How deep can the small blind shove Q4s?
Q4s shoves every time as the small blind up to 14.5bb. At 14.5bb its shove is worth -0.4727 big blinds against -0.5000 for folding. Between 15bb and 16bb it mixes, so either choice is close to break-even there. In that zone the shove is worth -0.5000 big blinds, level with the -0.5000 for folding. Past 16bb the chart folds it.
| Stack | Shove frequency | Shove EV | Fold EV | Equity when called |
|---|---|---|---|---|
| 1bb | 100% | +0.037 | -0.500 | 51.9% |
| 2bb | 100% | +0.074 | -0.500 | 51.9% |
| 3bb | 100% | +0.114 | -0.500 | 50.6% |
| 4bb | 100% | +0.079 | -0.500 | 47.0% |
| 5bb | 100% | +0.005 | -0.500 | 43.9% |
| 6bb | 100% | -0.081 | -0.500 | 41.7% |
| 7bb | 100% | -0.168 | -0.500 | 40.0% |
| 8bb | 100% | -0.246 | -0.500 | 39.0% |
| 9bb | 100% | -0.289 | -0.500 | 37.9% |
| 10bb | 100% | -0.325 | -0.500 | 37.4% |
| 11bb | 100% | -0.354 | -0.500 | 37.1% |
| 12bb | 100% | -0.380 | -0.500 | 36.9% |
| 13bb | 100% | -0.423 | -0.500 | 36.3% |
| 14bb | 100% | -0.454 | -0.500 | 36.0% |
| 15bb | 84% | -0.500 | -0.500 | 36.0% |
| 16bb | 97% | -0.500 | -0.500 | 35.6% |
| 17bb | 0% | -0.506 | -0.500 | 35.2% |
| 18bb | 0% | -0.525 | -0.500 | 35.0% |
| 19bb | 0% | -0.532 | -0.500 | 35.0% |
| 20bb | 0% | -0.537 | -0.500 | 35.1% |
When should the big blind call with Q4s?
Q4s calls every time as the big blind up to 8bb. At 8bb its call is worth -0.9548 big blinds against -1.0000 for folding. At 8bb a call breaks even at 43.8% equity, because the big blind has already posted a full blind that folding gives up. At 8.5bb 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 8.5bb the chart folds it.
| Stack | Call frequency | Call EV | Fold EV | Equity vs shoves |
|---|---|---|---|---|
| 1bb | 100% | +0.037 | -1.000 | 51.9% |
| 2bb | 100% | +0.004 | -1.000 | 50.1% |
| 3bb | 100% | -0.127 | -1.000 | 47.9% |
| 4bb | 100% | -0.248 | -1.000 | 46.9% |
| 5bb | 100% | -0.366 | -1.000 | 46.3% |
| 6bb | 100% | -0.549 | -1.000 | 45.4% |
| 7bb | 100% | -0.717 | -1.000 | 44.9% |
| 8bb | 100% | -0.955 | -1.000 | 44.0% |
| 9bb | 0% | -1.133 | -1.000 | 43.7% |
| 10bb | 0% | -1.296 | -1.000 | 43.5% |
| 11bb | 0% | -1.624 | -1.000 | 42.6% |
| 12bb | 0% | -1.805 | -1.000 | 42.5% |
| 13bb | 0% | -2.017 | -1.000 | 42.2% |
| 14bb | 0% | -2.238 | -1.000 | 42.0% |
| 15bb | 0% | -2.586 | -1.000 | 41.4% |
| 16bb | 0% | -2.746 | -1.000 | 41.4% |
| 17bb | 0% | -3.026 | -1.000 | 41.1% |
| 18bb | 0% | -3.294 | -1.000 | 40.9% |
| 19bb | 0% | -3.570 | -1.000 | 40.6% |
| 20bb | 0% | -3.761 | -1.000 | 40.6% |
What makes Q4s different from similar hands?
Q4s is 4 combos out of the 1,326 two-card hands and ranks number 76 of the 169 starting-hand classes by equity against a random hand. From the small blind, Q4s shoves cleanly 7bb deeper than Q4o (14.5bb against 7.5bb). From the big blind, Q4s calls cleanly 2bb deeper than Q4o (8bb against 6bb). Suited hands win more often because of flushes, which is why the suited version is the more playable of the pair.
Where can I check other hands like Q4s?
The stack pages show the full shove and call charts at each depth, and the hands closest to Q4s in strength, along with Q4o, have pages of their own. The combos page counts the specific hands that make up Q4s and how card removal changes them.
How were the numbers for Q4s 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 Q4s a shove at 10bb heads-up?
- Yes. At 10bb the small blind shoves Q4s: shoving is worth -0.325 big blinds and folding -0.500.
- Should the big blind call a shove with Q4s at 15bb?
- No. At 15bb calling with Q4s is worth -2.586 big blinds against -1.000 for folding, so the chart folds.
- Why does Q4s 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. Q4s shoves every time only up to 14.5bb.