TT vs KTs: preflop equity

If TT and KTs get all the chips in before the flop, TT owns 64.14% of the pot in the long run and KTs owns 35.86%.

TT

64.14%

Wins 63.14%, ties 2.00%

KTs

35.86%

Wins 34.86%, ties 2.00%

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

TT against KTs: the numbers

Exact preflop results for TT against KTs, in percent
HandWinsTiesLosesEquity
TT63.1441.99934.85764.143
KTs34.8571.99963.14435.857

TT is a pocket pair and KTs is a suited hand. 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 ahead, but KTs is far from dead: it takes 349 of every 1,000 deals outright. Ties are 2.00% of the outcomes here; each tied board gives both hands half the pot.

By strength against a random hand, TT holds place 5 of 169 and KTs holds place 22.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
TT12,975,000411,0007,162,000
KTs7,162,000411,00012,975,000

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 KTs read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
TT1.7891.5842.8690.559
KTs0.5592.8691.5841.789

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

The flop changes the picture. TT does best on low rainbow flops (nine high or lower), at 81.72%, and worst on rainbow flops topped by a ten or better, at 59.19%. 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 KTs by flop texture, in percent
FlopShare of flopsTT winsTiesKTs winsTT equity
Rainbow, ten or higher23.01158.1902.00139.80959.190
Rainbow, nine or lower7.77180.0513.34316.60681.723
Two-tone46.23660.6172.12237.26161.678
Monotone5.15158.7882.86438.34860.220
Paired17.83169.9780.84229.18070.399

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

A random hand would give TT 75.01% and KTs 61.79%. Against each other the change is -10.87 points for TT and -25.93 for KTs.

TT and KTs here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
TT, all flops64.14375.012-10.8690.85510
TT, rainbow, ten or higher59.19075.012-15.8220.78907
TT, rainbow, nine or lower81.72375.012+6.7111.08947
TT, two-tone61.67875.012-13.3340.82224
TT, monotone60.22075.012-14.7920.80280
TT, paired70.39975.012-4.6130.93850
KTs, all flops35.85761.789-25.9320.58031
KTs, rainbow, ten or higher40.81061.789-20.9790.66047
KTs, rainbow, nine or lower18.27761.789-43.5120.29580
KTs, two-tone38.32261.789-23.4670.62021
KTs, monotone39.78061.789-22.0090.64380
KTs, paired29.60161.789-32.1880.47907

Does a shared suit matter?

Every legal deal of TT against KTs leaves the hands with no suit in common, so the suit split does not apply here.

TT against KTs by suit overlap, in percent
DealsSpecific dealsShare of dealsTT winsTiesKTs winsTT equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0063.1441.99934.85764.143

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 12 are TT in one seat and KTs in the other (0.0007%); with the seats swapped too, 24 (0.0015%).

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average TT takes back $128.28 of it, which is $28.28 more than it put in, and KTs takes back $71.72, $28.28 less than it put in.

A thousand deals look like this: TT takes 631, KTs takes 349, 20 are ties.

The same matchup from the other side

KTs versus TT is this same page seen from the other hand: 35.86% for KTs, 64.14% for TT.

Try TsTh against KdTd 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

Each figure is a complete count over boards. Take the 12 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.

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

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