Nash Holdem

HeadsUp Push/Fold Nash Equilibrium - HoldemResources.net HeadsUp Push/Fold Nash Equilibrium The charts below show the Nash Equilibrium strategies for two player push-or-fold NLHE. This is a simplified game where the SB is only allowed to go all-in or fold,. The results are random every time, meaning that Holdem Nash Chartnothing in the game is rigged. To ensure fair play, only choose slots from approved Playing at any of these will give you a fair chance Holdem Nash Chartof winning.

1. Nash Holdings Llc
2. Holdemresources Nash Calculator

Push Fold Charts
These Push Fold Charts will help you understand when you need to either fold or shove your entire stack when you are short stacked in poker tournaments. Please use these charts as a study tool to help you improve your understanding of push fold scenarios.

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If you want to access these Push Fold Charts on your phone, download the PokerCoaching.com Mobile App With Free Push / Fold Charts

You can also access the Push / Fold App on your computer to access these and more charts for all seating positions, and several different blind levels.

Also check out our Push/Fold Quiz which will help you test and remember you skills when short stacked.

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These charts are meant to be used for study purposes. Make sure to check the Terms and Conditions of the sites that you play on to see if this is against the rules to use any of these while you’re in a poker game. If it is against the TOC of the game you are in, you should not use these tools while you play.

Nash Holdings Llc

The tables show the highest effective stack size in big blinds where a hand can be pushed or called. Values bigger than 20 are only displayed as 20+, which means the hand can be played for any stack size of 20bb or less. (Playing push-or-fold is typically only recommended up to around 10bb, depending on the situation. Using push-or-fold for >20bb is almost certainly a bad idea.)

Some hands have gaps in their pushing strategies, they are marked with * and the details are displayed below the charts. For example 63s is included in the pushing strategy for stack sizes between 7.1 and 5.1bb, and stacks below 2.3bb.

SB (9.0bb): T3s
BB (6.0bb): Q2o

Holdemresources Nash Calculator

The effective stack size is the smaller of the two, before posting any blinds. So the relevant stack size for both players in this hand is 6.0 big blinds.

To find the strategy for SB's T3s, check the green area (suited hands) of the 'Pusher' chart. The value for T3s is 7.7bb, and since that is larger than the current effective stacks the hand is a push in the Nash Equilibrium strategy.

To determine if the BB should call with his Q2o, check the orange area (offsuit hands) of the 'Caller' chart and locate Q2o. The value there is 5.6bb. The effective stacks in the current hand are larger than the value for Q2o, so this hand is a fold in the Nash Equilibrium strategy.

This example refers to the no ante solution. If the table values don't match the example then make sure the 'No Ante' tab is selected above.

The solution available on this site was independently calculated and published in 2007 as part of a coding experiment, inspired by the discussion of the topic in Mathematics of Poker.

Similar charts have been published by various sources, including SNGPT and Mathematics of Poker, and there are some minor differences between them. The exact Nash solution is considerably more complex and the chart only shows a simplified version. Most hands are actually played with mixed strategies for at least a few stack sizes, and many hands have multiple smaller gaps in their strategy, similar to the 63s, 53s, 43s hands. These details are omitted in the chart to allow a compact representation of the strategy.

The differences in published solutions are most likely due to choices made when simplifying the exact solution into easy-to-use charts. Due to the considerable number of rather arbitrary choices when simplifying into chart form, it is actually quite unlikely that two independently created charts would perfectly match.

The file linked below contains the unsimplified push-or-fold equilibrium strategies for all stacks of 1bb ≤ stacks ≤ 200bb in steps of 0.05bb. This data can be used to derive the charts. For practical purposes the chart form should be completely sufficient though.

The data linked here was re-calculated with a later version than the original chart data, so there may be some very slight differences.