TT vs AJo: preflop equity

Averaged over every possible board, TT is ahead of AJo by 14.04 points of equity, 57.02% to 42.98%.

TT

57.02%

Wins 56.83%, ties 0.38%

AJo

42.98%

Wins 42.79%, ties 0.38%

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

TT against AJo: the numbers

Exact preflop results for TT against AJo, in percent
HandWinsTiesLosesEquity
TT56.8320.37842.79057.021
AJo42.7900.37856.83242.979

The matchup pits a pocket pair against an offsuit hand. A pair against two higher cards is the classic race: the pair is usually a small favorite or close to even, and each overcard that pairs is a way to take the lead.

A 14.04 point lead is real, and AJo still takes about 428 of every 1,000 deals outright. 0.38% of boards are ties, so the equity of each hand is its win rate plus half of that.

Place 5 of 169 belongs to TT and place 15 belongs to AJo in the ranking against a random hand.

Boards behind the percentages: 123,285,888 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
TT70,066,000466,00052,754,000
AJo52,754,000466,00070,066,000

The board total is exact, 72 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

TT against AJo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
TT1.3271.7602.3370.754
AJo0.7542.3371.7601.327

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

If you know the kind of flop that came, the numbers shift: TT holds 74.55% on low rainbow flops (nine high or lower) and 50.15% on rainbow flops topped by a ten or better. 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 AJo by flop texture, in percent
FlopShare of flopsTT winsTiesAJo winsTT equity
Rainbow, ten or higher23.26050.0790.13949.78250.149
Rainbow, nine or lower7.77174.0680.96324.96974.549
Two-tone46.48555.6860.33143.98355.852
Monotone5.15151.9401.71246.34852.796
Paired17.33362.6950.16437.14162.777

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

Against one random hand instead, TT holds 75.01% and AJo holds 63.56%. Facing each other changes that by -17.99 points for TT and -20.58 points for AJo.

TT and AJo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
TT, all flops57.02175.012-17.9910.76016
TT, rainbow, ten or higher50.14975.012-24.8630.66855
TT, rainbow, nine or lower74.54975.012-0.4630.99383
TT, two-tone55.85275.012-19.1600.74457
TT, monotone52.79675.012-22.2160.70383
TT, paired62.77775.012-12.2350.83689
AJo, all flops42.97963.563-20.5840.67616
AJo, rainbow, ten or higher49.85163.563-13.7120.78428
AJo, rainbow, nine or lower25.45163.563-38.1120.40041
AJo, two-tone44.14863.563-19.4150.69456
AJo, monotone47.20463.563-16.3590.74263
AJo, paired37.22363.563-26.3400.58561

Does a shared suit matter?

Suit overlap shows up in the numbers. With a suit in common TT has 56.94% equity, and with none in common it has 57.42%. TT does better with no shared suit, by 0.48 points.

TT against AJo by suit overlap, in percent
DealsSpecific dealsShare of dealsTT winsTiesAJo winsTT equity
Share a suit6083.3356.7440.39442.86256.941
No shared suit1216.6757.2730.29942.42857.422

How often this matchup comes up

TT against AJo is made up of 72 specific-card matchups in one seat order, 0.0044% of the 1,624,350 ordered deals, and 144 counting both seat orders, 0.0089%.

A worked example

Try it with money: two players each put in $100 and the whole board runs out every possible way. TT averages $114.04 from the $200, up $14.04; AJo averages $85.96, down $14.04.

Over a long run, 1,000 deals split into about 568 for TT, 428 for AJo and 4 tied.

The same matchup from the other side

Swap the hands and you get AJo with 42.98% against TT with 57.02%. We keep one page per matchup, with the better-ranked hand first.

Try TsTh against AdJc 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

The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 72 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.

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

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