TT vs T9s: preflop equity

The exact count puts TT at 82.31% and T9s at 17.69% when the two hands see all five board cards.

TT

82.31%

Wins 80.96%, ties 2.70%

T9s

17.69%

Wins 16.34%, ties 2.70%

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

TT against T9s: the numbers

Exact preflop results for TT against T9s, in percent
HandWinsTiesLosesEquity
TT80.9582.70416.33882.310
T9s16.3382.70480.95817.690

Here a pocket pair (TT) meets a suited hand (T9s). One hand holds a card of the same rank as the pair, which removes a card the pair needs and makes the pair a bigger favorite.

TT is a big favorite here before anyone sees a flop. Ties are part of the picture: 2.70% of boards end in a split pot, and each side counts that as half a win.

Ranked by equity against a random hand, TT is number 5 of the 169 starting hands and T9s is number 64.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
TT16,635,000556,0003,357,000
T9s3,357,000556,00016,635,000

12 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.

TT against T9s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
TT4.6531.2356.1210.215
T9s0.2156.1211.2354.653

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

The flop changes the picture. TT does best on rainbow flops topped by a ten or better, at 85.14%, and worst on monotone flops, at 73.88%. TT stays ahead on all five textures.

TT against T9s by flop texture, in percent
FlopShare of flopsTT winsTiesT9s winsTT equity
Rainbow, ten or higher23.74083.7412.80213.45785.142
Rainbow, nine or lower7.04283.4732.89613.63184.921
Two-tone46.23679.3772.59818.02580.676
Monotone5.15172.2563.25224.49273.882
Paired17.83182.8722.61514.51384.180

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

How much does the opponent matter? Compared with its random-hand 75.01%, TT changes by +7.30 points, and T9s, from 54.03%, by -36.34.

TT and T9s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
TT, all flops82.31075.012+7.2981.09729
TT, rainbow, ten or higher85.14275.012+10.1301.13505
TT, rainbow, nine or lower84.92175.012+9.9091.13210
TT, two-tone80.67675.012+5.6641.07551
TT, monotone73.88275.012-1.1300.98494
TT, paired84.18075.012+9.1681.12222
T9s, all flops17.69054.028-36.3380.32742
T9s, rainbow, ten or higher14.85854.028-39.1700.27501
T9s, rainbow, nine or lower15.07954.028-38.9490.27910
T9s, two-tone19.32454.028-34.7040.35767
T9s, monotone26.11854.028-27.9100.48342
T9s, paired15.82054.028-38.2080.29281

Does a shared suit matter?

These two classes cannot share a suit in any legal deal, so there is only one row to read: TT holds 82.31% in every deal of this matchup.

TT against T9s by suit overlap, in percent
DealsSpecific dealsShare of dealsTT winsTiesT9s winsTT equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0080.9582.70416.33882.310

How often this matchup comes up

You will meet this exact matchup 0.0015% of the time in a random heads-up deal: 24 of 1,624,350, counting either seat order.

A worked example

Try it with money: two players each put in $100 and the whole board runs out every possible way. TT averages $164.62 from the $200, up $64.62; T9s averages $35.38, down $64.62.

Over a long run, 1,000 deals split into about 810 for TT, 163 for T9s and 27 tied.

The same matchup from the other side

The reversed view, T9s against TT, shows 17.69% for T9s and 82.31% for TT. It is the same count, so it redirects here.

Try TsTh against Td9d 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 12 ways to deal one TT and one T9s 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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