How deep can the small blind shove K3o?
K3o shoves every time as the small blind up to 12bb. At 12bb its shove is worth -0.4843 big blinds against -0.5000 for folding. At 12.5bb it mixes, so either choice is close to break-even at that stack. At that stack the shove is worth -0.5000 big blinds, level with the -0.5000 for folding. Past 12.5bb the chart folds it.
| Stack | Shove frequency | Shove EV | Fold EV | Equity when called |
|---|---|---|---|---|
| 1bb | 100% | +0.029 | -0.500 | 51.4% |
| 2bb | 100% | +0.057 | -0.500 | 51.4% |
| 3bb | 100% | +0.087 | -0.500 | 50.2% |
| 4bb | 100% | +0.102 | -0.500 | 47.4% |
| 5bb | 100% | +0.081 | -0.500 | 45.1% |
| 6bb | 100% | +0.006 | -0.500 | 43.0% |
| 7bb | 100% | -0.067 | -0.500 | 41.1% |
| 8bb | 100% | -0.164 | -0.500 | 39.6% |
| 9bb | 100% | -0.245 | -0.500 | 38.1% |
| 10bb | 100% | -0.333 | -0.500 | 36.7% |
| 11bb | 100% | -0.400 | -0.500 | 36.0% |
| 12bb | 100% | -0.484 | -0.500 | 35.1% |
| 13bb | 0% | -0.543 | -0.500 | 34.4% |
| 14bb | 0% | -0.597 | -0.500 | 33.9% |
| 15bb | 0% | -0.671 | -0.500 | 33.6% |
| 16bb | 0% | -0.711 | -0.500 | 32.7% |
| 17bb | 0% | -0.704 | -0.500 | 32.6% |
| 18bb | 0% | -0.724 | -0.500 | 32.6% |
| 19bb | 0% | -0.738 | -0.500 | 32.3% |
| 20bb | 0% | -0.831 | -0.500 | 31.3% |
When should the big blind call with K3o?
K3o calls every time as the big blind up to 8.5bb. At 8.5bb its call is worth -0.9319 big blinds against -1.0000 for folding. At 8.5bb a call breaks even at 44.1% equity, because the big blind has already posted a full blind that folding gives up. Past 8.5bb the chart folds it.
| Stack | Call frequency | Call EV | Fold EV | Equity vs shoves |
|---|---|---|---|---|
| 1bb | 100% | +0.029 | -1.000 | 51.4% |
| 2bb | 100% | -0.011 | -1.000 | 49.7% |
| 3bb | 100% | -0.113 | -1.000 | 48.1% |
| 4bb | 100% | -0.213 | -1.000 | 47.3% |
| 5bb | 100% | -0.311 | -1.000 | 46.9% |
| 6bb | 100% | -0.459 | -1.000 | 46.2% |
| 7bb | 100% | -0.592 | -1.000 | 45.8% |
| 8bb | 100% | -0.879 | -1.000 | 44.5% |
| 9bb | 0% | -1.081 | -1.000 | 44.0% |
| 10bb | 0% | -1.289 | -1.000 | 43.6% |
| 11bb | 0% | -1.648 | -1.000 | 42.5% |
| 12bb | 0% | -1.856 | -1.000 | 42.3% |
| 13bb | 0% | -2.106 | -1.000 | 41.9% |
| 14bb | 0% | -2.516 | -1.000 | 41.0% |
| 15bb | 0% | -2.891 | -1.000 | 40.4% |
| 16bb | 0% | -3.078 | -1.000 | 40.4% |
| 17bb | 0% | -3.370 | -1.000 | 40.1% |
| 18bb | 0% | -3.650 | -1.000 | 39.9% |
| 19bb | 0% | -3.892 | -1.000 | 39.8% |
| 20bb | 0% | -4.140 | -1.000 | 39.6% |
What makes K3o different from similar hands?
K3o is 12 combos out of the 1,326 two-card hands and ranks number 80 of the 169 starting-hand classes by equity against a random hand. From the small blind, K3o shoves cleanly 7.5bb shallower than K3s (12bb against 19.5bb). From the big blind, K3o calls cleanly 2.5bb shallower than K3s (8.5bb against 11bb). The offsuit version has three times as many combos but gives up the flush equity of its suited twin.
Where can I check other hands like K3o?
The stack pages show the full shove and call charts at each depth, and the hands closest to K3o in strength, along with K3s, have pages of their own. The combos page counts the specific hands that make up K3o and how card removal changes them.
How were the numbers for K3o computed?
The game has two players, blinds of 0.5 and 1, no ante and one effective stack. Every one of the 169 starting-hand classes is dealt in proportion to the card-compatible pairs of specific hands, and a showdown is settled with the exact equity from our preflop table. Each side keeps answering the other's average strategy until neither can gain, then the borderline hands are solved exactly.
Source: GeorgeLiPoker's own heads-up solver, run on its exact preflop equity table.
Questions
- Is K3o a shove at 10bb heads-up?
- Yes. At 10bb the small blind shoves K3o: shoving is worth -0.333 big blinds and folding -0.500.
- Should the big blind call a shove with K3o at 15bb?
- No. At 15bb calling with K3o is worth -2.891 big blinds against -1.000 for folding, so the chart folds.
- Why does K3o change from a shove to a fold as stacks grow?
- Deeper stacks put more chips at risk for the same blinds, and the big blind can afford to call a smaller share of hands. K3o shoves every time only up to 12bb.