KTo
67.41%
Wins 65.84%, ties 3.13%
T9s
32.59%
Wins 31.03%, ties 3.13%
KTo against T9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KTo | 65.842 | 3.129 | 31.029 | 67.407 |
| T9s | 31.029 | 3.129 | 65.842 | 32.593 |
One side is an offsuit hand, the other is a suited hand. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
KTo is the clear favorite, though T9s gets there on roughly one board in 3. Ties are part of the picture: 3.13% of boards end in a split pot, and each side counts that as half a win.
The hand ranking puts KTo at 33 and T9s at 64 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KTo | 40,587,000 | 1,929,000 | 19,127,000 |
| T9s | 19,127,000 | 1,929,000 | 40,587,000 |
The total is exact: 36 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) |
|---|---|---|---|---|
| KTo | 2.068 | 1.519 | 3.223 | 0.484 |
| T9s | 0.484 | 3.223 | 1.519 | 2.068 |
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
Break the boards down by their first three cards and KTo is strongest on rainbow flops topped by a ten or better (72.72%) and weakest on low rainbow flops (nine high or lower) (55.62%). KTo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | KTo wins | Ties | T9s wins | KTo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.905 | 71.290 | 2.851 | 25.859 | 72.716 |
| Rainbow, nine or lower | 7.042 | 54.239 | 2.760 | 43.001 | 55.619 |
| Two-tone | 46.527 | 64.214 | 2.664 | 33.122 | 65.546 |
| Monotone | 5.192 | 61.384 | 4.013 | 34.603 | 63.391 |
| Paired | 17.334 | 68.747 | 4.647 | 26.606 | 71.071 |
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 KTo 59.74% and T9s 54.03%. Against each other the change is +7.67 points for KTo and -21.44 for T9s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KTo, all flops | 67.407 | 59.739 | +7.668 | 1.12836 |
| KTo, rainbow, ten or higher | 72.716 | 59.739 | +12.977 | 1.21723 |
| KTo, rainbow, nine or lower | 55.619 | 59.739 | -4.120 | 0.93103 |
| KTo, two-tone | 65.546 | 59.739 | +5.807 | 1.09721 |
| KTo, monotone | 63.391 | 59.739 | +3.652 | 1.06113 |
| KTo, paired | 71.071 | 59.739 | +11.332 | 1.18969 |
| T9s, all flops | 32.593 | 54.028 | -21.435 | 0.60326 |
| T9s, rainbow, ten or higher | 27.284 | 54.028 | -26.744 | 0.50500 |
| T9s, rainbow, nine or lower | 44.381 | 54.028 | -9.647 | 0.82144 |
| T9s, two-tone | 34.454 | 54.028 | -19.574 | 0.63771 |
| T9s, monotone | 36.609 | 54.028 | -17.419 | 0.67759 |
| T9s, paired | 28.929 | 54.028 | -25.099 | 0.53544 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and KTo holds 68.42%. In 24 they do not, and it holds 66.90%. KTo does better with a shared suit, by 1.52 points.
| Deals | Specific deals | Share of deals | KTo wins | Ties | T9s wins | KTo equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 66.801 | 3.229 | 29.970 | 68.416 |
| No shared suit | 24 | 66.67 | 65.363 | 3.079 | 31.558 | 66.902 |
How often this matchup comes up
How often does it happen? 36 of the 1,624,350 ordered deals (0.0022%) are KTo against T9s, and 72 (0.0044%) if either hand may sit in either seat.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. KTo averages $134.82 from the $200, up $34.82; T9s averages $65.18, down $34.82.
Run 1,000 deals and the tally comes out near 659 for KTo, 310 for T9s and 31 ties.
The same matchup from the other side
One page covers both views. From T9s' side the equity is 32.59%, and from KTo's side it is 67.41%.
Keep exploring
KsTh against Td9d 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 36 specific deals of KTo against T9s, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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