QTo vs T9o: preflop equity

Averaged over every possible board, QTo is ahead of T9o by 44.52 points of equity, 72.26% to 27.74%.

QTo

72.26%

Wins 70.16%, ties 4.19%

T9o

27.74%

Wins 25.65%, ties 4.19%

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

QTo against T9o: the numbers

Exact preflop results for QTo against T9o, in percent
HandWinsTiesLosesEquity
QTo70.1644.18525.65172.256
T9o25.6514.18570.16427.744

Here offsuit hands face each other, QTo on one side and T9o on the other. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.

A lead of 44.52 points is large but not decisive: T9o still takes about 256 of every 1,000 deals. A split pot comes up on 4.19% of boards, so the wins and the equity differ by half of that.

The hand ranking puts QTo at 47 and T9o at 78 out of 169 starting hands.

Boards behind the percentages: 184,928,832 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
QTo129,753,0007,739,00047,436,000
T9o47,436,0007,739,000129,753,000

108 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.

QTo against T9o read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
QTo2.6041.4253.8980.384
T9o0.3843.8981.4252.604

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

Rainbow flops topped by a ten or better are the best for QTo (75.79%); low rainbow flops (nine high or lower) are the worst (59.38%). QTo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

QTo against T9o by flop texture, in percent
FlopShare of flopsQTo winsTiesT9o winsQTo equity
Rainbow, ten or higher24.00373.8223.93422.24475.789
Rainbow, nine or lower7.04258.1962.36839.43659.380
Two-tone46.47769.9903.49026.52071.735
Monotone5.14466.8584.12629.01668.921
Paired17.33471.4097.15221.43974.985

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

Against one random hand instead, QTo holds 57.29% and T9o holds 51.53%. Facing each other changes that by +14.97 points for QTo and -23.79 points for T9o.

QTo and T9o here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
QTo, all flops72.25657.291+14.9651.26121
QTo, rainbow, ten or higher75.78957.291+18.4981.32288
QTo, rainbow, nine or lower59.38057.291+2.0891.03646
QTo, two-tone71.73557.291+14.4441.25212
QTo, monotone68.92157.291+11.6301.20300
QTo, paired74.98557.291+17.6941.30884
T9o, all flops27.74451.532-23.7880.53838
T9o, rainbow, ten or higher24.21151.532-27.3210.46982
T9o, rainbow, nine or lower40.62051.532-10.9120.78825
T9o, two-tone28.26551.532-23.2670.54849
T9o, monotone31.07951.532-20.4530.60310
T9o, paired25.01551.532-26.5170.48543

Does a shared suit matter?

Split by suits, the deals give QTo 72.42% when the hands overlap in a suit and 71.68% when they do not. QTo does better with a shared suit, by 0.74 points.

QTo against T9o by suit overlap, in percent
DealsSpecific dealsShare of dealsQTo winsTiesT9o winsQTo equity
Share a suit8477.7870.3124.21725.47172.421
No shared suit2422.2269.6444.07326.28371.681

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 108 are QTo in one seat and T9o in the other (0.0066%); with the seats swapped too, 216 (0.0133%).

A worked example

Put $100 each into a $200 pot and deal every board once: QTo averages $144.52 back, ahead of its $100 by $44.52, while T9o averages $55.48, short of its $100 by $44.52.

Out of 1,000 deals you should see around 702 outright wins for QTo, 256 for T9o, and 42 split pots.

The same matchup from the other side

The mirror image, T9o against QTo, is 27.74% to 72.26%, and its address redirects to this page.

QsTh against Td9c 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 108 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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