How deep can the small blind shove 84s?
84s shoves every time as the small blind up to 7.5bb. At 7.5bb its shove is worth -0.4829 big blinds against -0.5000 for folding. Between 8bb and 10bb it mixes, so either choice is close to break-even there. At 8bb the shove is worth -0.5015 big blinds against -0.5000 for folding. Past 10bb the chart folds it.
| Stack | Shove frequency | Shove EV | Fold EV | Equity when called |
|---|---|---|---|---|
| 1bb | 100% | -0.146 | -0.500 | 42.7% |
| 2bb | 100% | -0.292 | -0.500 | 42.7% |
| 3bb | 100% | -0.424 | -0.500 | 41.0% |
| 4bb | 100% | -0.469 | -0.500 | 38.1% |
| 5bb | 100% | -0.474 | -0.500 | 36.8% |
| 6bb | 100% | -0.478 | -0.500 | 36.1% |
| 7bb | 100% | -0.469 | -0.500 | 36.1% |
| 8bb | 0% | -0.502 | -0.500 | 36.0% |
| 9bb | 0% | -0.501 | -0.500 | 35.5% |
| 10bb | 100% | -0.494 | -0.500 | 35.7% |
| 11bb | 0% | -0.523 | -0.500 | 35.5% |
| 12bb | 0% | -0.544 | -0.500 | 35.3% |
| 13bb | 0% | -0.550 | -0.500 | 35.2% |
| 14bb | 0% | -0.556 | -0.500 | 35.3% |
| 15bb | 0% | -0.605 | -0.500 | 35.3% |
| 16bb | 0% | -0.614 | -0.500 | 34.8% |
| 17bb | 0% | -0.628 | -0.500 | 34.3% |
| 18bb | 0% | -0.641 | -0.500 | 34.2% |
| 19bb | 0% | -0.638 | -0.500 | 34.4% |
| 20bb | 0% | -0.650 | -0.500 | 34.3% |
When should the big blind call with 84s?
84s calls every time as the big blind up to 4bb. At 4bb its call is worth -0.9615 big blinds against -1.0000 for folding. At 4bb a call breaks even at 37.5% equity, because the big blind has already posted a full blind that folding gives up. Past 4bb the chart folds it.
| Stack | Call frequency | Call EV | Fold EV | Equity vs shoves |
|---|---|---|---|---|
| 1bb | 100% | -0.146 | -1.000 | 42.7% |
| 2bb | 100% | -0.390 | -1.000 | 40.3% |
| 3bb | 100% | -0.710 | -1.000 | 38.2% |
| 4bb | 100% | -0.962 | -1.000 | 38.0% |
| 5bb | 0% | -1.200 | -1.000 | 38.0% |
| 6bb | 0% | -1.446 | -1.000 | 38.0% |
| 7bb | 0% | -1.688 | -1.000 | 37.9% |
| 8bb | 0% | -2.010 | -1.000 | 37.4% |
| 9bb | 0% | -2.260 | -1.000 | 37.4% |
| 10bb | 0% | -2.524 | -1.000 | 37.4% |
| 11bb | 0% | -2.900 | -1.000 | 36.8% |
| 12bb | 0% | -3.207 | -1.000 | 36.6% |
| 13bb | 0% | -3.558 | -1.000 | 36.3% |
| 14bb | 0% | -3.818 | -1.000 | 36.4% |
| 15bb | 0% | -4.129 | -1.000 | 36.2% |
| 16bb | 0% | -4.436 | -1.000 | 36.1% |
| 17bb | 0% | -4.780 | -1.000 | 35.9% |
| 18bb | 0% | -5.045 | -1.000 | 36.0% |
| 19bb | 0% | -5.311 | -1.000 | 36.0% |
| 20bb | 0% | -5.631 | -1.000 | 35.9% |
What makes 84s different from similar hands?
84s is 4 combos out of the 1,326 two-card hands and ranks number 129 of the 169 starting-hand classes by equity against a random hand. From the small blind, 84s shoves cleanly 5.5bb deeper than 84o (7.5bb against 2bb). From the big blind, 84s calls cleanly 1bb deeper than 84o (4bb against 3bb). 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 84s?
The stack pages show the full shove and call charts at each depth, and the hands closest to 84s in strength, along with 84o, have pages of their own. The combos page counts the specific hands that make up 84s and how card removal changes them.
How were the numbers for 84s 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 84s a shove at 10bb heads-up?
- Yes. At 10bb the small blind shoves 84s: shoving is worth -0.494 big blinds and folding -0.500.
- Should the big blind call a shove with 84s at 15bb?
- No. At 15bb calling with 84s is worth -4.129 big blinds against -1.000 for folding, so the chart folds.
- Why does 84s 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. 84s shoves every time only up to 7.5bb.