This article introduces the tools and knowledge to figure out your Pure Nash Ranges for push fold.
Nash Ranges – HoldemResources
To actually get Nash Ranges, we have to use heavy math tools. The best tool I know of is HoldemResources. They also have a very fast and graphical nash calculator which is the newer version of their old calculator. If you are unfamiliar with the range notation and the according percentages of a range, I suggest you check out their graphical nash calculator. I prefer their older calculator because it displays all the information in a compact fashion.
Nash Ranges early-mid game – Pure Nash Ranges
In order to get Nash Ranges for early mid game, use the setting winner take all. This means your payout structure is:
- 1st: 100%
- 2nd: 0
- 3rd: 0
That way ICM doesn’t matter and all stacks are valued according to stack size and not ICM value. I will call these ranges the Pure Nash Ranges for future reference. All Nash Ranges that incorporate a pay out structure I will reference as ICM Nash Ranges.
Nash Ranges and average stack
In order to get a basic feeling for what Nash Ranges might look like for various stack sizes, I suggest you calculate Nash Ranges for various average stack size and positions. This will be some work, but doing it will already give you a good feel for those ranges. Try to predict the outcome and the ranges.
Pure Nash Range example
Let me show you to get the Pure Nash Ranges by discussing an example. Assume we were interested in the Pure Nash Range for a 10BB average stack.The input on HoldemResources would be:
Please note that structure is set to 1 which means that first place gets 100% of price pool. Also note that it doesnt matter what SB and BB you use as long as the stack sizes are 10 times that to calculate our average stack of 10BB.
You can find the full results of the query above here. The key information you get from this calculation can be found in the table below:
I personally like to think of Pure Nash Ranges as percentages of all hands. I have a much easier time remembering 8.4% as opposed to 99+ ATs+ A5s AJo+ KTs+ QTs+.
Pure Nash Ranges vs Max Profit Range
I would like to stress out that Pure Nash Ranges are not constructed to maximize your profit! They do however grantee you not to lose in the long run (which is nice). I consider Nash Ranges a solid basis to construct your ranges. You can find more on this topic in my article Turbo Tournament Strategy – Poker Nash Equilibrium – Finding a Max Profit Strategy.
You can find ideas and reasons on how to adjust Pure Nash Range in future articles.