KTo
40.45%
Wins 40.21%, ties 0.48%
A4s
59.55%
Wins 59.31%, ties 0.48%
KTo against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KTo | 40.214 | 0.480 | 59.306 | 40.454 |
| A4s | 59.306 | 0.480 | 40.214 | 59.546 |
The matchup pits an offsuit hand against a suited hand. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A 19.10 point lead is real, and KTo still takes about 402 of every 1,000 deals outright. Ties are 0.48% of the outcomes here; each tied board gives both hands half the pot.
KTo ranks number 33 of 169 starting hands, and A4s ranks number 35, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KTo | 33,052,000 | 395,000 | 48,744,000 |
| A4s | 48,744,000 | 395,000 | 33,052,000 |
The total is exact: 48 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 | 0.679 | 2.487 | 1.686 | 1.472 |
| A4s | 1.472 | 1.686 | 2.487 | 0.679 |
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
Across the five flop textures A4s' equity moves by 24.02 points, from 52.11% on rainbow flops topped by a ten or better to 76.13% on low rainbow flops (nine high or lower). A4s 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 | A4s wins | KTo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 47.809 | 0.169 | 52.022 | 47.893 |
| Rainbow, nine or lower | 7.042 | 23.433 | 0.884 | 75.683 | 23.875 |
| Two-tone | 46.667 | 40.652 | 0.307 | 59.041 | 40.805 |
| Monotone | 5.212 | 42.528 | 2.401 | 55.071 | 43.728 |
| Paired | 17.091 | 34.568 | 0.637 | 64.795 | 34.887 |
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: 59.74% for KTo, 59.03% for A4s. Here the change is -19.29 and +0.52 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KTo, all flops | 40.454 | 59.739 | -19.285 | 0.67718 |
| KTo, rainbow, ten or higher | 47.893 | 59.739 | -11.846 | 0.80170 |
| KTo, rainbow, nine or lower | 23.875 | 59.739 | -35.864 | 0.39966 |
| KTo, two-tone | 40.805 | 59.739 | -18.934 | 0.68305 |
| KTo, monotone | 43.728 | 59.739 | -16.011 | 0.73198 |
| KTo, paired | 34.887 | 59.739 | -24.852 | 0.58399 |
| A4s, all flops | 59.546 | 59.034 | +0.512 | 1.00867 |
| A4s, rainbow, ten or higher | 52.107 | 59.034 | -6.927 | 0.88266 |
| A4s, rainbow, nine or lower | 76.125 | 59.034 | +17.091 | 1.28951 |
| A4s, two-tone | 59.195 | 59.034 | +0.161 | 1.00273 |
| A4s, monotone | 56.272 | 59.034 | -2.762 | 0.95321 |
| A4s, paired | 65.113 | 59.034 | +6.079 | 1.10297 |
Does a shared suit matter?
When the hands share a suit, A4s holds 59.21%; when they do not, it holds 59.89%. A4s does better with no shared suit, by 0.68 points.
| Deals | Specific deals | Share of deals | KTo wins | Ties | A4s wins | KTo equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 40.533 | 0.522 | 58.945 | 40.794 |
| No shared suit | 24 | 50.00 | 39.896 | 0.438 | 59.666 | 40.115 |
How often this matchup comes up
You will meet this exact matchup 0.0059% of the time in a random heads-up deal: 96 of 1,624,350, counting either seat order.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. A4s is worth $119.10 on average (+$19.10); KTo is worth $80.90 (-$19.10).
Run 1,000 deals and the tally comes out near 593 for A4s, 402 for KTo and 5 ties.
The same matchup from the other side
Swap the hands and you get A4s with 59.55% against KTo with 40.45%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
Try KsTh against Ad4d in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.
How this was computed
This is an exact count with no sampling. For the 48 ways to deal one KTo and one A4s without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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