KQs
50.60%
Wins 50.21%, ties 0.78%
33
49.40%
Wins 49.01%, ties 0.78%
KQs against 33: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KQs | 50.211 | 0.784 | 49.005 | 50.603 |
| 33 | 49.005 | 0.784 | 50.211 | 49.397 |
KQs, a suited hand, plays 33, a pocket pair. One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.
With only 1.20 points between them, the board decides this matchup far more than the cards in hand. A split pot comes up on 0.78% of boards, so the wins and the equity differ by half of that.
For context, KQs sits at number 16 of 169 starting hands and 33 at number 66 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KQs | 20,634,000 | 322,000 | 20,139,000 |
| 33 | 20,139,000 | 322,000 | 20,634,000 |
The board total is exact, 24 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| KQs | 1.024 | 1.992 | 2.041 | 0.976 |
| 33 | 0.976 | 2.041 | 1.992 | 1.024 |
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
If you know the kind of flop that came, the numbers shift: KQs holds 56.29% on rainbow flops topped by a ten or better and 23.40% on low rainbow flops (nine high or lower). The lead reverses on low rainbow flops (nine high or lower) and paired flops: there 33 is the favorite even though KQs is ahead overall.
| Flop | Share of flops | KQs wins | Ties | 33 wins | KQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 56.132 | 0.311 | 43.557 | 56.287 |
| Rainbow, nine or lower | 6.314 | 22.793 | 1.219 | 75.988 | 23.402 |
| Two-tone | 46.545 | 51.436 | 0.459 | 48.105 | 51.666 |
| Monotone | 5.212 | 48.789 | 3.271 | 47.940 | 50.424 |
| Paired | 17.334 | 48.932 | 1.422 | 49.646 | 49.643 |
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
How much does the opponent matter? Compared with its random-hand 63.40%, KQs changes by -12.80 points, and 33, from 53.69%, by -4.29.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KQs, all flops | 50.603 | 63.400 | -12.797 | 0.79815 |
| KQs, rainbow, ten or higher | 56.287 | 63.400 | -7.113 | 0.88781 |
| KQs, rainbow, nine or lower | 23.402 | 63.400 | -39.998 | 0.36912 |
| KQs, two-tone | 51.666 | 63.400 | -11.734 | 0.81492 |
| KQs, monotone | 50.424 | 63.400 | -12.976 | 0.79533 |
| KQs, paired | 49.643 | 63.400 | -13.757 | 0.78301 |
| 33, all flops | 49.397 | 53.693 | -4.296 | 0.91999 |
| 33, rainbow, ten or higher | 43.713 | 53.693 | -9.980 | 0.81413 |
| 33, rainbow, nine or lower | 76.598 | 53.693 | +22.905 | 1.42659 |
| 33, two-tone | 48.334 | 53.693 | -5.359 | 0.90019 |
| 33, monotone | 49.576 | 53.693 | -4.117 | 0.92332 |
| 33, paired | 50.357 | 53.693 | -3.336 | 0.93787 |
Does a shared suit matter?
The suit split reads 50.43% for KQs with a shared suit and 50.78% without one. KQs does better with no shared suit, by 0.35 points.
| Deals | Specific deals | Share of deals | KQs wins | Ties | 33 wins | KQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 50.018 | 0.815 | 49.167 | 50.426 |
| No shared suit | 12 | 50.00 | 50.403 | 0.753 | 48.844 | 50.780 |
How often this matchup comes up
How often does it happen? 24 of the 1,624,350 ordered deals (0.0015%) are KQs against 33, and 48 (0.0030%) if either hand may sit in either seat.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. KQs is worth $101.20 on average (+$1.20); 33 is worth $98.80 (-$1.20).
Run 1,000 deals and the tally comes out near 502 for KQs, 490 for 33 and 8 ties.
The same matchup from the other side
The mirror image, 33 against KQs, is 49.40% to 50.60%, and its address redirects to this page.
Keep exploring
The calculator link fills in KsQs against 3h3d, 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
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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