KTs vs 53s: preflop equity

The exact count puts KTs at 63.35% and 53s at 36.65% when the two hands see all five board cards.

KTs

63.35%

Wins 62.98%, ties 0.75%

53s

36.65%

Wins 36.27%, ties 0.75%

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

KTs against 53s: the numbers

Exact preflop results for KTs against 53s, in percent
HandWinsTiesLosesEquity
KTs62.9780.74936.27363.352
53s36.2730.74962.97836.648

Both hands are suited hands: KTs and 53s. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.

KTs is ahead, but 53s is far from dead: it takes 363 of every 1,000 deals outright. A split pot comes up on 0.75% of boards, so the wins and the equity differ by half of that.

By strength against a random hand, KTs holds place 22 of 169 and 53s holds place 146.

Boards behind the percentages: 27,396,864 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
KTs17,254,000205,0009,938,000
53s9,938,000205,00017,254,000

Exact total: 16 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.

KTs against 53s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
KTs1.7291.5882.7570.578
53s0.5782.7571.5881.729

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

Across the five flop textures KTs' equity moves by 31.25 points, from 38.79% on low rainbow flops (nine high or lower) to 70.04% on rainbow flops topped by a ten or better. On low rainbow flops (nine high or lower) the numbers flip and 53s is the one ahead.

KTs against 53s by flop texture, in percent
FlopShare of flopsKTs winsTies53s winsKTs equity
Rainbow, ten or higher24.59569.8630.34429.79370.035
Rainbow, nine or lower6.31438.3810.81260.80738.787
Two-tone46.72762.4740.40337.12362.676
Monotone5.27358.6723.61937.70960.481
Paired17.09164.8601.37233.76865.546

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

Compared with a random opponent, this matchup shifts KTs from 61.79% by +1.56 points and 53s from 39.69% by -3.04 points.

KTs and 53s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
KTs, all flops63.35261.789+1.5631.02530
KTs, rainbow, ten or higher70.03561.789+8.2461.13345
KTs, rainbow, nine or lower38.78761.789-23.0020.62773
KTs, two-tone62.67661.789+0.8871.01436
KTs, monotone60.48161.789-1.3080.97883
KTs, paired65.54661.789+3.7571.06080
53s, all flops36.64839.693-3.0450.92329
53s, rainbow, ten or higher29.96539.693-9.7280.75492
53s, rainbow, nine or lower61.21339.693+21.5201.54216
53s, two-tone37.32439.693-2.3690.94032
53s, monotone39.51939.693-0.1740.99562
53s, paired34.45439.693-5.2390.86801

Does a shared suit matter?

Does suit overlap move the numbers? KTs has 65.69% when the hands share a suit and 62.57% when they do not. KTs does better with a shared suit, by 3.12 points.

KTs against 53s by suit overlap, in percent
DealsSpecific dealsShare of dealsKTs winsTies53s winsKTs equity
Share a suit425.0065.2720.84033.88865.692
No shared suit1275.0062.2130.71937.06862.572

How often this matchup comes up

Counting specific cards, KTs against 53s appears in 16 of the 1,624,350 ordered heads-up deals (0.0010%), and in 32 when the seats are swapped too (0.0020%).

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average KTs takes back $126.70 of it, which is $26.70 more than it put in, and 53s takes back $73.30, $26.70 less than it put in.

A thousand deals look like this: KTs takes 630, 53s takes 363, 7 are ties.

The same matchup from the other side

The reversed view, 53s against KTs, shows 36.65% for 53s and 63.35% for KTs. It is the same count, so it redirects here.

The calculator link fills in KsTs against 5h3h, 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

Each figure is a complete count over boards. Take the 16 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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