ATs vs T8s: preflop equity

Before any board card is dealt, ATs holds 68.92% equity against T8s, which leaves T8s with 31.08%.

ATs

68.92%

Wins 67.88%, ties 2.06%

T8s

31.08%

Wins 30.06%, ties 2.06%

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

ATs against T8s: the numbers

Exact preflop results for ATs against T8s, in percent
HandWinsTiesLosesEquity
ATs67.8832.06330.05468.915
T8s30.0542.06367.88331.085

ATs and T8s are both suited hands. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.

A lead of 37.84 points is large but not decisive: T8s still takes about 300 of every 1,000 deals. Ties are 2.06% of the outcomes here; each tied board gives both hands half the pot.

Place 13 of 169 belongs to ATs and place 73 belongs to T8s in the ranking against a random hand.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
ATs13,948,000424,0006,175,000
T8s6,175,000424,00013,948,000

12 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.

ATs against T8s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
ATs2.2171.4733.3270.451
T8s0.4513.3271.4732.217

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 ATs is strongest on rainbow flops topped by a ten or better (73.89%) and weakest on low rainbow flops (nine high or lower) (55.97%). ATs stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

ATs against T8s by flop texture, in percent
FlopShare of flopsATs winsTiesT8s winsATs equity
Rainbow, ten or higher23.86772.9831.81125.20673.889
Rainbow, nine or lower7.04254.6412.65942.70055.971
Two-tone46.54366.5351.75831.70767.414
Monotone5.21560.4834.19635.32162.581
Paired17.33372.0842.34925.56773.258

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

How much does the opponent matter? Compared with its random-hand 64.60%, ATs changes by +4.32 points, and T8s, from 52.33%, by -21.25.

ATs and T8s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
ATs, all flops68.91564.602+4.3131.06676
ATs, rainbow, ten or higher73.88964.602+9.2871.14376
ATs, rainbow, nine or lower55.97164.602-8.6310.86640
ATs, two-tone67.41464.602+2.8121.04353
ATs, monotone62.58164.602-2.0210.96872
ATs, paired73.25864.602+8.6561.13399
T8s, all flops31.08552.334-21.2490.59397
T8s, rainbow, ten or higher26.11152.334-26.2230.49893
T8s, rainbow, nine or lower44.02952.334-8.3050.84131
T8s, two-tone32.58652.334-19.7480.62265
T8s, monotone37.41952.334-14.9150.71500
T8s, paired26.74252.334-25.5920.51099

Does a shared suit matter?

Every legal deal of ATs against T8s leaves the hands with no suit in common, so the suit split does not apply here.

ATs against T8s by suit overlap, in percent
DealsSpecific dealsShare of dealsATs winsTiesT8s winsATs equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0067.8832.06330.05468.915

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 12 are ATs in one seat and T8s in the other (0.0007%); with the seats swapped too, 24 (0.0015%).

A worked example

Put $100 each into a $200 pot and deal every board once: ATs averages $137.84 back, ahead of its $100 by $37.84, while T8s averages $62.16, short of its $100 by $37.84.

A thousand deals look like this: ATs takes 679, T8s takes 300, 21 are ties.

The same matchup from the other side

T8s against ATs adds nothing new: it is 31.08% for T8s and 68.92% for ATs, the same figures reversed.

The calculator link fills in AsTs against Th8h, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.

How this was computed

All 1,712,304 five-card boards are dealt for every suit pattern among the 12 specific deals of ATs against T8s, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.

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

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