Push or fold with 96s heads-up

The solved heads-up answer for 96s: out of the small blind it shoves at every stack up to 20bb, and out of the big blind it calls at every stack up to 5.5bb and folds deeper. No ante, no prize pool.

  • 20bbShoves every time up to
  • 5.5bbCalls every time up to
  • 103Rank of 169
  • 4Combos

How deep can the small blind shove 96s?

96s 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.

96s as the small blind, by stack
StackShove frequencyShove EVFold EVEquity when called
1bb100%-0.051-0.50047.4%
2bb100%-0.103-0.50047.4%
3bb100%-0.160-0.50045.7%
4bb100%-0.233-0.50041.7%
5bb100%-0.285-0.50039.5%
6bb100%-0.297-0.50038.8%
7bb100%-0.298-0.50038.3%
8bb100%-0.312-0.50038.3%
9bb100%-0.309-0.50038.0%
10bb100%-0.309-0.50037.8%
11bb100%-0.331-0.50037.6%
12bb100%-0.337-0.50037.8%
13bb100%-0.337-0.50037.7%
14bb100%-0.349-0.50037.6%
15bb100%-0.387-0.50037.6%
16bb100%-0.391-0.50037.1%
17bb100%-0.402-0.50036.8%
18bb100%-0.406-0.50036.8%
19bb100%-0.427-0.50036.5%
20bb100%-0.431-0.50036.5%

When should the big blind call with 96s?

96s calls every time as the big blind up to 5.5bb. At 5.5bb its call is worth -0.9422 big blinds against -1.0000 for folding. At 5.5bb a call breaks even at 40.9% equity, because the big blind has already posted a full blind that folding gives up. Past 5.5bb the chart folds it.

96s as the big blind, by stack
StackCall frequencyCall EVFold EVEquity vs shoves
1bb100%-0.051-1.00047.4%
2bb100%-0.201-1.00045.0%
3bb100%-0.463-1.00042.3%
4bb100%-0.671-1.00041.6%
5bb100%-0.844-1.00041.6%
6bb0%-1.026-1.00041.4%
7bb0%-1.190-1.00041.5%
8bb0%-1.492-1.00040.7%
9bb0%-1.678-1.00040.7%
10bb0%-1.825-1.00040.9%
11bb0%-2.146-1.00040.2%
12bb0%-2.378-1.00040.1%
13bb0%-2.651-1.00039.8%
14bb0%-2.956-1.00039.4%
15bb0%-3.374-1.00038.8%
16bb0%-3.565-1.00038.9%
17bb0%-3.880-1.00038.6%
18bb0%-4.109-1.00038.6%
19bb0%-4.428-1.00038.3%
20bb0%-4.698-1.00038.3%

What makes 96s different from similar hands?

96s is 4 combos out of the 1,326 two-card hands and ranks number 103 of the 169 starting-hand classes by equity against a random hand. From the small blind, 96s shoves at every stack from 1 to 20bb, while 96o shoves every time only up to 4.5bb. From the big blind, 96s calls cleanly 1.5bb deeper than 96o (5.5bb against 4bb). 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 96s?

The stack pages show the full shove and call charts at each depth, and the hands closest to 96s in strength, along with 96o, have pages of their own. The combos page counts the specific hands that make up 96s and how card removal changes them.

How were the numbers for 96s 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 96s a shove at 10bb heads-up?
Yes. At 10bb the small blind shoves 96s: shoving is worth -0.309 big blinds and folding -0.500.
Should the big blind call a shove with 96s at 15bb?
No. At 15bb calling with 96s is worth -3.374 big blinds against -1.000 for folding, so the chart folds.
Does 96s ever fold heads-up at 20bb or less?
Not from the small blind: 96s shoves at every stack from 1 to 20bb. As the big blind it calls cleanly up to 5.5bb and folds or mixes deeper.