Push or fold with Q6o heads-up

The solved heads-up answer for Q6o: out of the small blind it shoves at every stack up to 9.5bb and folds deeper, and out of the big blind it calls at every stack up to 7bb and folds deeper. No ante, no prize pool.

  • 9.5bbShoves every time up to
  • 7bbCalls every time up to
  • 81Rank of 169
  • 12Combos

How deep can the small blind shove Q6o?

Q6o shoves every time as the small blind up to 9.5bb. At 9.5bb its shove is worth -0.4849 big blinds against -0.5000 for folding. Past 9.5bb the chart folds it.

Q6o as the small blind, by stack
StackShove frequencyShove EVFold EVEquity when called
1bb100%+0.020-0.50051.0%
2bb100%+0.041-0.50051.0%
3bb100%+0.064-0.50049.7%
4bb100%+0.041-0.50046.1%
5bb100%-0.059-0.50042.7%
6bb100%-0.180-0.50040.1%
7bb100%-0.296-0.50037.9%
8bb100%-0.402-0.50036.8%
9bb100%-0.455-0.50035.6%
10bb0%-0.510-0.50034.8%
11bb0%-0.548-0.50034.5%
12bb0%-0.573-0.50034.5%
13bb0%-0.619-0.50033.8%
14bb0%-0.653-0.50033.5%
15bb0%-0.702-0.50033.6%
16bb0%-0.699-0.50033.3%
17bb0%-0.704-0.50032.9%
18bb0%-0.721-0.50032.7%
19bb0%-0.756-0.50032.2%
20bb0%-0.762-0.50032.4%

When should the big blind call with Q6o?

Q6o calls every time as the big blind up to 7bb. At 7bb its call is worth -0.8747 big blinds against -1.0000 for folding. At 7bb a call breaks even at 42.9% equity, because the big blind has already posted a full blind that folding gives up. Past 7bb the chart folds it.

Q6o as the big blind, by stack
StackCall frequencyCall EVFold EVEquity vs shoves
1bb100%+0.020-1.00051.0%
2bb100%-0.031-1.00049.2%
3bb100%-0.178-1.00047.0%
4bb100%-0.317-1.00046.0%
5bb100%-0.462-1.00045.4%
6bb100%-0.669-1.00044.4%
7bb100%-0.875-1.00043.8%
8bb0%-1.181-1.00042.6%
9bb0%-1.420-1.00042.1%
10bb0%-1.634-1.00041.8%
11bb0%-2.007-1.00040.9%
12bb0%-2.224-1.00040.7%
13bb0%-2.477-1.00040.5%
14bb0%-2.779-1.00040.1%
15bb0%-3.203-1.00039.3%
16bb0%-3.338-1.00039.6%
17bb0%-3.660-1.00039.2%
18bb0%-3.970-1.00039.0%
19bb0%-4.289-1.00038.7%
20bb0%-4.520-1.00038.7%

What makes Q6o different from similar hands?

Q6o is 12 combos out of the 1,326 two-card hands and ranks number 81 of the 169 starting-hand classes by equity against a random hand. From the small blind, Q6o shoves every time only up to 9.5bb, while Q6s shoves at every stack from 1 to 20bb. From the big blind, Q6o calls cleanly 2.5bb shallower than Q6s (7bb against 9.5bb). 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 Q6o?

The stack pages show the full shove and call charts at each depth, and the hands closest to Q6o in strength, along with Q6s, have pages of their own. The combos page counts the specific hands that make up Q6o and how card removal changes them.

How were the numbers for Q6o 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 Q6o a shove at 10bb heads-up?
No. At 10bb the small blind folds Q6o: shoving is worth -0.510 big blinds and folding -0.500.
Should the big blind call a shove with Q6o at 15bb?
No. At 15bb calling with Q6o is worth -3.203 big blinds against -1.000 for folding, so the chart folds.
Why does Q6o 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. Q6o shoves every time only up to 9.5bb.