OPTIMA

POKER TRAINER

By Kia Hamadani

 O.P.T.

A Proprietary Algorithm & Mobile App To Teach Game Theory Optimal Exploitative (GTOX) Poker Strategy

TABLE OF CONTENTS

12 STEP SYSTEM 

Introduction

Step 1: Game Theory Optimal (GTO) Preflop Hand

Rankings = 1 through 169

Step 2: Initial Bet GTO Hand Ranges

Step 3: Opponent Initial Call GTO Ranges

Step 4: Opponent Initial Raise GTO Ranges

Step 5: Calculating Estimated Hand Ranges

Step 6: Calculating Weighted Average Equity

Step 7: Opponent 3-Bet GTO Strategy

Step 8: Exploitative Strategy Adjustments

Step 9: GTO Strategy Adjustments

Step 10: GTO Default Bet/Raise Sizing

Step 11: Postflop GTO Strategy

Step 12: Revising Estimated Hand Ranges

Conclusion

Beyond the Poker Table

Minimizing House Edge In Other Games

INTRODUCTION

Optima Poker Trainer combines “Game Theory Optimal” (GTO) poker strategy and “Exploitative” poker strategy with a proprietary 12-step system. The underlying algorithm that drives Optima Poker Trainer has been patented with the USPTO, so you will not find this training process anywhere else in the world. The Patent Number is 11,847,929 with title “System and method for creating a poker algorithm capable of independently playing and training users how to play consistently optimal poker.”

This book was originally entitled “The Poker Algorithm,” but the title was changed to Optima Poker Trainer in order to match the name of the integrated FREE MOBILE APP now available on iOS and Google Play. To play while you read, just search for “Optima Poker Trainer” through the iOS or Google Play App Stores. The free mobile app provides an exciting platform to learn the Game Theory Optimal Exploitative (G.T.O.X.) poker strategy while enjoying the rush of playing REAL No Limit Texas Hold’em against computerized opponents. We’re talking about playing genuine multiplayer poker with TRILLIONS of completely random possible hands to learn from, not just limited pre-determined scenarios like all those other poker training apps that charge hundreds or even thousands of dollars to use. For more info and links visit www.OptimaPokerTrainer.com.

An algorithm is defined as a step-by-step process used to accomplish a specific task. Recently the use of algorithms has exploded in the field of Artificial Intelligence. Computer programmers have created revolutionary algorithms that can complete the most complex tasks imaginable in the blink of an eye. This trend is growing with each new day of advanced technology and human innovation.

Various intricate games of strategy such as chess, backgammon, and now even No Limit Texas Hold’em Poker have recently been solved through the use of artificially intelligent computer algorithms. The most advanced poker algorithms utilize some form of “Counterfactual Regret Minimization” as the basis for the program. This means the computer plays trillions of hands of poker against itself, and gradually learns from its own mistakes. Once this lengthy learning process is complete, the program is capable of determining the most optimal decisions in ANY possible hand of poker. Similar methods have been used to conclusively solve nearly ALL games of strategy. The potential real world applications of this form of neural network artificial intelligence are truly endless.

This powerful machine-learning process is ironically similar to the learning process which professional poker players employ in order to improve their skills. Elite poker players are generally required to endure a lifelong learning process that eventually (hopefully) results in an improved understanding of how to make optimal decisions at the poker table. This grueling process of trial by error can effectively be used to learn almost any complex task. But while “Counterfactual Regret Minimization” works great for an inanimate supercomputer, a lifetime of costly mistakes does not work out so well for living poker players.

Hence the need for Optima Poker Trainer! This is much more than just another book about optimal poker strategy. THIS IS A UNIQUE MATHEMATICAL SOLUTION TO TEXAS HOLD’EM POKER! With a proprietary algorithm that combines Game Theory Optimal poker strategy with Exploitative poker strategy, Optima Poker Trainer teaches players a straightforward process for how to improve and even perfect their poker skills.

The algorithm presented here is a proprietary 12-step system that applies to any possible hand of No Limit Texas Hold’em and with any number of opponents. See the Table Of Contents for a brief description of each of the 12 steps. The strategies described can also be applied to other variations of poker such as Omaha, Short Deck, Limit Hold’em, and more. The algorithm instructs users how to play consistently optimal No Limit Texas Hold’em in ANY particular situation, and against ANY unique opponent. Although various updates are still required and will be released soon.

The Optima Poker Trainer free mobile app includes the following customizable game features, with corresponding adjustments to the GTOX algorithm for each feature:

1. Number of Opponents: Choose from 1 to 9 Opponents

2. Opponent Types: Choose from Loose, Very Loose, Tight, Very Tight, GTO, GTOX, or Random Opponent Types

3. Chip Stack Sizes: Choose from Short (25 big blinds), Medium (50 Big Blinds), or Deep (100 Big Blinds) Stack Sizes

4. Additional customizable game features including Tournament Mode, Rakes, Antes, Omaha, Short Deck, and Limit Hold’em are all coming soon. As well as various additional updates and GTO adjustments. So make sure to keep your mobile app updated!

The 100% FREE playing mode within the app is "Pre & Flop Only," meaning you can play all hands only through to the end of the Flop round of betting. You also have the ability to see ALL cards at the table face up. This significantly increases the number of decisions you can learn from each hand. In Tournament Mode (in-app purchase for $1.99), you can play a complete 1 table “Sit & Go” tournament against 9 "Unknown" opponents. Each opponent’s type will be revealed after they lose all their chips, or after you do. Starting chip stack sizes will be 100 Big Blinds each, with the blinds doubling every 10 hands. If you are knocked out of the tournament, you will be able to continue watching the computerized opponents play all hands with all cards turned face up until there is a winner. 

THE MOBILE APP IS NOW AVAILABLE FOR FREE DOWNLOAD ON iOS AND GOOGLE PLAY WITH NO IN-APP PURCHASES REQUIRED, NO ADVERTISEMENTS, AND NO USER DATA COLLECTION!

In addition to all the details on the 12-step algorithm, the Optima Poker Trainer book includes 2 bonus chapters that extrapolate optimal poker strategy concepts into other realms of life. These fascinating ruminations conclude in a final chapter that outlines and explains the optimal betting strategy algorithms for Blackjack, Craps, Baccarat, and other casino games.

Have fun and good luck at the tables! For more information or to watch our VIDEO DEMO, visit us online at www.OptimaPokerTrainer.com!

STEP 1 

Game Theory Optimal Preflop Hand Rankings

In Texas Hold’Em there are 169 unique starting hands that a player can be dealt (without distinguishing between different suits). The most optimal decisions (raise/call/fold or check/bet) are determined based on detailed statistical calculations and game theory considerations. Step 1 of the Optima Poker Trainer algorithm is to rank all 169 unique starting hands in order of strength from the best starting hand of pocket-aces (Hand Rank = 1), down to the worst starting hand of seven-deuce off-suit (Hand Rank = 169). These hand strength rankings will be used to determine the Game Theory Optimal (also known as GTO) strategy that specifies the maximally optimal decisions in any possible situation.

The 169 hand rankings (see Table 1) are based on effective starting chip stack sizes of around 100 big blinds per player. Many of the rankings will require minor adjustments based on varying effective stack sizes (among other factors). With a shorter effective stack size, ace-highs and other regularly dominated hands will be ranked higher primarily because there is less risk from losing a very big pot with top pair. With a deeper effective stack size, suited and/or connected hands will be ranked higher because there is greater potential reward from winning a very big pot with a flush (for suited cards) or a straight (for connected cards).

The approximate rankings of each hand should be memorized, especially the top 50 hands because they are used most often. At a minimum, players need to understand the general relative order of the 169 unique hands. High pocket pairs such as pocket Aces and pocket Kings are clearly the top ranking starting hands. Also among the top ranking hands are 2 big cards (especially when suited), the best of which is Ace-King suited (with nut-flush potential and only 2 starting hands that dominate it). Connected cards such as Jack-Ten (the only hand with 4 different ways to make a nut-straight) are also ranked higher due to their increased likelihood to make a straight.

Table 1 differs from more typical Texas Hold’em starting hand ranking systems due to two unique factors:

1. Different hand types (pocket-pairs, ace-highs, suited-connectors, etc) are spread out more evenly throughout the rankings. This is done with the intention of making it harder for opponents to identify a player’s specific hand type within any given hand range.

2. Particular hands (such as ace-high with a bad “kicker”) that may be slight statistical favorites over other hands, but are also more regularly dominated and/or more easily bluffed, are ranked lower (particularly for deeper stacks).

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TABLE 1 

GTO Preflop Hand Rankings = 1 to 169

         “s” means suited, “o” means offsuit

• If accounting for different suits (clubs, diamonds, hearts, spades), then there are 1,326 different possible starting hand combinations. Each suited hand has probability = 4/1,326 ~ .30%, each pair has probability = 6/1,326 ~ .45%, and each offsuit hand has probability = 12/1,326 ~ .90%

• Table 1 rankings apply for a moderately deep effective stack size of approximately 70 - 150 big blinds at the start of a hand. Table 1 rankings will need to be adjusted for short stacks (0 - 30 big blinds), medium stacks (30 - 70 big blinds), and super-deep stacks (150+ big blinds).

Beyond The Poker Table

Poker is predominantly a game of skill. As with all things in life, luck is also a factor. But the odds will inevitably play out as mathematics has statistically ordained. Poker players with strategy and skill in their favor will win in the long run. While those that don’t understand how to make optimal decisions will eventually lose their chips. This fundamental concept of poker can also be applied to everyday life; In order to achieve true success, a person must consistently make wise and informed decisions. Failure to make the correct decisions will inevitably result in failure on a grander scale. This is one example of how poker strategy and principles can be applied to everyday life. The parallels between poker and real life do not end there.

One of the core characteristics of an optimal poker player is the ability to accurately identify and analyze ALL relevant information at hand. Steps 1 - 12 of the Optima Poker Trainer algorithm outline the various forms of analysis utilized by poker players to determine optimal decisions. Similarly, in real life, one of the most fundamental characteristics of a truly successful person is the ability to accurately size up their surroundings in order to determine the optimal pathways towards accomplishing their goals. Again the correlations between playing optimal poker and living a successful life are clear.

Similar direct correlations between poker and life can be seen in various other subject matters such as business and finance. The stock market is a fascinating parallel with poker in that both are public forums where individuals compete in a game of imperfect information while the winners are rewarded with profits financed in part from the losses of the losers. Although the stock market is not a zero-sum game the way poker is (as is the stock-options market). Stock market investors can be considered as competitors (as are poker players) with the goal of identifying the most profitable businesses in order to buy the most undervalued stocks, both in real time as well as with projections about the future prospects of a particular business and the overall economy.

Some people presume the stock market functions according to the principles of the “Efficient Markets Hypothesis”, which assumes perfect information by all market participants (meaning all investors are assumed to be fully aware of all market developments and all publicly available information). However, seasoned investors understand the competitive nature and significant value of superior investment research and analysis. Stock portfolio managers and traders with lifelong careers of profits that consistently outperform traditional market returns can be viewed as evidence that the Efficient Market Hypothesis does not always apply in the stock market. Poker players that reap the rewards of optimal poker strategy enjoy consistent profits similar to those of optimal stock traders. And artificial intelligence in both poker strategy and stock trading is leading the way towards developing optimization algorithms in both of these fields.

The correlations between poker and other aspects of life can even be found in more subjective concepts such as psychology. One of the most common and costly mistakes that often plagues countless poker players involves a concept known as “going on Tilt.” Tilt always centers around the human inability to control one’s emotions. Tilt regularly occurs as a result of psychological issues such as anger-management or ego. Tilt also often occurs as a result of financial issues; such as a person who feels they cannot afford to lose the money they are gambling, or inversely as a person with so much money in front of them that they simply don’t care whether they win or lose. Tilt also regularly manifests in the form of a momentary loss of patience, due to the fact that the tedious task of folding repeatedly requires a uniquely patient temperament. Other Tilt catalysts include factors like alcohol, drugs, lack of sleep, and other pitfalls.

These are all prime examples of how Tilt can negatively influence a poker player’s decision making process. If you take a moment to reflect on each of these circumstances, most people can likely identify at least a few events from their personal lives that were damaged or even destroyed as a result of “real life Tilt.” Learning the discipline to control and cultivate one’s emotions is a crucially important skill in both poker and life.  

The potential applications of optimal poker strategy to real world life are endless. It is for this reason that an artificially intelligent algorithm that is capable of playing optimal poker is such a profound feat. Because it provides a glimpse into a futuristic world where currently common mistakes become obsolete, and the world operates according to algorithmically designed perfection. This improvement in global efficiency will one day result in significant improvements in metrics such as GDP (Gross Domestic Product), as well as other measures of human productivity and quality of life. These societal developments will likely occur in tandem with scientific discoveries such as the Grand Unifying Theory, that could be utilized to accomplish the most complex tasks imaginable (even on a quantum level).

It is interesting to note that these supernatural scientific discoveries are occurring during the same time period that civilization is said to soon be entering the “Post-Messianic Era.” Which according to Kabbalah (Jewish Mysticism) has been prophesied to occur on or before the year 6000 in the Hebrew calendar (2240 AD in the western calendar). This 6,000 year timeline of modern human spiritual struggle and evolution is a metaphysical metaphor for God's original 6 days of creation from Genesis in the Old Testament (or Torah). With the final 7th day of rest (or Sabbath) being used as a metaphor for an endless utopia in the coming Messianic era.

Although in my personal opinion, it will not be a single human “messiah” born in Bethlehem from the bloodline of King David that ushers in this utopia (as is believed in both Kabbalah and Christianity). It will be modern science (specifically artificial intelligence) combined with a worldwide elevation of human consciousness resulting in the realization and universal acceptance that we as humanity are ALL “one nation, under god, indivisible, with liberty and justice for ALL.” With no single race or religion or even political group divided into conflicting factions. “Inshallah” (which means God willing in my native language of Farsi) we will actually get there within the next 200 years exactly as was prophesied thousands of years ago.

It is also interesting to note that while the Nash Equilibrium solution of Game Theory Optimal Exploitative poker that has been specified throughout this book does exist, that does not preclude the existence of alternative Nash Equilibrium poker strategies that are also optimal in their own right. In fact, it is a mathematical certainty that there ARE multiple alternative Nash Equilibriums that exist as a spectrum of optimal strategies, as opposed to 1 exclusive and unique solution. With adjustments leading to re-adjustments in an infinite cycle of back and forth.

Once again, the profound correlations between poker and real life continue in that there is also no one absolute and objective “solution” to life. Every person is their own unique microcosm and therefore has their own personal style of what constitutes “optimal” for them. So while there is no one universally accepted truth that must apply to all individuals, there are infinite individual universal truths that all adhere to the same set of principles in their own special way. Or at least that is a concept that Game Theory Optimal Exploitative poker strategy appears to support. Rumi and many other ancient philosophers throughout history would no doubt agree.

One final rumination: I have always considered the ultimate shortfall of a career in poker to be the zero-sum nature of the game. Meaning for any one player to win, there needs to be an equivalent loser on the other side of the hand (not to mention the Rake that is retained by the House). In direct contrast to other more productive endeavors of life, there is no potential in poker to create win-win scenarios where all parties involved come out ahead. Unless of course you account for the immeasurable entertainment value, as well as the wide-ranging education value often derived from the game. For the true poker player, these are the ultimate rewards. Although it never hurts to win some money and get paid in the process!

Minimizing The House Edge In Other Games

Poker is a unique form of gambling in that skilled players can actually make a living playing poker professionally. Most other casino games are designed to ensure that the house has an inherent statistical advantage, regardless of how the game is played. Meaning that in the very long run, the casino will always win and the player will always lose. This statistical advantage for the casino is called the “House Edge.”

When playing these casino games (such as blackjack, craps, baccarat, roulette, etc), the player’s goal should be to minimize the House Edge as much as possible. So it is important to know which games/bets have the greatest/least statistical advantage for the house. Players can then focus on the games and betting options that have the lowest percentage edge for the house.

The following summaries describe the optimal betting strategies for various casino table games. Each summary can be considered as an algorithm for the optimal betting strategy in that game. Including descriptions and statistics on the House Edge for each respective bet/game:

THE BLACKJACK ALGORITHM

The optimal algorithm for blackjack has been outlined in detail and can be found online by researching the “Blackjack Basic Strategy.” The House Edge can be reduced to as low as between 1 - 2 % in most blackjack games when players utilize the optimal basic strategy algorithm at all times. Furthermore, highly skilled blackjack players can actually turn the statistical advantage to their favor by employing card-counting tactics.

The basic premise of card-counting in blackjack is based on the fact that the player has a statistical advantage over the house when there are significantly more large cards (particularly 10s, Jacks, Queens, Kings, and Aces) left in the deck. So players that are able to keep track of the large vs. small cards that are exposed during play are able to increase their bet size when the remaining cards are larger, and decrease their bet size when the remaining cards are smaller. Player’s can also determine when to adjust the marginal basic strategy decisions when they know the remaining cards are larger or smaller. Thereby turning the statistical edge into the player’s favor.

In earlier eras of gambling, experienced blackjack players were able to take advantage of these tactics in order to win significant sums of money from casinos. However, at this point in time, most big casinos have employed various deterrents that make it nearly impossible to effectively count cards at blackjack. So generally speaking, the best that modern blackjack players can do is utilize the basic strategy and approximate card counting to minimize the house edge to near 0%

THE CRAPS ALGORITHM

Craps is an exciting dice game that offers players the ONLY table-game bet that always has a House Edge = 0%. Therefore, the optimal craps algorithm is to bet the maximum on this particular bet, and avoid placing ANY alternative bets. By utilizing this betting strategy, player’s can minimize the House Edge at craps to approximately 1%. The best part is this optimal craps strategy is very simple to employ and requires no skill whatsoever. Simply place your initial bet on the “pass-line,” then after the initial roll of the dice (assuming the game does not end), “back up” the pass-line bet with the “maximum odds.” Most casinos limit this “maximum odds” bet to 3, 4, or 5 times the original pass-line bet size (depending on which number comes up on the initial roll).

THE BACCARAT ALGORITHM

Baccarat is another casino table game that allows for an optimal strategy that reduces the house edge to approximately 1%. This baccarat algorithm is also very simple and requires no real skill to employ. In most versions of baccarat, the “Banker” bet has a house edge equal to about 1%. While the “Player” bet has a house edge equal to about 1.25%. All alternative bets have a house edge that is significantly higher. Therefore, the optimal strategy at baccarat is to always bet on Banker and avoid all other bets. If you have a gut feeling that the Banker bet is not going to win, you have the option to not bet at all and just wait for the next hand.

ALL OTHER GAMES

All other typical casino games (such as Roulette, Slots, Pai Gow, etc) have significantly worse odds than the optimal strategies described above. So the best way to minimize the house edge at these other games is to simply NOT PLAY! If you’re looking to enjoy the thrill of pure gambling, you should focus on the above mentioned optimal betting strategies in either blackjack, craps, or baccarat.

Just make sure to only gamble with what you can afford to lose. Also take advantage of all the comps and free food/beverages that many casinos offer to players. These comps are often enough to compensate for the minimal house edge lost to the casino. Allowing you to save your bankroll for the poker tables where the statistical edge can be in YOUR favor by employing the Optima Poker Trainer Game Theory Optimal Exploitative strategy!

To learn more just download the “Optima Poker Trainer” FREE MOBILE APP from the iOS or Google Play app stores. You can also download the Optima Poker Trainer E-book on Amazon for just $9.99. More info and links are available at www.OptimaPokerTrainer.com.