K9s
61.82%
Wins 61.44%, ties 0.76%
54s
38.18%
Wins 37.80%, ties 0.76%
K9s against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| K9s | 61.442 | 0.757 | 37.801 | 61.821 |
| 54s | 37.801 | 0.757 | 61.442 | 38.179 |
Here suited hands face each other, K9s on one side and 54s on the other. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.
K9s is ahead, but 54s is far from dead: it takes 378 of every 1,000 deals outright. Of every 100 boards, about 0.76 are split pots, and the equity figures already include them.
Place 29 of 169 belongs to K9s and place 136 belongs to 54s in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| K9s | 16,833,000 | 207,000 | 10,356,000 |
| 54s | 10,356,000 | 207,000 | 16,833,000 |
Exact total: 16 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| K9s | 1.619 | 1.628 | 2.645 | 0.618 |
| 54s | 0.618 | 2.645 | 1.628 | 1.619 |
The final column gives the least the pot must offer for each unit called for a call to break even at this equity.
Who is ahead on which flops
By flop texture, K9s' equity runs from 45.65% on low rainbow flops (nine high or lower) up to 65.54% on rainbow flops topped by a ten or better. 54s takes over on low rainbow flops (nine high or lower), so the favorite before the flop is the underdog on those boards.
| Flop | Share of flops | K9s wins | Ties | 54s wins | K9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 65.361 | 0.358 | 34.281 | 65.540 |
| Rainbow, nine or lower | 5.689 | 45.235 | 0.832 | 53.933 | 45.651 |
| Two-tone | 46.727 | 60.909 | 0.407 | 38.684 | 61.112 |
| Monotone | 5.273 | 57.513 | 3.612 | 38.875 | 59.319 |
| Paired | 17.091 | 63.727 | 1.398 | 34.875 | 64.426 |
Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.
Compared with a random hand
A random hand would give K9s 59.99% and 54s 41.45%. Against each other the change is +1.83 points for K9s and -3.27 for 54s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| K9s, all flops | 61.821 | 59.988 | +1.833 | 1.03056 |
| K9s, rainbow, ten or higher | 65.540 | 59.988 | +5.552 | 1.09255 |
| K9s, rainbow, nine or lower | 45.651 | 59.988 | -14.337 | 0.76100 |
| K9s, two-tone | 61.112 | 59.988 | +1.124 | 1.01874 |
| K9s, monotone | 59.319 | 59.988 | -0.669 | 0.98885 |
| K9s, paired | 64.426 | 59.988 | +4.438 | 1.07398 |
| 54s, all flops | 38.179 | 41.453 | -3.274 | 0.92102 |
| 54s, rainbow, ten or higher | 34.460 | 41.453 | -6.993 | 0.83130 |
| 54s, rainbow, nine or lower | 54.349 | 41.453 | +12.896 | 1.31110 |
| 54s, two-tone | 38.888 | 41.453 | -2.565 | 0.93812 |
| 54s, monotone | 40.681 | 41.453 | -0.772 | 0.98138 |
| 54s, paired | 35.574 | 41.453 | -5.879 | 0.85818 |
Does a shared suit matter?
Of the deals of this matchup, 4 share a suit (K9s at 63.98%) and 12 do not (61.10%). K9s does better with a shared suit, by 2.88 points.
| Deals | Specific deals | Share of deals | K9s wins | Ties | 54s wins | K9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 63.558 | 0.848 | 35.594 | 63.982 |
| No shared suit | 12 | 75.00 | 60.737 | 0.727 | 38.536 | 61.101 |
How often this matchup comes up
K9s against 54s is made up of 16 specific-card matchups in one seat order, 0.0010% of the 1,624,350 ordered deals, and 32 counting both seat orders, 0.0020%.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. K9s is worth $123.64 on average (+$23.64); 54s is worth $76.36 (-$23.64).
In 1,000 deals of exactly this matchup, expect about 614 won outright by K9s, about 378 won outright by 54s and about 8 split.
The same matchup from the other side
54s against K9s adds nothing new: it is 38.18% for 54s and 61.82% for K9s, the same figures reversed.
Keep exploring
Open the calculator with Ks9s against 5h4h 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
Nothing here is simulated. The 16 deals of K9s against 54s 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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