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Push or fold with A2o heads-up

By GeorgeLiPokerUpdated

The solved heads-up answer for A2o: 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 15.5bb, mixes at 16bb alone and folds deeper. No ante, no prize pool.

  • 20bbShoves every time up to
  • 15.5bbCalls every time up to
  • 59Rank of 169
  • 12Combos

How deep can the small blind shove A2o?

A2o 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.

A2o as the small blind, by stack
StackShove frequencyShove EVFold EVEquity when called
1bb100%+0.099-0.50054.9%
2bb100%+0.197-0.50054.9%
3bb100%+0.286-0.50053.9%
4bb100%+0.387-0.50052.2%
5bb100%+0.446-0.50051.0%
6bb100%+0.448-0.50049.8%
7bb100%+0.446-0.50048.8%
8bb100%+0.424-0.50048.0%
9bb100%+0.368-0.50046.6%
10bb100%+0.323-0.50045.5%
11bb100%+0.263-0.50044.5%
12bb100%+0.212-0.50043.6%
13bb100%+0.154-0.50042.6%
14bb100%+0.094-0.50041.6%
15bb100%+0.040-0.50041.1%
16bb100%+0.004-0.50040.5%
17bb100%-0.032-0.50039.8%
18bb100%-0.098-0.50038.9%
19bb100%-0.129-0.50038.5%
20bb100%-0.191-0.50037.6%

When should the big blind call with A2o?

A2o calls every time as the big blind up to 15.5bb. At 15.5bb its call is worth -0.9597 big blinds against -1.0000 for folding. At 15.5bb a call breaks even at 46.8% equity, because the big blind has already posted a full blind that folding gives up. At 16bb 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 16bb the chart folds it.

A2o as the big blind, by stack
StackCall frequencyCall EVFold EVEquity vs shoves
1bb100%+0.099-1.00054.9%
2bb100%+0.147-1.00053.7%
3bb100%+0.161-1.00052.7%
4bb100%+0.176-1.00052.2%
5bb100%+0.181-1.00051.8%
6bb100%+0.173-1.00051.4%
7bb100%+0.159-1.00051.1%
8bb100%+0.067-1.00050.4%
9bb100%+0.007-1.00050.0%
10bb100%-0.039-1.00049.8%
11bb100%-0.151-1.00049.3%
12bb100%-0.267-1.00048.9%
13bb100%-0.396-1.00048.5%
14bb100%-0.626-1.00047.8%
15bb100%-0.857-1.00047.1%
16bb27%-1.000-1.00046.9%
17bb0%-1.231-1.00046.4%
18bb0%-1.355-1.00046.2%
19bb0%-1.607-1.00045.8%
20bb0%-1.802-1.00045.5%

What makes A2o different from similar hands?

A2o is 12 combos out of the 1,326 two-card hands and ranks number 59 of the 169 starting-hand classes by equity against a random hand. From the small blind, A2o and A2s both shove at every stack from 1 to 20bb. From the big blind, A2o calls every time only up to 15.5bb, while A2s calls at every stack from 1 to 20bb. 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 A2o?

The stack pages show the full shove and call charts at each depth, and the hands closest to A2o in strength have pages of their own. The combos page counts the specific hands that make up A2o and how card removal changes them.

How were the numbers for A2o 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 A2o a shove at 10bb heads-up?
Yes. At 10bb the small blind shoves A2o: shoving is worth +0.323 big blinds and folding -0.500.
Should the big blind call a shove with A2o at 15bb?
Yes. At 15bb calling with A2o is worth -0.857 big blinds against -1.000 for folding, so the chart calls.
Does A2o ever fold heads-up at 20bb or less?
Not from the small blind: A2o shoves at every stack from 1 to 20bb. As the big blind it calls cleanly up to 15.5bb and folds or mixes deeper.