TT vs ATo: preflop equity

Over all 1,712,304 boards that can follow this deal, TT finishes with 69.13% of the pot and ATo with 30.87%.

TT

69.13%

Wins 68.03%, ties 2.20%

ATo

30.87%

Wins 29.77%, ties 2.20%

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

TT against ATo: the numbers

Exact preflop results for TT against ATo, in percent
HandWinsTiesLosesEquity
TT68.0332.20029.76769.133
ATo29.7672.20068.03330.867

The matchup pits a pocket pair against an offsuit hand. One hand holds a card of the same rank as the pair, which removes a card the pair needs and makes the pair a bigger favorite.

A lead of 38.26 points is large but not decisive: ATo still takes about 298 of every 1,000 deals. Of every 100 boards, about 2.20 are split pots, and the equity figures already include them.

Ranked by equity against a random hand, TT is number 5 of the 169 starting hands and ATo is number 19.

Boards behind the percentages: 61,642,944 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
TT41,938,0001,356,00018,349,000
ATo18,349,0001,356,00041,938,000

36 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, rounded to the nearest thousand.

TT against ATo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
TT2.2401.4703.3590.446
ATo0.4463.3591.4702.240

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

Break the boards down by their first three cards and TT is strongest on low rainbow flops (nine high or lower) (84.10%) and weakest on monotone flops (62.10%). TT stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

TT against ATo by flop texture, in percent
FlopShare of flopsTT winsTiesATo winsTT equity
Rainbow, ten or higher23.05362.3692.17335.45863.456
Rainbow, nine or lower7.77182.2843.64014.07684.104
Two-tone46.21566.6592.42530.91667.872
Monotone5.13060.7752.64736.57862.098
Paired17.83174.7920.89924.30975.241

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

Start from the random-hand figures, 75.01% for TT and 62.72% for ATo. This opponent changes them by -5.88 and -31.85 points.

TT and ATo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
TT, all flops69.13375.012-5.8790.92163
TT, rainbow, ten or higher63.45675.012-11.5560.84594
TT, rainbow, nine or lower84.10475.012+9.0921.12121
TT, two-tone67.87275.012-7.1400.90482
TT, monotone62.09875.012-12.9140.82784
TT, paired75.24175.012+0.2291.00305
ATo, all flops30.86762.722-31.8550.49212
ATo, rainbow, ten or higher36.54462.722-26.1780.58263
ATo, rainbow, nine or lower15.89662.722-46.8260.25344
ATo, two-tone32.12862.722-30.5940.51223
ATo, monotone37.90262.722-24.8200.60429
ATo, paired24.75962.722-37.9630.39474

Does a shared suit matter?

Of the deals of this matchup, 24 share a suit (TT at 69.07%) and 12 do not (69.26%). The two rows differ by only 0.19 points, so suits barely change this matchup.

TT against ATo by suit overlap, in percent
DealsSpecific dealsShare of dealsTT winsTiesATo winsTT equity
Share a suit2466.6767.9512.23629.81369.069
No shared suit1233.3368.1962.12829.67669.260

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

Take a $200 pot built from $100 each. TT's equity of 69.13% is worth $138.26, a $38.26 edge, and ATo's 30.87% is worth $61.74, which is $38.26 under its stake.

Think in thousands: about 680 of 1,000 go to TT, about 298 go to ATo, and about 22 are chopped.

The same matchup from the other side

One page covers both views. From ATo's side the equity is 30.87%, and from TT's side it is 69.13%.

TsTh against AdTc 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

We counted every case. Each suit pattern of the 36 specific TT against ATo 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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