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Texas holdem equilibrium

A competitive Texas Hold’em poker player via automated abstraction and real-time equilibrium computation∗ Andrew Gilpin and Tuomas . Computing an Approximate Jam/Fold Equilibrium for 3-player No-Limit Texas Hold’em Tournaments∗ Sam Ganzfried Department of Computer . The Nash-equilibrium solution for Holdem tournaments is profitable open-push ranges from the SB & calling ranges from the BB in heads-up, push-or-fold play.

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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. Indeed, pushing Nash against this type of opponent will be profitable but it will be far more profitable to push even wider i. If one player deviates from Nash then the other player can do better by re-adjusting their ranges accordingly. On the reverse, there will be situations where you can profitably push wider than Nash when your opponent is calling tighter so for the most part playing Nash poker will be far from optimal. 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.

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HeadsUp Push/Fold Nash Equilibrium

If one player deviates from Nash then the other player can do better by re-adjusting their ranges accordingly. This is useful since it allows you to understand what ranges are optimal in different spots and generally what players will be doing if they are adopting this strategy.

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It is also able to generate these optimal ranges for each individual player at the table and not just the hero or player in action. To carry out this calculation in the program all you have to do is hit the Calculate Nash Equilibrium button and the Nash ranges for each of the stacks will be assigned. One of the most common situations in poker where people adopt Nash ranges is HU at high blind levels against a tough opponent. If you revert to this style of play then your opponent will have to do the same to avoid being exploited.

So why do it? Adopting the Nash range against an inferior opponent for instance who is letting you limp in a lot, steal the blinds pre-flop often and pick up pots on the cheap side post-flop will be far from optimal.

Before electing to adopt Nash Equilibrium ranges, there are several important assumptions Nash makes that must be understood:. On the reverse, there will be situations where you can profitably push wider than Nash when your opponent is calling tighter so for the most part playing Nash poker will be far from optimal. The most profitable thing you can do is adjust to your opponents ranges, whether that means pushing wider than Nash, pushing tighter than Nash, or perhaps not pushing at all.

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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 tables show the highest effective stack size in big blinds where a hand can be pushed or called. Playing push-or-fold is typically only recommended up to around 10bb, depending on the situation. For example 63s is included in the pushing strategy for stack sizes between 7. 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.

To find the strategy for SB's T3s, check the green area suited hands of the "Pusher" chart. The value for T3s is 7. 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. 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. 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.

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Similar charts have been published by various sources, including SNGPT and Mathematics of Poker, and there are some minor differences between them. The exact Nash solution is considerably more complex and the chart only shows a simplified version. 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. These details are omitted in the chart to allow a compact representation of the strategy.

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. This data can be used to derive the charts.

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Holdem 888

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Patch for PokerStars and Microgaming sites. Patch for Party Poker. Patch for Ignition Poker , Bodog Poker. Patch for Microgaming MPN sites. Supports the new Svenska Spel Poker. Supports the new Unibet Poker. Supports new site Ourgame Poker. Due to technical reason, make sure you open the first Holdem Indicator before you launch your BetOnline poker client. Supports new site Fulpot Poker English version only. Patch for the new PKR software. Due to technical reason, make sure you already have one Holdem Indicator works with the existing PKR game table before you open a new one.

Patch for the new iPoker clients and Winamax. Patch for Winamax and Unibet Poker. Improvements to meet the 3rd party software requirements of PokerStars and Full Tilt. Show "Rank" , 1 is the best hand instead of "Group" for starting hands. Don't show player profiling icons on HUD. This is for PokerStars and Full Tilt only. Patch for Full Tilt. Patch for Revolution Gaming Cake Network. Adds new feature - Stats Graphs. You can review your sessions with graphs. Patch for iPoker sites Titan Poker , etc.

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Holdem Indicator is the first online Poker Odds Calculator that supports this poker network. Supports Cake Poker version 2. Holdem Indicator is the first online Poker Calculator that supports Cake poker network. Supports the new Zoom games on PokerStars. Calculateur de cotes de poker Winamax. Bug fixings and improvement for Hand Replayer. Added new functionality - Hand Replayer.

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You can visualize hands you played with the exact player stats and win odds for yourself and players with known cards. Patch for Bodog Poker. Patch for Merge Gaming Network Sportsbook, etc. HUD supports Bodog not available for multi-table tournaments. Patch for PKR and Poker. Performance improvement for HUD. Added feature to auto-launch Holdem Indicator for new game tables. Color-coded text for HUD stats.

Patch release for Party Poker. Patch release for PKR. Patch release for the new Betfair Poker client. Patch release for iPoker sites Titan Poker , etc.

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