99 vs QTs: preflop equity

If 99 and QTs get all the chips in before the flop, 99 owns 51.99% of the pot in the long run and QTs owns 48.01%.

99

51.99%

Wins 51.78%, ties 0.41%

QTs

48.01%

Wins 47.81%, ties 0.41%

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

99 against QTs: the numbers

Exact preflop results for 99 against QTs, in percent
HandWinsTiesLosesEquity
9951.7830.40947.80851.988
QTs47.8080.40951.78348.012

The matchup pits a pocket pair against a suited hand. One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.

That is a slim edge: neither hand is far ahead. Ties are part of the picture: 0.41% of boards end in a split pot, and each side counts that as half a win.

For context, 99 sits at number 6 of 169 starting hands and QTs at number 34 when each is run against a random hand.

Boards behind the percentages: 41,095,296 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
9921,280,000168,00019,647,000
QTs19,647,000168,00021,280,000

The total is exact: 24 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and rounded to the nearest thousand.

99 against QTs read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
991.0831.9312.0920.924
QTs0.9242.0921.9311.083

The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.

Who is ahead on which flops

The flop changes the picture. 99 does best on low rainbow flops (nine high or lower), at 76.67%, and worst on rainbow flops topped by a ten or better, at 45.53%. The overall edge for 99 hides rainbow flops topped by a ten or better and two-tone flops, where QTs comes out in front.

99 against QTs by flop texture, in percent
FlopShare of flops99 winsTiesQTs wins99 equity
Rainbow, ten or higher24.59545.4440.17454.38245.531
Rainbow, nine or lower6.31476.2330.86622.90176.666
Two-tone46.54549.5730.29250.13549.719
Monotone5.21249.6402.38847.97250.834
Paired17.33458.4530.29541.25258.601

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

Start from the random-hand figures, 72.06% for 99 and 59.47% for QTs. This opponent changes them by -20.07 and -11.46 points.

99 and QTs here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
99, all flops51.98872.057-20.0690.72148
99, rainbow, ten or higher45.53172.057-26.5260.63187
99, rainbow, nine or lower76.66672.057+4.6091.06396
99, two-tone49.71972.057-22.3380.69000
99, monotone50.83472.057-21.2230.70547
99, paired58.60172.057-13.4560.81326
QTs, all flops48.01259.468-11.4560.80736
QTs, rainbow, ten or higher54.46959.468-4.9990.91594
QTs, rainbow, nine or lower23.33459.468-36.1340.39238
QTs, two-tone50.28159.468-9.1870.84551
QTs, monotone49.16659.468-10.3020.82676
QTs, paired41.39959.468-18.0690.69616

Does a shared suit matter?

Two kinds of deal exist here. In 12 of them the hands share a suit and 99 holds 52.11%. In 12 they do not, and it holds 51.87%. The two rows differ by only 0.24 points, so suits barely change this matchup.

99 against QTs by suit overlap, in percent
DealsSpecific dealsShare of deals99 winsTiesQTs wins99 equity
Share a suit1250.0051.8810.44947.67052.106
No shared suit1250.0051.6860.36847.94651.870

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

To see what the equity is worth, imagine $100 each in a $200 pot. 99 is worth $103.98 on average (+$3.98); QTs is worth $96.02 (-$3.98).

Over a long run, 1,000 deals split into about 518 for 99, 478 for QTs and 4 tied.

The same matchup from the other side

QTs versus 99 is this same page seen from the other hand: 48.01% for QTs, 51.99% for 99.

Try 9s9h against QdTd 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

The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 24 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.

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

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