TT vs 87s: preflop equity

If TT and 87s get all the chips in before the flop, TT owns 80.28% of the pot in the long run and 87s owns 19.72%.

TT

80.28%

Wins 80.05%, ties 0.46%

87s

19.72%

Wins 19.49%, ties 0.46%

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

TT against 87s: the numbers

Exact preflop results for TT against 87s, in percent
HandWinsTiesLosesEquity
TT80.0540.45819.48880.283
87s19.4880.45880.05419.717

One side is a pocket pair, the other is a suited hand. A pair against two lower cards is a lopsided matchup: the pair is ahead and the other hand has no overcard to catch.

This is one of the lopsided matchups: 87s wins only 19.49% of the boards outright. The tie share is 0.46%: on those boards the pot is chopped and neither hand wins outright.

By strength against a random hand, TT holds place 5 of 169 and 87s holds place 100.

Boards behind the percentages: 41,095,296 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
TT32,898,000188,0008,009,000
87s8,009,000188,00032,898,000

Exact total: 24 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.

TT against 87s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
TT4.0721.2495.1310.246
87s0.2465.1311.2494.072

In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.

Who is ahead on which flops

Rainbow flops topped by a ten or better are the best for TT (85.01%); low rainbow flops (nine high or lower) are the worst (70.20%). TT stays ahead on all five textures.

TT against 87s by flop texture, in percent
FlopShare of flopsTT winsTies87s winsTT equity
Rainbow, ten or higher24.59584.8710.27014.85985.006
Rainbow, nine or lower6.31470.0130.37329.61470.200
Two-tone46.54578.2740.27421.45278.411
Monotone5.21273.3622.38724.25174.555
Paired17.33483.6660.67415.66084.003

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

Each hand has a baseline against a random hand: 75.01% for TT, 47.94% for 87s. Here the change is +5.27 and -28.22 points.

TT and 87s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
TT, all flops80.28375.012+5.2711.07027
TT, rainbow, ten or higher85.00675.012+9.9941.13323
TT, rainbow, nine or lower70.20075.012-4.8120.93585
TT, two-tone78.41175.012+3.3991.04531
TT, monotone74.55575.012-0.4570.99391
TT, paired84.00375.012+8.9911.11986
87s, all flops19.71747.936-28.2190.41132
87s, rainbow, ten or higher14.99447.936-32.9420.31279
87s, rainbow, nine or lower29.80047.936-18.1360.62166
87s, two-tone21.58947.936-26.3470.45037
87s, monotone25.44547.936-22.4910.53081
87s, paired15.99747.936-31.9390.33372

Does a shared suit matter?

Looking only at deals where the hands share a suit, TT has 80.84%; looking only at deals where they do not, 79.73%. TT does better with a shared suit, by 1.11 points.

TT against 87s by suit overlap, in percent
DealsSpecific dealsShare of dealsTT winsTies87s winsTT equity
Share a suit1250.0080.5900.50118.90980.840
No shared suit1250.0079.5180.41620.06679.726

How often this matchup comes up

You will meet this exact matchup 0.0030% of the time in a random heads-up deal: 48 of 1,624,350, counting either seat order.

A worked example

With $100 from each side, the $200 pot is split on average as $160.56 for TT and $39.44 for 87s; the first side gains $60.56 per all-in and the second gives up $60.56.

Run 1,000 deals and the tally comes out near 800 for TT, 195 for 87s and 5 ties.

The same matchup from the other side

One page covers both views. From 87s' side the equity is 19.72%, and from TT's side it is 80.28%.

The calculator link fills in TsTh against 8d7d, 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

The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 24 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.

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

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