KQo
60.16%
Wins 59.82%, ties 0.68%
75s
39.84%
Wins 39.50%, ties 0.68%
KQo against 75s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KQo | 59.822 | 0.678 | 39.500 | 60.161 |
| 75s | 39.500 | 0.678 | 59.822 | 39.839 |
One side is an offsuit hand, the other is a suited hand. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. Ties are 0.68% of the outcomes here; each tied board gives both hands half the pot.
KQo ranks number 23 of 169 starting hands, and 75s ranks number 124, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KQo | 49,168,000 | 557,000 | 32,465,000 |
| 75s | 32,465,000 | 557,000 | 49,168,000 |
48 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.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| KQo | 1.510 | 1.672 | 2.532 | 0.662 |
| 75s | 0.662 | 2.532 | 1.672 | 1.510 |
The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.
Who is ahead on which flops
Split by what the flop looks like, KQo peaks at 68.80% on rainbow flops topped by a ten or better and bottoms out at 32.52% on low rainbow flops (nine high or lower). Low rainbow flops (nine high or lower) favor 75s, the hand that is behind overall.
| Flop | Share of flops | KQo wins | Ties | 75s wins | KQo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 68.641 | 0.313 | 31.046 | 68.798 |
| Rainbow, nine or lower | 6.313 | 32.125 | 0.781 | 67.094 | 32.516 |
| Two-tone | 46.667 | 58.402 | 0.387 | 41.211 | 58.595 |
| Monotone | 5.212 | 57.202 | 2.483 | 40.315 | 58.443 |
| Paired | 17.091 | 61.978 | 1.411 | 36.611 | 62.684 |
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
Each hand has a baseline against a random hand: 61.46% for KQo, 43.68% for 75s. Here the change is -1.30 and -3.84 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KQo, all flops | 60.161 | 61.456 | -1.295 | 0.97893 |
| KQo, rainbow, ten or higher | 68.798 | 61.456 | +7.342 | 1.11947 |
| KQo, rainbow, nine or lower | 32.516 | 61.456 | -28.940 | 0.52909 |
| KQo, two-tone | 58.595 | 61.456 | -2.861 | 0.95345 |
| KQo, monotone | 58.443 | 61.456 | -3.013 | 0.95097 |
| KQo, paired | 62.684 | 61.456 | +1.228 | 1.01998 |
| 75s, all flops | 39.839 | 43.676 | -3.837 | 0.91215 |
| 75s, rainbow, ten or higher | 31.202 | 43.676 | -12.474 | 0.71440 |
| 75s, rainbow, nine or lower | 67.484 | 43.676 | +23.808 | 1.54510 |
| 75s, two-tone | 41.405 | 43.676 | -2.271 | 0.94800 |
| 75s, monotone | 41.557 | 43.676 | -2.119 | 0.95148 |
| 75s, paired | 37.316 | 43.676 | -6.360 | 0.85438 |
Does a shared suit matter?
The suit split reads 60.87% for KQo with a shared suit and 59.45% without one. KQo does better with a shared suit, by 1.42 points.
| Deals | Specific deals | Share of deals | KQo wins | Ties | 75s wins | KQo equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 60.514 | 0.719 | 38.767 | 60.873 |
| No shared suit | 24 | 50.00 | 59.131 | 0.636 | 40.233 | 59.449 |
How often this matchup comes up
The class pair covers 48 combinations of specific cards in a fixed seat order, 0.0030% of 1,624,350, and 96 (0.0059%) in either order.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. KQo is worth $120.32 on average (+$20.32); 75s is worth $79.68 (-$20.32).
Out of 1,000 deals you should see around 598 outright wins for KQo, 395 for 75s, and 7 split pots.
The same matchup from the other side
75s against KQo adds nothing new: it is 39.84% for 75s and 60.16% for KQo, the same figures reversed.
Keep exploring
Open the calculator with KsQh against 7d5d already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.
How this was computed
Method: exact enumeration. The 48 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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