What Percentage of Hands Should You Shove? Nash Ranges by Seat, 1 to 25 BB

Fold to you on the button with 10 big blinds and the Nash answer is to shove 43% of your hands. Under the gun with the same 10, it's 15%. The stack hasn't changed. The button moves in with about three times as many hands.

The cutoff sits in between at 34%. The small blind, with only the big blind left to get past, shoves 72%. Those are nine-handed numbers with a big blind ante, and chips are counted at face value. At six-max, read the lojack row as under the gun: 24.3% at 10 big blinds.

Every number here comes from the same solve that draws our push/fold chart. The chart answers one hand at a time. This page lays the whole solve out by seat and stack, so you can see where the big changes happen. A chart built on another ante or a different model will give different figures.

Shove percentage by seat, 5 to 25 big blinds

Each cell is the share of all 1,326 starting-hand combinations that are a profitable shove when the action folds to you.

Why seat matters more than stack size

Double your stack on the button, from 10 big blinds to 20, and the range drops from 43% to 32%. Keep the 10 and move to under the gun, and it drops to 15%. Between 10 and 20 big blinds, your seat matters more than your stack. Every player still to act behind you is one more chance that somebody has a hand worth calling with.

The small blind has one player to get past and half a blind already in the pot. At 10 big blinds it shoves 72% of hands, and it doesn't drop below half the deck until 23 big blinds. Every other seat is under half by 7 big blinds.

The button shoves 60.5% at 5 big blinds and 43.0% at 10. Fifteen more big blinds only take it down to 30.0%.

Below 5 big blinds the seats bunch together. At 3 big blinds the big blind calls a shove from any seat with every hand, because the price is too good to fold anything. The table shows every seat from under the gun to the button at 86.7% there, which is the button's number. The raw solve had the early seats a little wider, because it lets only one player call, and that flatters the early seats when stacks are this short. So the table never lets an earlier seat shove wider than a later one. Any two cards only becomes a shove at 1.5 big blinds or less, or 2 from the small blind.

Against a button shove at 10 big blinds, the big blind calls with 35% of hands, where the button was shoving 43%. Against the small blind it calls 54% against a 72% shove. The shover also wins every time everyone folds. The caller only wins at showdown. The big blind calling range article has the calling side for every seat.

The 25 big blind column is the roughest. That deep, a lot of shoves are worth a fraction of a big blind either way, so small differences move whole hands in and out. The lojack drops from 16.7% at 20 big blinds to 9.2% at 25, while the hijack barely moves (18.3% to 17.2%). The solve stops at 25, so it says nothing about deeper stacks.

Which hands to shove at 10 big blinds, by seat

These are the 10 big blind percentages written out as hands. A plus sign means every hand above it in the same family, so A7s+ is A7s, A8s and up to AKs.

How deep some hands still shove

The other way to read the solve is to take a hand and find the deepest stack where it is still a shove. 25+ means it shoves at every stack the solve covers.

Pocket deuces shove up to 8.5 big blinds under the gun and at every stack from the cutoff on. A2o is a button shove up to 21.5 big blinds. From the hijack, A5s goes deeper than A6s (25+ against 18.5). It can make the wheel, A-2-3-4-5, which gives it about a point more equity against the hands that call. Past 20 big blinds that edge is thin.

For the small blind against an opponent who can see your cards, the Sklansky-Chubukov numbers give a stricter version of the last column.

How these numbers were made

• They are chip-EV Nash ranges: the shove and call strategies where neither side can do better by changing theirs, with every chip worth the same.
• Blinds are 0.5 and 1 with a 1 big blind ante, the big blind ante most tournaments now use, so 2.5 big blinds are in the pot before anyone acts.
• Seats count the players left to act behind you on a nine-handed table.
• Only one player ever calls. There are no three-way all-ins in the model, the usual simplification for push/fold. That only matters for the early seats at very short stacks.
• Hand against hand equities come from simulated boards for every pairing of the 169 starting hands.
• Stacks run in half big blind steps. Each hand's shove EV is averaged over the stacks a big blind either side, to take out the solver's wobble from one stack to the next. The cut-off is the deepest stack where that average is still positive, and a dip of less than 0.06 big blinds doesn't end it.
• An earlier seat never shoves a hand that a later seat folds, and a bigger pocket pair never stops shoving before a smaller one.

Two things it doesn't know. It doesn't know about the money: near the bubble a chip you lose costs more than a chip you win, so calling ranges get much tighter and shoving ranges usually do too. The bubble factor calculator puts a number on how much. And it doesn't know your opponents. It assumes everyone behind you calls with exactly their Nash range. Against a table that folds too much you can shove wider.

What to keep in your head

If you only remember one column, make it 10 big blinds: under the gun 15%, cutoff 34%, button 43%, small blind 72%. For the exact hands, set your seat and stack on the push/fold chart.

In M terms, 10 big blinds with a big blind ante is an M of 4, Harrington's red zone (the M to big blinds tables convert the rest). The M-ratio calculator converts your own stack, and part nine of the lessons plays these spots hand by hand.