Push or Fold: When Is It Only Shove or Fold?
There is no threshold beyond which you “just shove”. What changes is the selection — and not the way people expect: at 8 big blinds the solver opens 48 of 169 hands, at 15 only 30. Tighter, not wider.
The number
Counted are spots where nobody has entered the pot before you. A hand counts when the solver does not fold it in the majority of those spots.
| Stack | Hands of 169 | Spots |
|---|---|---|
| 8 big blinds | 48 | 21 |
| 10 big blinds | 47 | 18 |
| 12 big blinds | 46 | 17 |
| 15 big blinds | 30 | 15 |
The right-hand column belongs there: every step rests on 15 to 21 spots. That is enough for a direction and too little for a threshold. Anyone reading a cut-off out of this table is reading more than it says.
What that looks like
Each chart shows all 169 starting hands. The coloured cells are the ones you open.
8 big blinds — 48 hands
12 big blinds — 46 hands
15 big blinds — 30 hands
Why it gets tighter, not wider
At 8 big blinds every open is an all-in anyway. You risk little, you win the blinds often enough, and a mistake costs a manageable amount — so the selection is allowed to be wide.
At 15 big blinds you can raise and still fold afterwards. That is precisely what narrows the selection: get put under pressure after raising and you lose more than three blinds. The rule of thumb “the shorter, the tighter” has it backwards here.
You can see it in the charts, in the small pairs and the weak aces: at 8 big blinds they are in, at 15 they are gone.
Where this answer stops
All numbers describe the first entry into the pot, in tournaments with a payout ladder. Once somebody has raised in front of you it is a different question. And the steps are averaged across seats — under the gun every row looks tighter than it does on the button.