Through the development over the recent years of poker technology used for off-table study (i.e. various poker solvers and applications), knowledge and implementation of optimal, unexploitable poker strategies and plays.

For the purpose of this article, specifically, those involving appropriate push/fold and call ranges for various stack sizes, have surged to the forefront.

One such tool that has helped better the playing of tournament players is something called the “Nash Push/Fold Equilibrium”.

The chart below shows which hands you can be open-shoving with (e.g. when you’re getting short-stacked in a tournament) depending on your stack size, whereby you can remain indifferent to if your opponent calls or folds.

Ultimately, in the long-term, shoving as per the chart’s recommendations will lead to +EV situations, whether it’s through the fold equity you have if your opponent folds, or the equity that you’ll have against an appropriate calling range for the situation.

Table of Contents

Understanding Push/Fold Equilibrium Charts

It must be noted that the charts below are intended explicitly for heads-up play. Therefore, for games with more than 2 players, the shove (all-in) tables below are applicable for SB open-shoving ranges, and the call chart below are relevant only for BB situations vs a SB shove.

Here’s the Nash Push/Fold Equilibrium chart, as referenced above:

Nash Push-Fold Equilibrium chart


It should be noted that the push chart below can also be used when you’re short-stacked and are looking to push from the Button. When doing this, to account for the extra player that you’ll be shoving into (the player in the Small Blind), simply divide all the numbers in the chart by 2.

If you have 95s on the Button and the action is folded to you, you can profitably shove, if you have a stack of 7.2bb or less.

By the same thought, if you divide all of the original numbers in the chart by 4, you’ll find a solid pushing range from the CO. Some of the figures will be impossible to calculate accurately for the CO, though, and/or positions further to the right of the blinds because the highest value that the chart provides is “20+” big blinds, which is used for many hands in the table.

How To Improve your Push/Fold Game for Other Positions

To assist you with optimal push/shoving ranges for the rest of the positions (EP/MP/CO) and stack sizes at the table, poker pro, Max Silver developed an incredible phone application called SnapShove just for that purpose! (The app is available on the App Store for iOS and Google Play for Android.)

A free version is available with a more “basic” version of the app, but for a nominal one-time price, you can unlock the full version, which provides complete flexibility and customizability for any position you may find yourself in at the table:

  • Number of Players
  • Ante/Big Blind
  • Number of Big Blinds you have (or the effective stack is)
  • Your Position

Simply input the above information accordingly, tap “Calculate”, and watch the application spit out the correct shoving range for that given situation.

Here’s a screenshot of the layout within the app:



Furthermore, if you’re looking for something to tell you how wide (or narrow) a range you should be calling with when facing a shove, this app has you covered, too.

See the “call” tab along the top? With all of the same customisability (yet merely adding in a box for inputting the position of your opponent who’s shoving), you can then press calculate and see the appropriate ranges you should be calling within that situation. 

Other Uses and Applications for Push/Fold Charts

It’s not only in MTT’s where you can use these tools to improve your game. Think about how a SNG grinder can up their game using these charts. With most of their money always coming from the top 3 spots, the skills of a solid push/fold game become mighty prevalent and can add huge profits to their bottom line.

In Conclusion

Ultimately, using the Nash Push/Fold chart provided above, in conjunction with Apps like SnapShove, is going to improve your short-stack game significantly in tournaments, helping you make more deep runs and consistent profits.

That said, always stay modest in your results and keep in mind the variance that is naturally a part of tournaments (with the number of all-in shove/call-off moments there are where you either have to hold or improve).

Using these apps will help arm you with the knowledge you need to make long-term +EV shortstack decisions, but variance is still going to play its course over the short-term.

With that in mind, as you improve and get better, remember that volume will help you overcome whatever variance you’ll experience.

The more tournaments you play, the more your skill edge in all the push/fold situations you’ll encounter will be shown.

Good luck on the felts!

About the Author
Matthew Cluff is a poker player who specialises in 6-Max No Limit Hold’em games. He also periodically provides online poker content for various sites.
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