99 vs KQo: preflop equity

Counting every board, the equity split is 55.25% for 99 and 44.75% for KQo, so 99 leads by 10.50 points.

99

55.25%

Wins 55.05%, ties 0.40%

KQo

44.75%

Wins 44.55%, ties 0.40%

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

99 against KQo: the numbers

Exact preflop results for 99 against KQo, in percent
HandWinsTiesLosesEquity
9955.0480.39644.55655.246
KQo44.5560.39655.04844.754

99 is a pocket pair and KQo is an offsuit hand. This is a pair against two overcards, a matchup that stays close because the other hand only needs one of its ranks to appear.

A 10.50 point lead is real, and KQo still takes about 446 of every 1,000 deals outright. 0.40% of boards are ties, so the equity of each hand is its win rate plus half of that.

The hand ranking puts 99 at 6 and KQo at 23 out of 169 starting hands.

Boards behind the percentages: 123,285,888 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
9967,866,000488,00054,931,000
KQo54,931,000488,00067,866,000

The total is exact: 72 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 KQo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
991.2341.8172.2440.810
KQo0.8102.2441.8171.234

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. 99 does best on low rainbow flops (nine high or lower), at 80.93%, and worst on rainbow flops topped by a ten or better, at 47.59%. The overall edge for 99 hides rainbow flops topped by a ten or better, where KQo comes out in front.

99 against KQo by flop texture, in percent
FlopShare of flops99 winsTiesKQo wins99 equity
Rainbow, ten or higher24.71747.5120.15952.32947.591
Rainbow, nine or lower6.31480.3771.10118.52280.928
Two-tone46.48553.8730.33645.79154.041
Monotone5.15150.6501.71547.63551.507
Paired17.33361.0290.24938.72261.153

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

The table below sets each hand against its own random-hand baseline: a change of -16.81 points for 99, from 72.06%, and -16.71 for KQo, from 61.46%.

99 and KQo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
99, all flops55.24672.057-16.8110.76670
99, rainbow, ten or higher47.59172.057-24.4660.66046
99, rainbow, nine or lower80.92872.057+8.8711.12311
99, two-tone54.04172.057-18.0160.74998
99, monotone51.50772.057-20.5500.71481
99, paired61.15372.057-10.9040.84868
KQo, all flops44.75461.456-16.7020.72823
KQo, rainbow, ten or higher52.40961.456-9.0470.85279
KQo, rainbow, nine or lower19.07261.456-42.3840.31034
KQo, two-tone45.95961.456-15.4970.74784
KQo, monotone48.49361.456-12.9630.78907
KQo, paired38.84761.456-22.6090.63211

Does a shared suit matter?

When the hands share a suit, 99 holds 55.16%; when they do not, it holds 55.66%. 99 does better with no shared suit, by 0.50 points.

99 against KQo by suit overlap, in percent
DealsSpecific dealsShare of deals99 winsTiesKQo wins99 equity
Share a suit6083.3354.9570.41244.63155.163
No shared suit1216.6755.5060.31744.17755.664

How often this matchup comes up

Counting specific cards, 99 against KQo appears in 72 of the 1,624,350 ordered heads-up deals (0.0044%), and in 144 when the seats are swapped too (0.0089%).

A worked example

Put $100 each into a $200 pot and deal every board once: 99 averages $110.50 back, ahead of its $100 by $10.50, while KQo averages $89.50, short of its $100 by $10.50.

Per 1,000 deals: 99 wins about 550, KQo wins about 446, and about 4 end in a split pot.

The same matchup from the other side

The reversed view, KQo against 99, shows 44.75% for KQo and 55.25% for 99. It is the same count, so it redirects here.

9s9h against KdQc 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

Nothing here is simulated. The 72 deals of 99 against KQo fall into a few suit patterns, each dealt against all 1,712,304 boards, with both best five-card hands compared on every board. Ties give each hand half a win, and the flop rows count a board under each of its ten flops.

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

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