System and Method for Creating a Poker Algorithm Capable of Independently Playing and Training Users How to Play Consistently Optimal Poker.

Abstract

An original system and method for solving the card game known as Texas Hold'em Poker is disclosed. Mathematical calculations as well as game theory tactics are utilized to determine the optimal strategy for any possible situation that could potentially arise in Texas Hold'em Poker, as well as other variations of poker where the methodology also applies. One embodiment of the invention involves a fully automated electronic poker simulator that would allow the user to play a complete and genuine game of electronic poker against any number of computerized or live opponents, while simultaneously utilizing features of the poker simulator to learn how to play consistently optimal poker. Another embodiment would be to utilize the unique and specific methodology described herein to develop an artificially intelligent poker algorithm that can independently play consistently optimal poker in any possible scenario.

Description

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable

REFERENCE TO SEQUENCE LISTING, A TABLE, OR A COMPUTER PROGRAM LISTING COMPACT DISC APPENDIX

Not Applicable

FIELD OF THE INVENTION

The invention's field relates to a system and method for developing an optimal strategy for playing various forms of Poker, utilizing a wide range of mathematical calculations and game theory tactics.

BACKGROUND OF THE INVENTION

The game of Poker, and Texas Hold'em Poker in particular, has gained tremendous popularity in recent decades. Part of the appeal of the game is the combination of both luck and skill that is required to win. In the short run, luck is the primary factor that determines who wins and who loses each hand. However, players with superior strategy and skills will win in the long run. This has driven many professional and recreational poker players to seek out effective methods of improving their poker skills.

Various training methods aimed at improving user poker skills are widely available. Countless books and online tutorials exist with an array of varying poker strategies and guidelines. There are also a number of proprietary poker training methods that have been granted patents in recent years. The closest published patent application to the current invention is Patent# U.S. Pat. No. 8,152,618 B1 (Advancements in Computerized Poker Training and Analysis, Blay et al). This prior art application is primarily limited as follows:

1. The method and system disclosed can generally only be applied to a pre-determined field of potential poker scenarios. This limitation inhibits users from being able to play a complete game of genuine poker while they learn the optimal poker decision making process.

2. The method and system disclosed is often dependent on poker strategy advice from human professionals. As such, the process is not fully automated and provides little certainty regarding the accuracy of said professional advice.

There have also been various computerized Texas Hold'em Poker algorithms created in recent years. These algorithms primarily utilize some form of Counterfactual Regret Minimization in which the algorithm learns from millions of iterations of playing poker against itself in order to learn the optimal decisions in every possible scenario.

However, due to the high degree of complexity inherent to optimal Texas Hold'em Poker strategy (particularly multiplayer No Limit Hold'em), to date no one has been capable of developing a fully automated algorithm that can play and train users in playing consistently optimal Texas Hold'em Poker in any possible scenarios, and against any number of opponents. While there are various Poker training softwares currently available, none of these softwares allow a user to play a complete game of genuine no limit hold'em poker against any number of opponents during a fully automated training process.

Furthermore, the existing poker algorithms that utilize Counterfactual Regret Minimization involve highly complex mathematical calculations that inhibit everyday individuals from being capable of performing the processes involved. Whereas the methodology presented herein is simple enough that everyday individuals (with proper training) would be capable of learning how to play consistently optimal Texas Hold'em Poker in any possible scenarios. Therefore, this invention is a significant improvement upon the existing art in this field.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 describes the 169 unique Texas Hold'em starting hands and ranks each hand in order of strength.

FIG. 2 describes the Basic Optimal Strategy fora player's initial preflop decision to raise/call/fold assuming 0 opponents have voluntarily entered the hand. FIG. 2 also describes the Expected Frequencies of various initial raise/call/fold decisions when 0 opponents have voluntarily entered the hand.

FIG. 3 describes the Basic Optimal Strategy for a player's initial preflop decision to raise/call/fold after 1 or more opponents call the big blind. FIG. 3 also describes the Expected Frequencies of various initial raise/call/fold decisions when facing 1 or more opponent calls.

FIG. 4 describes the Basic Optimal Strategy for a player's initial preflop decision to raise/call/fold after 1 opponent has made a pot sized raise. FIG. 4 also describes the Expected Frequencies of all possible initial raise/call/fold decisions when facing an opponent raise.

FIG. 5 describes the process for calculating a particular hand's Weighted Average Equity against an opponent's Estimated Hand Range.

FIG. 6 describes the Basic Optimal Strategy for a player's decision to raise/call/fold after an opponent 3-Bet.

FIG. 7 describes 3 general categories of opponents.

FIG. 8 describes various detailed categories of opponents.

FIG. 9 describes various Adjustments to the Basic Optimal Strategy that are required in order to play consistently optimal Texas Hold'em Poker.

FIG. 10 describes various postflop examples of hands with Weighted Average Equity ranging from 0-100%

FIG. 11 describes the Basic Optimal Strategy default bet/raise sizes

FIG. 12 provides a detailed outline of the Basic Optimal Strategy for a Player's initial decision after the flop, and other postflop decisions.

FIG. 13 describes the process for revising an opponent estimated hand range based on opponent decisions, and determining updated opponent hand likelihood weightings.

FIG. 14 describes various features of one embodiment of the invention involving a Poker Simulator/Trainer.

DETAILED DESCRIPTION OF THE INVENTION

Described herein is a unique system and method for solving the various forms of Texas Hold'em Poker, and developing an optimal strategy that can be applied to any possible situation that could potentially arise while playing any variation of Texas Hold'em Poker and against any number of opponents. The most complex form of Texas Hold'em Poker is No Limit at a full table (generally 9 or 10 players total). Therefore this summary will focus on No limit Texas Hold'em at a full table. However, this same methodology can be applied to various other forms of Poker that include but are not limited to Limit Hold'em, Short Deck, and Omaha. The same methodology also applies against any number of opponents.

In Texas Hold'Em there are 169 unique starting hands that a player can be dealt (without distinguishing between different suits). The optimal decisions (raise/call/fold or check/bet) are determined based on detailed statistical calculations and game theory considerations. FIG. 1 ranks all 169 unique Texas Hold'em starting hands in order of strength. This hand strength ranking will be used to determine a specific Basic Optimal Strategy in any possible situation. FIG. 1 is based on effective stack sizes of around 100 big blinds.

FIG. 2 describes the Basic Optimal Strategy for a player's initial preflop decision to raise/call/fold, assuming 0 opponents have voluntarily entered the hand. FIG. 2 also describes the Expected Frequencies of various initial raise/call/fold decisions when the player is the initial bettor.

To avoid giving away the strength of any hand, all preflop raises should have a default sizing relative to the pot size. Assuming players have effective stack sizes around 100 big blinds, all preflop raises should be pot sized bets (initial raise size=3.5 big blinds). Shorter stack sizes may require smaller than pot raise sizing. Deeper stack sizes may require larger than pot raise sizing.

The next step is to determine how to handle opponent raises/calls. This is where Opponent Analysis (information gathered by observing opponent behavior) becomes crucial to making maximally optimal decisions. Assuming it is the first hand of play and there is no Opponent Analysis available, FIG. 3 outlines the Basic Optimal Strategy for a player's initial preflop decision to raise/call/fold after 1 or more opponents have called the big blind. FIG. 3 also describes the Expected Frequencies of various initial raise/call/fold decisions in hands where 1 or more opponents have called the big blind.

Similarly, FIG. 4 describes the Basic Optimal Strategy for a player's initial preflop decision to raise/call/fold, after 1 Opponent has made a pot size raise. FIG. 4 also describes the Expected Frequencies of various initial raise/call/fold decisions in hands where 1 opponent has raised.

As described in FIGS. 2-4, there is a range of hands where Basic Optimal Strategy advises a particular preflop decision (fold/call/raise). Below are 3 examples that will help illustrate how to utilize the data from FIGS. 1-4 to determine an opponent's Estimated Hand Range in a given situation:

• • 1. Player is on the button (2 opponents behind) and all opponents fold to Player. Basic Optimal Strategy would be for Player to raise with all hands ranging from AA (Hand 1) down to 78o (Hand 72). Therefore, if Player raises, then Player's Estimated Hand Range=1 to 72.
  • 2. Player raises with 8 opponents behind (no limpers), and opponent calls from the button. Player's Estimated Hand Range=1 to 18, and opponent's Estimated Hand Range=8 to 30.
  • 3. Player raises with 8 opponents behind (no limpers), and opponent 3-bets from the button. Opponent's Estimated<Hand Range=1 to 7.

Once a player has determined an opponent's Estimated Hand Range in a particular situation, a player can also determine their own hand's Weighted Average Equity against the opponent Estimated Hand Range. FIG. 5 provides a detailed example of how to calculate a hand's Weighted Average Equity against an opponent Estimated Hand Range.

A hand's Weighted Average Equity is revised after almost every opponent decision, and will be the primary factor in determining the Basic Optimal Strategy throughout all postflop decisions. A player can also determine their own estimated hand range's Weighted Average Equity against each hand within an opponent's Estimated Hand Range (player's range vs opponent's range).

The next step is to determine the Basic Optimal Strategy against an opponent 3-bet (or 4-bet etc.). The Basic Optimal Strategy for dealing with opponent re-raises is reliant on determining an accurate opponent Estimated Hand Range for any possible situation, then utilizing that Estimated Hand Range to calculate the payer's Weighted Average Equity (as per FIG. 5). FIG. 6 provides a detailed description for how to utilize Weighted Average Equity to determine the optimal strategy for a player's response to an opponent 3-bet.

The following are 2 additional examples that illustrate the Basic Optimal Strategy decision making process when facing an opponent 3-bet:

• • 1. All opponents fold to the button, who raises with Ace of hearts and Ace of diamonds. The small blind folds, then the big blind 3-bets (pot size raise). The big blind's Estimated Hand Range=1 to 21. So the button's Weighted Average Equity can be calculated as follows:

	Big Blind	Possible	Button Equity
	Estimated Hands	Combinations	with AA
	AA	1	50%
	KK	6	82%
	AKs	2	88%
	QQ	6	81%
	JJ	6	81%
	AKo	6	93%
	AQs	2	87%
	1010	6	81%
	AQo	6	93%
	KQs	4	83%
	AJs	2	87%
	99	6	81%
	KJs	4	82%
	QJs	4	81%
	A10s	2	87%
	88	6	81%
	KQo	12	87%
	AJo	6	92%
	J10s	4	79%
	Q10s	4	80%
	K10s	4	82%
	Total	99	85%

• • 99 total hand combinations within opponent Estimated Hand Range
  • Button has VVeighted Average Equity˜85%
  • Because 85% is greater than the 65% 4-bet with position threshold, the Basic Optimal Strategy would be for Button to make a pot size 4-bet.
  • 2. Player has 8 opponents behind (no limpers) and raises with Queen of hearts and Queen of diamonds. Opponent with 7 opponents behind 3-bets, and all other opponents fold. Opponent's Estimated Hand Range=1 to 6. Player's Weighted Average Equity can be calculated as follows:

	Opponent	Possible
	Estimated Hands	Combinations	Player Equity
	AA	6	19%
	KK	6	18%
	AKs	4	54%
	QQ	1	50%
	JJ	6	82%
	AKo	12	56%
	Total	35	47%

• • 35 total hand combinations within standard opponent Estimated Hand Range
  • Player has Weighted Average Equity˜47%
  • Because 47% is greater than 36% but less than 63%, Basic Optimal Strategy would be for Player to call the opponent 3-Bet.

The Basic Optimal Strategy described thus far is optimal only if playing against opponents that are also playing according to the same Basic Optimal Strategy. However, many opponents do not play according to the Basic Optimal Strategy. Therefore, playing consistently optimal Texas Hold'em Poker requires numerous adjustments to the Basic Optimal Strategy based on a wide range of factors.

First and foremost, Opponent Analysis allows a player to categorize each opponent's playing style in order to determine when to adjust the Basic Optimal Strategy against that particular opponent. This is the fundamental principle of Exploitative poker strategy. FIG. 7 describes the 3 general categories of opponents: Loose, Optimal, and Tight.

All opponents are initially considered optimal. That is why the Basic Optimal Strategy applies to all hands when there is no hand history with an opponent. Over the course of play, through attentive observation of every opponent decision that takes place within each hand, optimal players categorize each opponent's decisions as either loose, optimal, or tight in various situations.

Based on the Expected Frequencies calculated in FIGS. 2-4 and 6, a player is able to gather data on opponent raise/call/fold frequencies as compared to the Expected Frequencies. Opponents that consistently raise/call/fold more (or less) often than Basic Optimal Strategy expectations are categorized accordingly. Those opponents' Estimated Hand Ranges will be adjusted based on their tendencies. And the Basic Optimal Strategy when playing against those opponents would be adjusted accordingly.

In addition to analyzing each opponent's betting statistics, optimal players must also analyze each opponent's playing style based on the opponent's cards that are exposed. When opponent cards are exposed at the completion of a hand, optimal players must count and categorize each mistake an opponent made during that hand. Opponent mistakes are considered significant deviations from the Basic Optimal Strategy, taking all adjustments into account. Keeping track and categorizing all opponent mistakes can be used in combination with each opponent's fold/call/raise statistics in order to determine how to best categorize each opponent. This method of Opponent Analysis will allow optimal players to determine how often and to what extent to adjust the Basic Optimal Strategy against each particular opponent. This is accomplished by further categorizing all non Basic Optimal Strategy opponents into the Detailed Opponent Categories described in FIG. 8.

In addition to Opponent Analysis, there are numerous additional “Adjustments” to the Basic Optimal Strategy that are required in order to play consistently optimal Texas Hold'em Poker. FIG. 9 describes many of these adjustments in detail, although additional adjustments may also be required. Each of the adjustments hated in FIG. 9 will affect the Basic Optimal Strategy decisions in various ways.

The final step to playing consistently>optimal Texas Hold'em Poker is to determine how to play the seemingly infinite possible hand scenarios that can arise on the flop, turn, and river. The primary factor that determines all postflop decisions is a players Weighted Average Equity. FIG. 10 provides a general outline and examples of flop hand strength tiers, based on a hand's Weighted Average Equity against opponent Estimated Hand Ranges on the flop.

Basic Optimal Strategy bet/raise sizing on the flop should remain standard as a percentage of the pot size (similar to preflop raise sizing). The default bet/raise on the flop is ⅔ the pot size. Short stacks may require less than ⅔ pot bet/raise sizing. Deep stacks may require greater than ⅔ pot bet/raise sizing. Modifying the default bet size will also modify the optimal WAE ranges for postflop decisions.

Turn and river bet/raise sizing should ideally have multiple bet size options. However, using a default bet/raise size of ½ pot on the turn, and 40% pot on the river, can provide nearly optimal results. This simplified bet/raise sizing will also make it significantly easier for people to learn the Basic Optimal Strategy decision making process. FIG. 11 describes the default bet/raise size for each of the 4 rounds of betting.

The primary factor that determines all postflop Basic Optimal Strategy is a player's Weighted Average Equity, calculated using an accurate opponent Estimated Hand Range. Secondary factors that also affect postflop strategy are:

• • 1. Number of active opponents in the hand
  • 2. Who was the last aggressor (who raised/bet vs who checked/called).
  • 3. Position

Each of the Adjustments described in FIG. 9 are tertiary factors that may or may not adjust the postflop Basic Optimal Strategy.

FIG. 12 outlines the Basic Optimal Strategy strategy for all possible initial player decisions on the Flop. FIG. 12 includes decision trees that cover all possible WAE figures. (0-100%) and all possible secondary factors (listed above). Minor revisions to the WAE ranges from FIG. 12 may be required.

Almost every decision an opponent makes during a hand will affect their Estimated Hand Range. FIG. 13 provides a more detailed example for the process of revising an opponent Estimated Hand Range. The opponent's revised Estimated Hand Range with likelihood weightings from FIG. 13 would be used to calculate the player's revised Weighted Average Equity on the Turn (4th community card). A similar process would apply on the River (fifth and final community card).

The methodology described herein can be applied to any possible situation that could potentially arise while playing any variation of Texas Hold'em Poker and against any number of opponents. Resulting in a fully automated computer algorithm that can play consistently optimal Poker in all possible scenarios. The algorithm contains elements of artificial intelligence in that it analyzes opponent decisions and makes adjustments to its strategy based on that analysis. The algorithm could also be programmed to play loose, tight, or various other player styles.

One embodiment of the invention involves the use of an electronic “Poker Trainer” that would allow the user to play a complete and genuine game of electronic poker against a computer and/or other live individuals, and to simultaneously utilize the features of the Poker Trainer to learn how to play consistently optimal poker. The Poker Trainer would display the various statistics and strategies presented herein in an easy to read manner while users are playing real poker against the computer and/or against other live players. This would allow users to learn how to play consistently optimal poker according to the detailed methodology presented during play. Some of the Poker Trainer's salient features are described in FIG. 14.

Another embodiment of the invention would be to utilize the unique and specific methodology presented herein to develop an artificially intelligent poker algorithm that is capable of independently playing consistently optimal poker against any number of opponents. The algorithm would be programmed to initially play according to the Basic Optimal Strategy. And the algorithm would be programmed to adjust the Basic Optimal Strategy based on Opponent Analysis and the various other Basic Optimal Strategy Adjustments from FIG. 9.

An artificially intelligent algorithm that can independently play consistently optimal Poker has tremendous application potential throughout the Poker Industry. Although the description above contains many specific details, these should not be construed as limiting the scope of the embodiment. But merely as illustrations of some of the potential applications. The embodiments described above are meant solely as examples of the potential application, and in no way limit the scope of application. Thus, the scope of the invention should be construed broadly as set forth in the claims.

Claims

1. A system and method for providing an electronic poker trainer that enables users to learn how to play consistently optimal poker, comprising: a. Providing the user with the ability to play a complete game of poker against a computer and/or against other live opponents.b. Providing the user with fully automated real time descriptions of various specific statistics and tactics that instruct the user on how to play consistently optimal poker according to the unique methodology presented during play.

2. The method of claim 1 wherein said poker game is one of the forms commonly known as No Limit Texas Hold'em, Limit Texas Hold'em, Pot Limit Texas Hold'em, Short Deck Texas Hold'em, Pot Limit Omaha, or any other variation of poker where the methodology applies.

3. The method of claim 1 wherein said poker game consists of any number of opponents.

4. The method of claim 1 wherein said descriptions of various specific statistics and tactics may include but are not limited to the following subjects: a. Preflop starting hands ranked in order of strengthb. Series of basic optimal strategy tactics that may include but are not limited to: i. Preflop initial basic optimal strategyii. Preflop opponent raise basic optimal strategyiii. Preflop opponent re-raise basic optimal strategyc. Series of adjustments to the basic optimal strategy that may include but are not limited to: i. Opponent analysis adjustments based on: 1. Opponent fold/call/raise/check/bet frequencies2. Observed opponent deviations from the basic optimal strategy when opponent cards are exposedii. Opponent bet/raise sizing adjustmentiii. Rakes or antes adjustmentiv. Position adjustmentv. Number and playing styles of players left to act adjustmentvi. Discount from blinds adjustmentvii. Stack size adjustmentsviii. Drawing hands adjustmentix. Limp then raise adjustmentx. Bluff bet adjustmentxi. Randomization adjustmentxii. Hand Balancing adjustmentxiii. Overcall adjustmentxiv. Pot odds adjustmentxv. Squeeze play adjustmentxvi. Polarized hand situation adjustmentxvii. Tournament bubble adjustmentxviii. Table Image adjustmentxix. Opponent bet/raise sizing patterns adjustmentxx. Physical tells/patterns adjustmentxxi. etc.d. Postflop basic optimal strategy based primarily on each hand's weighted average equity against opponent estimated hand ranges.e. Revising opponent estimated hand ranges based on a specific opponent hand likelihood determination process.

5. The method of claim 1 wherein said electronic poker trainer includes features that may include but are not limited to: a. Providing the user with the ability to customize opponent playing styles.b. Providing the user with the ability to customize the number of opponents.c. Providing the user with the ability to customize player and/or opponent chip stack sizes.d. Providing the user with the ability to customize rakes or antes.e. Providing the user with the ability to play in regular mode or in tournament mode.

6. A system and method for developing a fully automated and artificially intelligent poker algorithm that is capable of playing consistently optimal poker, comprising: a. A series of unique and specific computer codes involving various mathematical calculations and poker tactics.b. Ability for the algorithm to independently play consistently optimal poker against other computer programs, and/or against live opponents.

7. The method of claim 6 wherein said poker game is one of the forms commonly known as No Limit Texas Hold'em, Limit Texas Hold'em, Pot Limit Texas Hold'em, Short Deck Texas Hold'em, Pot Limit Omaha, or any other variation of poker where the methodology applies.

8. The method of claim 6 wherein said poker game consists of any number of opponents.

9. The method of claim 6 wherein said artificially intelligent poker algorithm is programmed to initially play according to a specific basic optimal strategy, and programmed to adjust that strategy based on an opponent an process and other specific factors.

10. The method of claim 6 wherein said series of unique and specific computer codes may include but are not limited to the following subjects: a. Preflop starting hands ranked in order of strengthb. Series of basic optimal strategy tactics that may include but are not limited to: i. Preflop initial basic optimal strategyii. Preflop opponent raise basic optimal strategyiii. Preflop opponent re-raise basic optimal strategyc. Series of adjustments to the basic optimal strategy that may include but are not limited to: i. Opponent analysis adjustments based on: 1. Opponent fold/call/raise/check/bet frequencies2. Observed opponent deviations from the basic optimal strategy when opponent cards are exposedii. Opponent bet/raise sizing adjustmentiii. Rakes or antes adjustmentiv. Position adjustmentv. Number and playing styles of opponents left to act adjustmentvi. Discount from blinds adjustmentvii. Stack sizes adjustmentsviii. Drawing hands adjustmentix. Limp then raise adjustmentx. Bluff bet adjustmentxi. Randomization adjustmentxii. Hand Balancing adjustmentxiii. Overcall adjustmentxiv. Pot odds adjustmentxv. Squeeze play adjustmentxvi. Polarized hand situation adjustmentxvii. Tournament bubble adjustmentxviii. Table Image adjustmentxix. Opponent bet/raise sizing patterns adjustmentxx. Physical tells/patterns adjustmentxxi. etc.d. Postflop basic optimal strategy based primarily on each hand's weighted average equity against opponent estimated hand ranges.e. Revising opponent estimated hand ranges based on a specific opponent hand likelihood determination process.

11. The method of claim 6 wherein said artificially intelligent poker algorithm can be programmed to play according to a range of playing styles that may include but are not limited to: a. Looseb. Optimalc. Tight