KJo vs 76s: preflop equity

Over all 1,712,304 boards that can follow this deal, KJo finishes with 59.54% of the pot and 76s with 40.46%.

KJo

59.54%

Wins 59.23%, ties 0.63%

76s

40.46%

Wins 40.14%, ties 0.63%

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

KJo against 76s: the numbers

Exact preflop results for KJo against 76s, in percent
HandWinsTiesLosesEquity
KJo59.2300.62640.14459.543
76s40.1440.62659.23040.457

KJo, an offsuit hand, plays 76s, a suited hand. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.

KJo is ahead, but 76s is far from dead: it takes 402 of every 1,000 deals outright. Ties are 0.63% of the outcomes here; each tied board gives both hands half the pot.

In the ranking of all 169 starting hands, KJo is number 26 and 76s is number 115.

Boards behind the percentages: 82,190,592 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
KJo48,681,000515,00032,995,000
76s32,995,000515,00048,681,000

Exact total: 48 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.

KJo against 76s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
KJo1.4721.6882.4910.679
76s0.6792.4911.6881.472

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

Across the five flop textures KJo's equity moves by 35.55 points, from 32.46% on low rainbow flops (nine high or lower) to 68.01% on rainbow flops topped by a ten or better. The lead reverses on low rainbow flops (nine high or lower): there 76s is the favorite even though KJo is ahead overall.

KJo against 76s by flop texture, in percent
FlopShare of flopsKJo winsTies76s winsKJo equity
Rainbow, ten or higher24.71767.8760.27731.84768.014
Rainbow, nine or lower6.31332.1620.59467.24432.459
Two-tone46.66757.8580.32641.81658.021
Monotone5.21256.7902.43740.77358.008
Paired17.09161.2151.41137.37461.921

Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.

Compared with a random hand

Relative to a random opponent, KJo changes by -1.03 points (baseline 60.57%) and 76s by -4.91 points (baseline 45.37%).

KJo and 76s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
KJo, all flops59.54360.569-1.0260.98306
KJo, rainbow, ten or higher68.01460.569+7.4451.12292
KJo, rainbow, nine or lower32.45960.569-28.1100.53590
KJo, two-tone58.02160.569-2.5480.95793
KJo, monotone58.00860.569-2.5610.95772
KJo, paired61.92160.569+1.3521.02232
76s, all flops40.45745.372-4.9150.89167
76s, rainbow, ten or higher31.98645.372-13.3860.70497
76s, rainbow, nine or lower67.54145.372+22.1691.48861
76s, two-tone41.97945.372-3.3930.92522
76s, monotone41.99245.372-3.3800.92550
76s, paired38.07945.372-7.2930.83926

Does a shared suit matter?

Two kinds of deal exist here. In 24 of them the hands share a suit and KJo holds 60.24%. In 24 they do not, and it holds 58.85%. KJo does better with a shared suit, by 1.39 points.

KJo against 76s by suit overlap, in percent
DealsSpecific dealsShare of dealsKJo winsTies76s winsKJo equity
Share a suit2450.0059.9050.66839.42760.239
No shared suit2450.0058.5540.58540.86158.847

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 48 are KJo in one seat and 76s in the other (0.0030%); with the seats swapped too, 96 (0.0059%).

A worked example

With $100 from each side, the $200 pot is split on average as $119.08 for KJo and $80.92 for 76s; the first side gains $19.08 per all-in and the second gives up $19.08.

Run 1,000 deals and the tally comes out near 592 for KJo, 402 for 76s and 6 ties.

The same matchup from the other side

Swap the hands and you get 76s with 40.46% against KJo with 59.54%. We keep one page per matchup, with the better-ranked hand first.

Try KsJh against 7d6d 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

This is an exact count with no sampling. For the 48 ways to deal one KJo and one 76s 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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