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Push or fold with T9s heads-up

By GeorgeLiPokerUpdated

The solved heads-up answer for T9s: 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 11bb, mixes at 11.5bb alone and folds deeper. No ante, no prize pool.

  • 20bbShoves every time up to
  • 11bbCalls every time up to
  • 64Rank of 169
  • 4Combos

How deep can the small blind shove T9s?

T9s 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.

T9s as the small blind, by stack
StackShove frequencyShove EVFold EVEquity when called
1bb100%+0.081-0.50054.0%
2bb100%+0.161-0.50054.0%
3bb100%+0.226-0.50052.6%
4bb100%+0.175-0.50048.5%
5bb100%+0.113-0.50045.7%
6bb100%+0.076-0.50044.2%
7bb100%+0.022-0.50042.8%
8bb100%-0.003-0.50042.3%
9bb100%-0.026-0.50041.5%
10bb100%-0.033-0.50041.2%
11bb100%-0.055-0.50040.8%
12bb100%-0.064-0.50040.8%
13bb100%-0.059-0.50040.8%
14bb100%-0.069-0.50040.6%
15bb100%-0.099-0.50040.6%
16bb100%-0.098-0.50040.2%
17bb100%-0.101-0.50040.0%
18bb100%-0.098-0.50040.1%
19bb100%-0.112-0.50039.8%
20bb100%-0.102-0.50039.9%

When should the big blind call with T9s?

T9s calls every time as the big blind up to 11bb. At 11bb its call is worth -0.9401 big blinds against -1.0000 for folding. At 11bb a call breaks even at 45.5% equity, because the big blind has already posted a full blind that folding gives up. At 11.5bb 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 11.5bb the chart folds it.

T9s as the big blind, by stack
StackCall frequencyCall EVFold EVEquity vs shoves
1bb100%+0.081-1.00054.0%
2bb100%+0.084-1.00052.1%
3bb100%-0.027-1.00049.6%
4bb100%-0.125-1.00048.4%
5bb100%-0.196-1.00048.0%
6bb100%-0.283-1.00047.6%
7bb100%-0.341-1.00047.6%
8bb100%-0.497-1.00046.9%
9bb100%-0.547-1.00047.0%
10bb100%-0.654-1.00046.7%
11bb100%-0.940-1.00045.7%
12bb0%-1.069-1.00045.5%
13bb0%-1.205-1.00045.4%
14bb0%-1.363-1.00045.1%
15bb0%-1.675-1.00044.4%
16bb0%-1.811-1.00044.3%
17bb0%-2.068-1.00043.9%
18bb0%-2.293-1.00043.6%
19bb0%-2.527-1.00043.3%
20bb0%-2.678-1.00043.3%

What makes T9s different from similar hands?

T9s is 4 combos out of the 1,326 two-card hands and ranks number 64 of the 169 starting-hand classes by equity against a random hand. From the small blind, T9s and T9o both shove at every stack from 1 to 20bb. From the big blind, T9s calls cleanly 3bb deeper than T9o (11bb against 8bb). 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 T9s?

The stack pages show the full shove and call charts at each depth, and the hands closest to T9s in strength, along with T9o, have pages of their own. The combos page counts the specific hands that make up T9s and how card removal changes them.

How were the numbers for T9s computed?

The game has two players, blinds of 0.5 and 1, no ante and one effective stack. Every one of the 169 starting-hand classes is dealt in proportion to the card-compatible pairs of specific hands, and a showdown is settled with the exact equity from our preflop table. Each side keeps answering the other's average strategy until neither can gain, then the borderline hands are solved exactly.

Source: GeorgeLiPoker's own heads-up solver, run on its exact preflop equity table.

Questions

Is T9s a shove at 10bb heads-up?
Yes. At 10bb the small blind shoves T9s: shoving is worth -0.033 big blinds and folding -0.500.
Should the big blind call a shove with T9s at 15bb?
No. At 15bb calling with T9s is worth -1.675 big blinds against -1.000 for folding, so the chart folds.
Does T9s ever fold heads-up at 20bb or less?
Not from the small blind: T9s shoves at every stack from 1 to 20bb. As the big blind it calls cleanly up to 11bb and folds or mixes deeper.