by Pro Player Chris "Fox" Wallace
Many situations in poker are very tough to solve. This is one of the reasons that computers are unable to compete at a high level in most poker games. One of the places where the game has truly been solved is short stacked tournament play, and many players now use push fold charts for the later stages of tournaments when stacks are small compared to the blinds and antes. Heads up sit-and-go tournaments are also a great place for these charts because many of them end up in the critical push or fold stage before they are finished. Our charts only go up to 10 big blinds because with deeper stacks it is typically better to raise and make a decision once your opponent responds to your raise instead of pushing all-in.
To help players understand push/fold and play correctly when short stacked, we have created these charts with the correct Nash Equilibrium all-in ranges. For now, the push fold charts for full ring and 6max games assume a 90/10 payout structure, which approximates multi-table tournament play for most of the tournament, and soon we'll have charts up for single table sit and go tournaments as well as the various double or nothing and step structures available online. Assuming you have a significant edge over the field, the 90/10 structure should be close to correct until you reach the final table of a multi-table tournament. As you approach the final table you can play somewhat tighter than these sheets recommend because of payout structure changes.
The heads up charts are even stronger than the others because heads up play requires no approximation. The two players are fighting over the difference between the two payouts, with the winner taking the entire difference, so all heads up confrontations are essentially “winner take all” tournaments and no adjustments for payout structure are necessary.
We know these ranges seem a little wide, and to some players they will be shocking. The math is accurate, and in playing against computers programmed to play this way we have proven that the ranges are unbeatable. We are also working on a short stack, heads up simulator that will allow you to play against these strategies and see how well you do.
The Nash ranges assume opponents who play perfectly. When they make mistakes, you make a profit, but if their mistakes are large you can make more profit by adjusting your push/fold ranges. In almost all cases the correct adjustments are to tighten up by dropping a very small percentage of the optimal pushing range. Most players adjust far too much because they are uncomfortable with the width of the ranges, but a correct adjustment for a weak opponent is usually to drop around 5% of the total range.
For more information about the Nash Equilibrium check out the wikipedia page at http://en.wikipedia.org/wiki/Nash_equilibrium
For more information about making your own push/fold charts, the HoldemResources.net ICM calculator is an excellent resource for getting started with push/fold calculations of your own. Most players are probably best off just using the charts we have available; they will keep you within 1% of absolutely perfect play when the stacks are short.