QTs vs QTo: preflop equity

Averaged over every possible board, QTs is ahead of QTo by 4.98 points of equity, 52.49% to 47.51%.

QTs

52.49%

Wins 7.16%, ties 90.67%

QTo

47.51%

Wins 2.17%, ties 90.67%

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

QTs against QTo: the numbers

Exact preflop results for QTs against QTo, in percent
HandWinsTiesLosesEquity
QTs7.15890.6692.17352.492
QTo2.17390.6697.15847.508

QTs, a suited hand, plays QTo, an offsuit hand. The cards are the same ranks, so any difference in equity comes from suitedness alone.

With only 4.98 points between them, the board decides this matchup far more than the cards in hand. A split pot comes up on 90.67% of boards, so the wins and the equity differ by half of that.

Place 34 of 169 belongs to QTs and place 47 belongs to QTo in the ranking against a random hand.

Boards behind the percentages: 41,095,296 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
QTs2,942,00037,261,000893,000
QTo893,00037,261,0002,942,000

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.

QTs against QTo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
QTs1.10513.97046.0190.905
QTo0.90546.01913.9701.105

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

Break the boards down by their first three cards and QTs is strongest on two-tone flops (53.28%) and weakest on monotone flops (50.28%). QTs stays ahead on all five textures.

QTs against QTo by flop texture, in percent
FlopShare of flopsQTs winsTiesQTo winsQTs equity
Rainbow, ten or higher23.1383.26596.7350.00051.633
Rainbow, nine or lower7.7713.40996.5910.00051.705
Two-tone46.3638.82988.9012.27053.280
Monotone5.15218.51463.54017.94650.284
Paired17.5766.20192.6811.11852.541

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

Against one random hand instead, QTs holds 59.47% and QTo holds 57.29%. Facing each other changes that by -6.98 points for QTs and -9.78 points for QTo.

QTs and QTo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
QTs, all flops52.49259.468-6.9760.88269
QTs, rainbow, ten or higher51.63359.468-7.8350.86825
QTs, rainbow, nine or lower51.70559.468-7.7630.86946
QTs, two-tone53.28059.468-6.1880.89594
QTs, monotone50.28459.468-9.1840.84556
QTs, paired52.54159.468-6.9270.88352
QTo, all flops47.50857.291-9.7830.82924
QTo, rainbow, ten or higher48.36757.291-8.9240.84423
QTo, rainbow, nine or lower48.29557.291-8.9960.84298
QTo, two-tone46.72057.291-10.5710.81549
QTo, monotone49.71657.291-7.5750.86778
QTo, paired47.45957.291-9.8320.82838

Does a shared suit matter?

A shared suit is impossible for this matchup, so QTs' 52.49% is the answer for every suit pattern.

QTs against QTo by suit overlap, in percent
DealsSpecific dealsShare of dealsQTs winsTiesQTo winsQTs equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit24100.007.15890.6692.17352.492

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

A $100 all-in from each player makes a $200 pot, and the exact equity says QTs gets $104.98 of it on average and QTo gets $95.02.

Scaled to 1,000 deals, that is roughly 71 wins for QTs, 22 for QTo and 907 chopped pots.

The same matchup from the other side

One page covers both views. From QTo's side the equity is 47.51%, and from QTs' side it is 52.49%.

QsTs against QhTd 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

Each figure is a complete count over boards. Take the 24 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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