AJo vs KJo: preflop equity

Averaged over every possible board, AJo is ahead of KJo by 48.70 points of equity, 74.35% to 25.65%.

AJo

74.35%

Wins 73.56%, ties 1.56%

KJo

25.65%

Wins 24.88%, ties 1.56%

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

AJo against KJo: the numbers

Exact preflop results for AJo against KJo, in percent
HandWinsTiesLosesEquity
AJo73.5641.56424.87274.346
KJo24.8721.56473.56425.654

Both hands are offsuit hands: AJo and KJo. Because the hands share one rank, the one with the higher kicker is ahead when that rank pairs and the other hand is mostly drawing.

AJo is well ahead, and KJo needs a specific kind of board to catch up. Split pots make up 1.56% of the boards, and both equity figures count them as half a win each.

Among the 169 starting hands, AJo is number 15 and KJo is number 26 by strength against a random hand.

Boards behind the percentages: 184,928,832 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AJo136,041,0002,892,00045,995,000
KJo45,995,0002,892,000136,041,000

Exact total: 108 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.

AJo against KJo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AJo2.8981.3594.0210.345
KJo0.3454.0211.3592.898

The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.

Who is ahead on which flops

Across the five flop textures AJo's equity moves by 17.78 points, from 68.63% on monotone flops to 86.41% on low rainbow flops (nine high or lower). AJo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

AJo against KJo by flop texture, in percent
FlopShare of flopsAJo winsTiesKJo winsAJo equity
Rainbow, ten or higher23.27569.6651.25429.08170.292
Rainbow, nine or lower7.77185.4291.95212.61986.405
Two-tone46.47772.9891.37425.63773.676
Monotone5.14467.4612.32830.21168.625
Paired17.33376.8332.09021.07777.878

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

Compared with a random opponent, this matchup shifts AJo from 63.56% by +10.79 points and KJo from 60.57% by -34.92 points.

AJo and KJo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AJo, all flops74.34663.563+10.7831.16964
AJo, rainbow, ten or higher70.29263.563+6.7291.10586
AJo, rainbow, nine or lower86.40563.563+22.8421.35936
AJo, two-tone73.67663.563+10.1131.15910
AJo, monotone68.62563.563+5.0621.07964
AJo, paired77.87863.563+14.3151.22521
KJo, all flops25.65460.569-34.9150.42355
KJo, rainbow, ten or higher29.70860.569-30.8610.49048
KJo, rainbow, nine or lower13.59560.569-46.9740.22445
KJo, two-tone26.32460.569-34.2450.43461
KJo, monotone31.37560.569-29.1940.51800
KJo, paired22.12260.569-38.4470.36524

Does a shared suit matter?

Two kinds of deal exist here. In 84 of them the hands share a suit and AJo holds 74.45%. In 24 they do not, and it holds 73.99%. AJo does better with a shared suit, by 0.46 points.

AJo against KJo by suit overlap, in percent
DealsSpecific dealsShare of dealsAJo winsTiesKJo winsAJo equity
Share a suit8477.7873.6551.58724.75874.448
No shared suit2422.2273.2461.48225.27273.987

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 108 are AJo in one seat and KJo in the other (0.0066%); with the seats swapped too, 216 (0.0133%).

A worked example

Try it with money: two players each put in $100 and the whole board runs out every possible way. AJo averages $148.70 from the $200, up $48.70; KJo averages $51.30, down $48.70.

A thousand deals look like this: AJo takes 735, KJo takes 249, 16 are ties.

The same matchup from the other side

One page covers both views. From KJo's side the equity is 25.65%, and from AJo's side it is 74.35%.

AsJh against KdJc 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

This is an exact count with no sampling. For the 108 ways to deal one AJo and one KJo without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.

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

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