• Nash Push Fold Charts
• Nash Chart Poker

Developed by professional poker player Max Silver, SnapShove combines unexploitable nash equilibrium ranges with an instant, easy to use and flexible interface allowing you to get the perfect play for any. Poker Software & Tools: Nash: 2: June 9th, 2020 8:24 PM: Learning Poker: Nash Shove Chart(push or fold) MTT: 8: April 22nd, 2020 4:41 PM: Tournament Poker: Question about Nash push or fold: 3.

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

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.

Level 1: The MacroAnalysis

The MacroAnalysis evaluates the overall strategy of Hero's range. The primary focus at this level is on range advantage, position and SPR, since typically these factors significantly influence how specific holdings within the range are played.

These grids show the possible hands which each player is likely to hold given prior actions. Hands which are more likely to be in a player's range are shaded darker. The GTOx dashboard juxtaposes both player's ranges since in GTO, strategies are wholly devised based upon how the ranges stack up against each other relative to the board.

The strategy sunburst shows the frequencies of the possible actions at the current node for the entire range, as well as the actions available at prior decision points in the game. This visual depiction of actions can assist users in learning to assess how prior actions define each player's range, which is a critical skill in GTO.

Nash Push Fold Charts

This table shows the average frequencies and resulting EV for each possible action for the range as a whole. Also shown is the Range EV Regret for each action, which measures the maximum amount of EV that will be lost if a player takes that action with 100% of the hands in the range and can aid in simplifying strategies. EV Regret is standardized by the pot size so each player can set his/her own EV Regret significance threshold based on his/her experience and skill level. Finally, this table shows 'Fold Leverage', which is equal to the percentage of the opponent's range that folds to each bet at the nash-equilibrium.

Nash Chart Poker

This table shows the average EV, average equity and equity distribution for each player. EV measures the expected number of chips the player will win on average if it follows the optimal strategies. Equity measures the probability of the player winning or tying at showdown if no further betting occurs. The equity distribution aids in an understanding of overall composition of each player's range (e.g. polarized, capped, condensed, merged, etc.).