K9s
62.57%
Wins 62.22%, ties 0.72%
75s
37.43%
Wins 37.06%, ties 0.72%
K9s against 75s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| K9s | 62.217 | 0.715 | 37.068 | 62.574 |
| 75s | 37.068 | 0.715 | 62.217 | 37.426 |
Each side holds one of the suited hands: K9s and 75s. 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. Split pots make up 0.72% of the boards, and both equity figures count them as half a win each.
Ranked by equity against a random hand, K9s is number 29 of the 169 starting hands and 75s is number 124.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| K9s | 17,046,000 | 196,000 | 10,155,000 |
| 75s | 10,155,000 | 196,000 | 17,046,000 |
The total is exact: 16 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.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| K9s | 1.672 | 1.607 | 2.698 | 0.598 |
| 75s | 0.598 | 2.698 | 1.607 | 1.672 |
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
K9s prefers rainbow flops topped by a ten or better, where it holds 66.82%, and likes low rainbow flops (nine high or lower) least, where it holds 44.76%. Watch for low rainbow flops (nine high or lower): on those flops 75s holds the better equity.
| Flop | Share of flops | K9s wins | Ties | 75s wins | K9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 66.645 | 0.350 | 33.005 | 66.820 |
| Rainbow, nine or lower | 5.689 | 44.474 | 0.571 | 54.955 | 44.759 |
| Two-tone | 46.727 | 61.680 | 0.359 | 37.961 | 61.860 |
| Monotone | 5.273 | 58.016 | 3.500 | 38.484 | 59.766 |
| Paired | 17.091 | 64.353 | 1.412 | 34.235 | 65.059 |
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
Against one random hand instead, K9s holds 59.99% and 75s holds 43.68%. Facing each other changes that by +2.58 points for K9s and -6.25 points for 75s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| K9s, all flops | 62.574 | 59.988 | +2.586 | 1.04311 |
| K9s, rainbow, ten or higher | 66.820 | 59.988 | +6.832 | 1.11389 |
| K9s, rainbow, nine or lower | 44.759 | 59.988 | -15.229 | 0.74613 |
| K9s, two-tone | 61.860 | 59.988 | +1.872 | 1.03121 |
| K9s, monotone | 59.766 | 59.988 | -0.222 | 0.99630 |
| K9s, paired | 65.059 | 59.988 | +5.071 | 1.08453 |
| 75s, all flops | 37.426 | 43.676 | -6.250 | 0.85690 |
| 75s, rainbow, ten or higher | 33.180 | 43.676 | -10.496 | 0.75968 |
| 75s, rainbow, nine or lower | 55.241 | 43.676 | +11.565 | 1.26479 |
| 75s, two-tone | 38.140 | 43.676 | -5.536 | 0.87325 |
| 75s, monotone | 40.234 | 43.676 | -3.442 | 0.92119 |
| 75s, paired | 34.941 | 43.676 | -8.735 | 0.80000 |
Does a shared suit matter?
Two kinds of deal exist here. In 4 of them the hands share a suit and K9s holds 64.88%. In 12 they do not, and it holds 61.81%. K9s does better with a shared suit, by 3.07 points.
| Deals | Specific deals | Share of deals | K9s wins | Ties | 75s wins | K9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 64.478 | 0.803 | 34.719 | 64.880 |
| No shared suit | 12 | 75.00 | 61.463 | 0.685 | 37.852 | 61.806 |
How often this matchup comes up
Exactly 16 specific deals fit this matchup in one seat order, which is 0.0010% of 1,624,350; both orders together give 32, or 0.0020%.
A worked example
Worked example: both players commit $100, so $200 sits in the middle. Over every board, K9s' average share is $125.14 (a gain of $25.14) and 75s' is $74.86 (a loss of $25.14).
Per 1,000 deals: K9s wins about 622, 75s wins about 371, and about 7 end in a split pot.
The same matchup from the other side
Swap the hands and you get 75s with 37.43% against K9s with 62.57%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
The calculator link fills in Ks9s against 7h5h, 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
Nothing here is simulated. The 16 deals of K9s against 75s 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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