# About the Solution

Further information about the HeadsUp Push/Fold Equilibrium charts.

## Source

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.

## Differences to Other Solutions

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.

## Raw Data

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.