AJo vs 65s: preflop equity

Averaged over every possible board, AJo is ahead of 65s by 17.94 points of equity, 58.97% to 41.03%.

AJo

58.97%

Wins 58.74%, ties 0.46%

65s

41.03%

Wins 40.80%, ties 0.46%

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

AJo against 65s: the numbers

Exact preflop results for AJo against 65s, in percent
HandWinsTiesLosesEquity
AJo58.7350.46340.80258.966
65s40.8020.46358.73541.034

AJo and 65s are an offsuit hand and a suited hand, in that order. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.

AJo is ahead, but 65s is far from dead: it takes 408 of every 1,000 deals outright. Ties are part of the picture: 0.46% of boards end in a split pot, and each side counts that as half a win.

AJo ranks number 15 of 169 starting hands, and 65s ranks number 128, by equity against a random hand.

Boards behind the percentages: 82,190,592 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AJo48,275,000381,00033,535,000
65s33,535,000381,00048,275,000

The board total is exact, 48 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

AJo against 65s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AJo1.4371.7032.4510.696
65s0.6962.4511.7031.437

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: AJo holds 67.58% on rainbow flops topped by a ten or better and 30.24% on low rainbow flops (nine high or lower). AJo is the favorite overall but falls behind on low rainbow flops (nine high or lower).

AJo against 65s by flop texture, in percent
FlopShare of flopsAJo winsTies65s winsAJo equity
Rainbow, ten or higher24.71767.4890.17332.33867.576
Rainbow, nine or lower6.31329.8400.79169.36930.235
Two-tone46.66757.1300.28342.58757.271
Monotone5.21256.2572.41541.32857.464
Paired17.09161.8880.65737.45562.217

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

Compared with a random opponent, this matchup shifts AJo from 63.56% by -4.59 points and 65s from 43.13% by -2.10 points.

AJo and 65s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AJo, all flops58.96663.563-4.5970.92768
AJo, rainbow, ten or higher67.57663.563+4.0131.06313
AJo, rainbow, nine or lower30.23563.563-33.3280.47567
AJo, two-tone57.27163.563-6.2920.90101
AJo, monotone57.46463.563-6.0990.90405
AJo, paired62.21763.563-1.3460.97882
65s, all flops41.03443.133-2.0990.95134
65s, rainbow, ten or higher32.42443.133-10.7090.75172
65s, rainbow, nine or lower69.76543.133+26.6321.61744
65s, two-tone42.72943.133-0.4040.99063
65s, monotone42.53643.133-0.5970.98616
65s, paired37.78343.133-5.3500.87597

Does a shared suit matter?

Suit overlap shows up in the numbers. With a suit in common AJo has 59.66% equity, and with none in common it has 58.28%. AJo does better with a shared suit, by 1.38 points.

AJo against 65s by suit overlap, in percent
DealsSpecific dealsShare of dealsAJo winsTies65s winsAJo equity
Share a suit2450.0059.4030.50440.09359.655
No shared suit2450.0058.0670.42241.51158.278

How often this matchup comes up

Counting specific cards, AJo against 65s appears in 48 of the 1,624,350 ordered heads-up deals (0.0030%), and in 96 when the seats are swapped too (0.0059%).

A worked example

A $100 all-in from each player makes a $200 pot, and the exact equity says AJo gets $117.94 of it on average and 65s gets $82.06.

Scaled to 1,000 deals, that is roughly 587 wins for AJo, 408 for 65s and 5 chopped pots.

The same matchup from the other side

Read it from the other side: 65s against AJo is the same matchup with the numbers swapped, so 65s holds 41.03% and AJo holds 58.97%. That address sends you back to this page.

Open the calculator with AsJh against 6d5d already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.

How this was computed

The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 48 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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