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Using the Nash Charts

  • Jan 29, 2014

General information about the HeadsUp Push/Fold charts and their usage.



General Information


The charts show the Nash Equilibrium solution of the heads-up push-or-fold game. This is a simplified game where the SB is only allowed to go all-in or fold, and the BB can either call or fold when facing a shove.

It is important to keep in mind that this is not the solution for the full game where limps and smaller raises are also available. The push-or-fold solution is generally assumed to be very close to the solution of the full game up to around 8bb. In practice the strategy can likely be used at least until 10bb without being too exploitable.

Usage


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.

Example


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 SBs 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.

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