KQo vs T8s: preflop equity

If KQo and T8s get all the chips in before the flop, KQo owns 61.60% of the pot in the long run and T8s owns 38.40%.

KQo

61.60%

Wins 61.26%, ties 0.67%

T8s

38.40%

Wins 38.07%, ties 0.67%

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

KQo against T8s: the numbers

Exact preflop results for KQo against T8s, in percent
HandWinsTiesLosesEquity
KQo61.2620.66838.07061.596
T8s38.0700.66861.26238.404

We compare an offsuit hand with a suited hand. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.

That is a modest edge, the kind that shows up over many hands and is easy to miss in one. Ties are 0.67% of the outcomes here; each tied board gives both hands half the pot.

Among the 169 starting hands, KQo is number 23 and T8s is number 73 by strength against a random hand.

Boards behind the percentages: 82,190,592 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
KQo50,352,000549,00031,290,000
T8s31,290,000549,00050,352,000

48 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.

KQo against T8s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
KQo1.6041.6322.6270.623
T8s0.6232.6271.6321.604

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

Across the five flop textures KQo's equity moves by 16.21 points, from 50.49% on low rainbow flops (nine high or lower) to 66.70% on rainbow flops topped by a ten or better. KQo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

KQo against T8s by flop texture, in percent
FlopShare of flopsKQo winsTiesT8s winsKQo equity
Rainbow, ten or higher23.98866.5490.30433.14766.701
Rainbow, nine or lower7.04250.1290.73049.14150.494
Two-tone46.66759.9560.37339.67160.142
Monotone5.21258.4052.45439.14159.632
Paired17.09162.8681.41435.71863.575

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

Start from the random-hand figures, 61.46% for KQo and 52.33% for T8s. This opponent changes them by +0.14 and -13.93 points.

KQo and T8s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
KQo, all flops61.59661.456+0.1401.00228
KQo, rainbow, ten or higher66.70161.456+5.2451.08535
KQo, rainbow, nine or lower50.49461.456-10.9620.82163
KQo, two-tone60.14261.456-1.3140.97862
KQo, monotone59.63261.456-1.8240.97032
KQo, paired63.57561.456+2.1191.03448
T8s, all flops38.40452.334-13.9300.73383
T8s, rainbow, ten or higher33.29952.334-19.0350.63628
T8s, rainbow, nine or lower49.50652.334-2.8280.94596
T8s, two-tone39.85852.334-12.4760.76161
T8s, monotone40.36852.334-11.9660.77135
T8s, paired36.42552.334-15.9090.69601

Does a shared suit matter?

The suit split reads 62.30% for KQo with a shared suit and 60.89% without one. KQo does better with a shared suit, by 1.41 points.

KQo against T8s by suit overlap, in percent
DealsSpecific dealsShare of dealsKQo winsTiesT8s winsKQo equity
Share a suit2450.0061.9490.70937.34262.304
No shared suit2450.0060.5750.62838.79760.889

How often this matchup comes up

How often does it happen? 48 of the 1,624,350 ordered deals (0.0030%) are KQo against T8s, and 96 (0.0059%) if either hand may sit in either seat.

A worked example

Try it with money: two players each put in $100 and the whole board runs out every possible way. KQo averages $123.20 from the $200, up $23.20; T8s averages $76.80, down $23.20.

Think in thousands: about 612 of 1,000 go to KQo, about 381 go to T8s, and about 7 are chopped.

The same matchup from the other side

T8s against KQo adds nothing new: it is 38.40% for T8s and 61.60% for KQo, the same figures reversed.

The calculator link fills in KsQh against Td8d, 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

Method: exact enumeration. The 48 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.

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

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