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Push or fold with 87s heads-up

By GeorgeLiPokerUpdated

87s shoves at every stack up to 20bb from the small blind. From the big blind it calls at every stack up to 6.5bb and folds deeper. Both come from a solved heads-up game with no ante.

  • 20bbShoves every time up to
  • 6.5bbCalls every time up to
  • 100Rank of 169
  • 4Combos

How deep can the small blind shove 87s?

87s 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.

87s as the small blind, by stack
StackShove frequencyShove EVFold EVEquity when called
1bb100%-0.041-0.50047.9%
2bb100%-0.083-0.50047.9%
3bb100%-0.135-0.50046.2%
4bb100%-0.164-0.50042.9%
5bb100%-0.191-0.50041.0%
6bb100%-0.189-0.50040.3%
7bb100%-0.174-0.50040.2%
8bb100%-0.184-0.50040.2%
9bb100%-0.172-0.50039.9%
10bb100%-0.162-0.50039.9%
11bb100%-0.184-0.50039.6%
12bb100%-0.194-0.50039.5%
13bb100%-0.184-0.50039.6%
14bb100%-0.178-0.50039.7%
15bb100%-0.211-0.50039.7%
16bb100%-0.215-0.50039.3%
17bb100%-0.228-0.50038.9%
18bb100%-0.232-0.50038.9%
19bb100%-0.251-0.50038.5%
20bb100%-0.253-0.50038.5%

When should the big blind call with 87s?

87s calls every time as the big blind up to 6.5bb. At 6.5bb its call is worth -0.9617 big blinds against -1.0000 for folding. At 6.5bb a call breaks even at 42.3% equity, because the big blind has already posted a full blind that folding gives up. Past 6.5bb the chart folds it.

87s as the big blind, by stack
StackCall frequencyCall EVFold EVEquity vs shoves
1bb100%-0.041-1.00047.9%
2bb100%-0.178-1.00045.5%
3bb100%-0.404-1.00043.3%
4bb100%-0.576-1.00042.8%
5bb100%-0.722-1.00042.8%
6bb100%-0.895-1.00042.5%
7bb0%-1.058-1.00042.4%
8bb0%-1.339-1.00041.6%
9bb0%-1.492-1.00041.7%
10bb0%-1.643-1.00041.8%
11bb0%-1.894-1.00041.4%
12bb0%-2.110-1.00041.2%
13bb0%-2.362-1.00040.9%
14bb0%-2.588-1.00040.8%
15bb0%-2.859-1.00040.5%
16bb0%-3.091-1.00040.3%
17bb0%-3.308-1.00040.3%
18bb0%-3.478-1.00040.3%
19bb0%-3.689-1.00040.3%
20bb0%-3.920-1.00040.2%

What makes 87s different from similar hands?

87s is 4 combos out of the 1,326 two-card hands and ranks number 100 of the 169 starting-hand classes by equity against a random hand. From the small blind, 87s shoves at every stack from 1 to 20bb, while 87o shoves every time only up to 14.5bb. From the big blind, 87s calls cleanly 2bb deeper than 87o (6.5bb against 4.5bb). 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 87s?

The stack pages show the full shove and call charts at each depth, and the hands closest to 87s in strength, along with 87o, have pages of their own. The combos page counts the specific hands that make up 87s and how card removal changes them.

How were the numbers for 87s 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 87s a shove at 10bb heads-up?
Yes. At 10bb the small blind shoves 87s: shoving is worth -0.162 big blinds and folding -0.500.
Should the big blind call a shove with 87s at 15bb?
No. At 15bb calling with 87s is worth -2.859 big blinds against -1.000 for folding, so the chart folds.
Does 87s ever fold heads-up at 20bb or less?
Not from the small blind: 87s shoves at every stack from 1 to 20bb. As the big blind it calls cleanly up to 6.5bb and folds or mixes deeper.