How deep can the small blind shove A4o?
A4o shoves at every stack from 1 to 20 big blinds as the small blind. Its shove EV stays above the -0.5000 big blinds it earns by folding at each of them.
| Stack | Shove frequency | Shove EV | Fold EV | Equity when called |
|---|---|---|---|---|
| 1bb | 100% | +0.135 | -0.500 | 56.7% |
| 2bb | 100% | +0.269 | -0.500 | 56.7% |
| 3bb | 100% | +0.409 | -0.500 | 55.9% |
| 4bb | 100% | +0.482 | -0.500 | 53.8% |
| 5bb | 100% | +0.529 | -0.500 | 52.4% |
| 6bb | 100% | +0.542 | -0.500 | 51.2% |
| 7bb | 100% | +0.532 | -0.500 | 50.1% |
| 8bb | 100% | +0.520 | -0.500 | 49.4% |
| 9bb | 100% | +0.471 | -0.500 | 48.0% |
| 10bb | 100% | +0.416 | -0.500 | 46.8% |
| 11bb | 100% | +0.366 | -0.500 | 45.9% |
| 12bb | 100% | +0.320 | -0.500 | 45.0% |
| 13bb | 100% | +0.260 | -0.500 | 44.0% |
| 14bb | 100% | +0.206 | -0.500 | 43.1% |
| 15bb | 100% | +0.159 | -0.500 | 42.7% |
| 16bb | 100% | +0.119 | -0.500 | 41.8% |
| 17bb | 100% | +0.073 | -0.500 | 40.9% |
| 18bb | 100% | +0.012 | -0.500 | 40.0% |
| 19bb | 100% | -0.025 | -0.500 | 39.6% |
| 20bb | 100% | -0.083 | -0.500 | 38.8% |
When should the big blind call with A4o?
A4o calls every time as the big blind up to 18bb. At 18bb its call is worth -0.9030 big blinds against -1.0000 for folding. At 18bb a call breaks even at 47.2% equity, because the big blind has already posted a full blind that folding gives up. At 18.5bb it mixes, so either choice is close to break-even at that stack. At that stack the call is worth -1.0000 big blinds, level with the -1.0000 for folding. Past 18.5bb the chart folds it.
| Stack | Call frequency | Call EV | Fold EV | Equity vs shoves |
|---|---|---|---|---|
| 1bb | 100% | +0.135 | -1.000 | 56.7% |
| 2bb | 100% | +0.225 | -1.000 | 55.6% |
| 3bb | 100% | +0.257 | -1.000 | 54.3% |
| 4bb | 100% | +0.299 | -1.000 | 53.7% |
| 5bb | 100% | +0.350 | -1.000 | 53.5% |
| 6bb | 100% | +0.355 | -1.000 | 53.0% |
| 7bb | 100% | +0.382 | -1.000 | 52.7% |
| 8bb | 100% | +0.297 | -1.000 | 51.9% |
| 9bb | 100% | +0.281 | -1.000 | 51.6% |
| 10bb | 100% | +0.275 | -1.000 | 51.4% |
| 11bb | 100% | +0.167 | -1.000 | 50.8% |
| 12bb | 100% | +0.105 | -1.000 | 50.4% |
| 13bb | 100% | +0.000 | -1.000 | 50.0% |
| 14bb | 100% | -0.264 | -1.000 | 49.1% |
| 15bb | 100% | -0.462 | -1.000 | 48.5% |
| 16bb | 100% | -0.574 | -1.000 | 48.2% |
| 17bb | 100% | -0.808 | -1.000 | 47.6% |
| 18bb | 100% | -0.903 | -1.000 | 47.5% |
| 19bb | 0% | -1.121 | -1.000 | 47.0% |
| 20bb | 0% | -1.282 | -1.000 | 46.8% |
What makes A4o different from similar hands?
A4o is 12 combos out of the 1,326 two-card hands and ranks number 49 of the 169 starting-hand classes by equity against a random hand. From the small blind, A4o and A4s both shove at every stack from 1 to 20bb. From the big blind, A4o calls every time only up to 18bb, while A4s calls at every stack from 1 to 20bb. 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 A4o?
The stack pages show the full shove and call charts at each depth, and the hands closest to A4o in strength have pages of their own. The combos page counts the specific hands that make up A4o and how card removal changes them.
How were the numbers for A4o computed?
We solve a chips-only game for two players: small blind 0.5, big blind 1, no ante, equal stacks. Starting hands are the 169 classes, weighted so that shared cards are impossible, and equity comes from counting every five-card board. The solver plays itself with best responses, averages them, and fixes the hands on the edge so they are exactly indifferent.
Source: GeorgeLiPoker's own heads-up solver, run on its exact preflop equity table.
Questions
- Is A4o a shove at 10bb heads-up?
- Yes. At 10bb the small blind shoves A4o: shoving is worth +0.416 big blinds and folding -0.500.
- Should the big blind call a shove with A4o at 15bb?
- Yes. At 15bb calling with A4o is worth -0.462 big blinds against -1.000 for folding, so the chart calls.
- Does A4o ever fold heads-up at 20bb or less?
- Not from the small blind: A4o shoves at every stack from 1 to 20bb. As the big blind it calls cleanly up to 18bb and folds or mixes deeper.