TT vs 65s: preflop equity

The exact count puts TT at 78.20% and 65s at 21.80% when the two hands see all five board cards.

TT

78.20%

Wins 77.95%, ties 0.49%

65s

21.80%

Wins 21.56%, ties 0.49%

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

TT against 65s: the numbers

Exact preflop results for TT against 65s, in percent
HandWinsTiesLosesEquity
TT77.9540.49221.55478.200
65s21.5540.49277.95421.800

Here a pocket pair (TT) meets a suited hand (65s). The pair outranks both of the other hand's cards, which is why the pair is a strong favorite.

TT is well ahead, and 65s needs a specific kind of board to catch up. 0.49% of boards are ties, so the equity of each hand is its win rate plus half of that.

Ranked by equity against a random hand, TT is number 5 of the 169 starting hands and 65s is number 128.

Boards behind the percentages: 41,095,296 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
TT32,035,000202,0008,858,000
65s8,858,000202,00032,035,000

The board total is exact, 24 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

TT against 65s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
TT3.5871.2834.6400.279
65s0.2794.6401.2833.587

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

Break the boards down by their first three cards and TT is strongest on rainbow flops topped by a ten or better (84.31%) and weakest on low rainbow flops (nine high or lower) (61.77%). 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 65s by flop texture, in percent
FlopShare of flopsTT winsTies65s winsTT equity
Rainbow, ten or higher24.59584.1830.24915.56884.308
Rainbow, nine or lower6.31461.4520.64337.90561.774
Two-tone46.54576.1640.31323.52376.320
Monotone5.21271.9282.44325.62973.150
Paired17.33481.7480.67417.57882.085

Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.

Compared with a random hand

How much does the opponent matter? Compared with its random-hand 75.01%, TT changes by +3.19 points, and 65s, from 43.13%, by -21.33.

TT and 65s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
TT, all flops78.20075.012+3.1881.04250
TT, rainbow, ten or higher84.30875.012+9.2961.12393
TT, rainbow, nine or lower61.77475.012-13.2380.82352
TT, two-tone76.32075.012+1.3081.01744
TT, monotone73.15075.012-1.8620.97518
TT, paired82.08575.012+7.0731.09429
65s, all flops21.80043.133-21.3330.50541
65s, rainbow, ten or higher15.69243.133-27.4410.36380
65s, rainbow, nine or lower38.22643.133-4.9070.88624
65s, two-tone23.68043.133-19.4530.54900
65s, monotone26.85043.133-16.2830.62249
65s, paired17.91543.133-25.2180.41534

Does a shared suit matter?

Does suit overlap move the numbers? TT has 78.77% when the hands share a suit and 77.64% when they do not. TT does better with a shared suit, by 1.13 points.

TT against 65s by suit overlap, in percent
DealsSpecific dealsShare of dealsTT winsTies65s winsTT equity
Share a suit1250.0078.4970.53620.96778.765
No shared suit1250.0077.4120.44722.14177.636

How often this matchup comes up

TT against 65s is made up of 24 specific-card matchups in one seat order, 0.0015% of the 1,624,350 ordered deals, and 48 counting both seat orders, 0.0030%.

A worked example

Put $100 each into a $200 pot and deal every board once: TT averages $156.40 back, ahead of its $100 by $56.40, while 65s averages $43.60, short of its $100 by $56.40.

A thousand deals look like this: TT takes 779, 65s takes 216, 5 are ties.

The same matchup from the other side

If you came looking for 65s against TT, the numbers are the same with the hands swapped: 21.80% and 78.20%.

TsTh against 6d5d is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.

How this was computed

This is an exact count with no sampling. For the 24 ways to deal one TT and one 65s 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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