πŸ€‘ Nash Calculator and Nash Equilibrium in poker explained | ICMIZER

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A Nash equilibrium is a scenario where none of the game participants In no-​limit Texas Hold'em, bet sizes that differ by just one dollar cause.


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D.5 Dominant strategies and Nash equilibrium - Game Theory - Microeconomics

This data can be used to derive the charts. So the relevant stack size for both players in this hand is 6. The exact Nash solution is considerably more complex and the chart only shows a simplified version. The value there is 5. Differences to Other Solutions. 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. For example 63s is included in the pushing strategy for stack sizes between 7. 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. Raw Data.{/INSERTKEYS}{/PARAGRAPH} Download Raw Data. This example refers to the no ante solution. The effective stack size is the smaller of the two, before posting any blinds. 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. Similar charts have been published by various sources, including SNGPT and Mathematics of Poker, and there are some minor differences between them. {PARAGRAPH}{INSERTKEYS}The tables show the highest effective stack size in big blinds where a hand can be pushed or called. Free Tools. If the table values don't match the example then make sure the "No Ante" tab is selected above. The value for T3s is 7. Using the Solution. Suited Offsuit Pockets. 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. The solution available on this site was independently calculated and published in as part of a coding experiment, inspired by the discussion of the topic in Mathematics of Poker. 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. Playing push-or-fold is typically only recommended up to around 10bb, depending on the situation. These details are omitted in the chart to allow a compact representation of the strategy. To determine if the BB should call with his Q2o, check the orange area offsuit hands of the "Caller" chart and locate Q2o. To find the strategy for SB's T3s, check the green area suited hands of the "Pusher" chart.