How deep can the small blind shove Q4o?
Q4o shoves every time as the small blind up to 7.5bb. At 7.5bb its shove is worth -0.4462 big blinds against -0.5000 for folding. At 8bb 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 8bb the chart folds it.
| Stack | Shove frequency | Shove EV | Fold EV | Equity when called |
|---|---|---|---|---|
| 1bb | 100% | -0.017 | -0.500 | 49.1% |
| 2bb | 100% | -0.035 | -0.500 | 49.1% |
| 3bb | 100% | -0.042 | -0.500 | 47.8% |
| 4bb | 100% | -0.102 | -0.500 | 43.9% |
| 5bb | 100% | -0.195 | -0.500 | 40.6% |
| 6bb | 100% | -0.299 | -0.500 | 38.3% |
| 7bb | 100% | -0.403 | -0.500 | 36.5% |
| 8bb | 19% | -0.500 | -0.500 | 35.4% |
| 9bb | 0% | -0.551 | -0.500 | 34.4% |
| 10bb | 0% | -0.597 | -0.500 | 33.8% |
| 11bb | 0% | -0.634 | -0.500 | 33.5% |
| 12bb | 0% | -0.670 | -0.500 | 33.3% |
| 13bb | 0% | -0.719 | -0.500 | 32.7% |
| 14bb | 0% | -0.757 | -0.500 | 32.3% |
| 15bb | 0% | -0.816 | -0.500 | 32.3% |
| 16bb | 0% | -0.816 | -0.500 | 31.9% |
| 17bb | 0% | -0.820 | -0.500 | 31.5% |
| 18bb | 0% | -0.844 | -0.500 | 31.3% |
| 19bb | 0% | -0.853 | -0.500 | 31.3% |
| 20bb | 0% | -0.863 | -0.500 | 31.4% |
When should the big blind call with Q4o?
Q4o calls every time as the big blind up to 6bb. At 6bb its call is worth -0.9275 big blinds against -1.0000 for folding. At 6bb a call breaks even at 41.7% equity, because the big blind has already posted a full blind that folding gives up. Past 6bb the chart folds it.
| Stack | Call frequency | Call EV | Fold EV | Equity vs shoves |
|---|---|---|---|---|
| 1bb | 100% | -0.017 | -1.000 | 49.1% |
| 2bb | 100% | -0.110 | -1.000 | 47.3% |
| 3bb | 100% | -0.307 | -1.000 | 44.9% |
| 4bb | 100% | -0.493 | -1.000 | 43.8% |
| 5bb | 100% | -0.674 | -1.000 | 43.3% |
| 6bb | 100% | -0.928 | -1.000 | 42.3% |
| 7bb | 0% | -1.163 | -1.000 | 41.7% |
| 8bb | 0% | -1.475 | -1.000 | 40.8% |
| 9bb | 0% | -1.721 | -1.000 | 40.4% |
| 10bb | 0% | -1.952 | -1.000 | 40.2% |
| 11bb | 0% | -2.358 | -1.000 | 39.3% |
| 12bb | 0% | -2.606 | -1.000 | 39.1% |
| 13bb | 0% | -2.888 | -1.000 | 38.9% |
| 14bb | 0% | -3.181 | -1.000 | 38.6% |
| 15bb | 0% | -3.605 | -1.000 | 38.0% |
| 16bb | 0% | -3.831 | -1.000 | 38.0% |
| 17bb | 0% | -4.179 | -1.000 | 37.7% |
| 18bb | 0% | -4.520 | -1.000 | 37.4% |
| 19bb | 0% | -4.866 | -1.000 | 37.2% |
| 20bb | 0% | -5.128 | -1.000 | 37.2% |
What makes Q4o different from similar hands?
Q4o is 12 combos out of the 1,326 two-card hands and ranks number 93 of the 169 starting-hand classes by equity against a random hand. From the small blind, Q4o shoves cleanly 7bb shallower than Q4s (7.5bb against 14.5bb). From the big blind, Q4o calls cleanly 2bb shallower than Q4s (6bb against 8bb). 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 Q4o?
The stack pages show the full shove and call charts at each depth, and the hands closest to Q4o in strength, along with Q4s, have pages of their own. The combos page counts the specific hands that make up Q4o and how card removal changes them.
How were the numbers for Q4o computed?
Both players hold one of the 169 starting-hand classes, weighted by the pairs of specific hands that share no card, so blockers count. Blinds are 0.5 and 1 with no ante and equal stacks. Each pair of classes is scored with its exact equity over every five-card board, and the solver repeats best responses against the other side's running average until the hands on the edge are made exactly indifferent.
Source: GeorgeLiPoker's own heads-up solver, run on its exact preflop equity table.
Questions
- Is Q4o a shove at 10bb heads-up?
- No. At 10bb the small blind folds Q4o: shoving is worth -0.597 big blinds and folding -0.500.
- Should the big blind call a shove with Q4o at 15bb?
- No. At 15bb calling with Q4o is worth -3.605 big blinds against -1.000 for folding, so the chart folds.
- Why does Q4o 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. Q4o shoves every time only up to 7.5bb.