Nash Equilibrium - Pushbot Charts & Call Charts
Powerful poker tools and mathematical models have have enabled poker players to develop and implement game-theory based unexploitable and optimal poker strategies and plays in specific, key situations.
One concept which is highly applicable to poker tournaments and SNGs is "Nash Equilibrium".
For heads-up play (e.g. blind vs blind hands) it's possible to calculate game-theory optimal (GTO) shove and calls ranges which are profitable in the long run, based on your stack size, and cards / those of your opponents.
Poker Pushbot charts can answer important questions quickly- for heads-up situations, for example:
- Can I go all in with this hand profitably?
- Which hands can I profitably call a shove with vs my opponents stack size, when they go all in for X big-blinds?
Equilibrium rankings are meant as a guide to help you to develop an idea of which hands and hand ranges are good enough to warrant an all-in and which hands are good enough to call an all-in vs an aggressive opponent.
It folds to you in the small-blind. You have 12 big-blinds and Queen ten offsuit. What's your play? Can you profitably and unexploitably go all in, or do you wait for a better sport?
You can Shove (go "all in") profitably if:
- If you are in the small blind,
- everyone before you has folded,
- your effective stack (the smallest of the stack sizes of you vs your opponent in blinds blinds) is smaller than the number given in the table below for your specific hand
in this spot when you have 12 big-blinds.. From the pushbot chart below, we can see that QTo is a profitable SHOVE (as is Q9, and Q8, but NOT Q7o)
*Pro Tip: the push chart can also be used when you’re short-stacked and interested in jamming "all in" from the button. In this case account for the extra player that you’ll be shoving into (the Small Blind) by dividing all the stack size numbers in the chart by 2. Similarly you could divide by 4 for stack size for a protiable cutoff jam.
Nash Equilibrium pushbot chart for going all-in from the small-blind (SB)
Nash Equilibrium chart for calling an all-in in the big blind
The action folds to the small-blind who goes "all in" for 15 BBs - half of your 30bb Stack. You look down at King Queen Suited.
Can you call the all-in profitably?
- If you are in the big blind (BB)
- everyone before the small blind has folded,
- The SB moved all-in,
- and your effective stack (in BBs) is smaller than the number specified in the table above.
Looking at the chart we can see that we can profitably call with QKO, as well as KJo, KTo and K9o
* The maximum stack size considered in this model is 50 BBs
Data Source: Mathematics of Poker (2006) by Bill Chen