TT vs K9o: preflop equity

The exact count puts TT at 72.08% and K9o at 27.92% when the two hands see all five board cards.

TT

72.08%

Wins 71.89%, ties 0.38%

K9o

27.92%

Wins 27.73%, ties 0.38%

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

TT against K9o: the numbers

Exact preflop results for TT against K9o, in percent
HandWinsTiesLosesEquity
TT71.8920.37927.72972.082
K9o27.7290.37971.89227.918

We compare a pocket pair with an offsuit hand. The pair sits between the other hand's two cards: one is higher and one is lower, so the pair is exposed to the higher card.

TT is the clear favorite, though K9o gets there on roughly one board in 4. About 0.38% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.

For context, TT sits at number 5 of 169 starting hands and K9o at number 40 when each is run against a random hand.

Boards behind the percentages: 123,285,888 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
TT88,633,000467,00034,186,000
K9o34,186,000467,00088,633,000

The total is exact: 72 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and rounded to the nearest thousand.

TT against K9o read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
TT2.5821.3913.6060.387
K9o0.3873.6061.3912.582

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

By flop texture, TT's equity runs from 67.34% on monotone flops up to 82.63% on low rainbow flops (nine high or lower). 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 K9o by flop texture, in percent
FlopShare of flopsTT winsTiesK9o winsTT equity
Rainbow, ten or higher23.98868.9680.17530.85769.056
Rainbow, nine or lower7.04282.2220.82416.95482.634
Two-tone46.48571.4410.31028.24971.596
Monotone5.15166.4901.69931.81167.340
Paired17.33474.5570.27425.16974.694

A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.

Compared with a random hand

Start from the random-hand figures, 75.01% for TT and 57.81% for K9o. This opponent changes them by -2.93 and -29.89 points.

TT and K9o here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
TT, all flops72.08275.012-2.9300.96094
TT, rainbow, ten or higher69.05675.012-5.9560.92060
TT, rainbow, nine or lower82.63475.012+7.6221.10161
TT, two-tone71.59675.012-3.4160.95446
TT, monotone67.34075.012-7.6720.89772
TT, paired74.69475.012-0.3180.99576
K9o, all flops27.91857.812-29.8940.48291
K9o, rainbow, ten or higher30.94457.812-26.8680.53525
K9o, rainbow, nine or lower17.36657.812-40.4460.30039
K9o, two-tone28.40457.812-29.4080.49132
K9o, monotone32.66057.812-25.1520.56493
K9o, paired25.30657.812-32.5060.43773

Does a shared suit matter?

Looking only at deals where the hands share a suit, TT has 72.12%; looking only at deals where they do not, 71.89%. The two rows differ by only 0.23 points, so suits barely change this matchup.

TT against K9o by suit overlap, in percent
DealsSpecific dealsShare of dealsTT winsTiesK9o winsTT equity
Share a suit6083.3371.9220.39527.68372.119
No shared suit1216.6771.7440.30027.95671.894

How often this matchup comes up

You will meet this exact matchup 0.0089% of the time in a random heads-up deal: 144 of 1,624,350, counting either seat order.

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average TT takes back $144.16 of it, which is $44.16 more than it put in, and K9o takes back $55.84, $44.16 less than it put in.

In 1,000 deals of exactly this matchup, expect about 719 won outright by TT, about 277 won outright by K9o and about 4 split.

The same matchup from the other side

The reversed view, K9o against TT, shows 27.92% for K9o and 72.08% for TT. It is the same count, so it redirects here.

Try TsTh against Kd9c 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 72 ways to deal one TT and one K9o 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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