Share a suit1233.3368.8211.51929.66069.580
No shared suit2466.6767.3281.41431.25868.035

How often this matchup comes up

You will meet this exact matchup 0.0044% of the time in a random heads-up deal: 72 of 1,624,350, counting either seat order.

A worked example

Try it with money: two players each put in $100 and the whole board runs out every possible way. AQo averages $137.10 from the $200, up $37.10; QTs averages $62.90, down $37.10.

Over a long run, 1,000 deals split into about 678 for AQo, 307 for QTs and 15 tied.

The same matchup from the other side

Read it from the other side: QTs against AQo is the same matchup with the numbers swapped, so QTs holds 31.45% and AQo holds 68.55%. That address sends you back to this page.

AsQh against QdTd 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

Nothing here is simulated. The 36 deals of AQo against QTs fall into a few suit patterns, each dealt against all 1,712,304 boards, with both best five-card hands compared on every board. Ties give each hand half a win, and the flop rows count a board under each of its ten flops.

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

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