What if you could play online poker at Bovada and never lose? There are no such guarantees, of course – you can win or lose an entire stack at No-Limit Hold’em on any one hand, depending on which cards come out at random. However, in the long run, there is a certain style of play that will allow you at least to break even if you do it right, and to profit from other players’ mistakes when they happen.

He used poker as an example and addressed the problem of bluffing and second-guessing the opponent in a game of imperfect information. Borel envisioned game theory as being used in economic and military applications. Borel's ultimate goal was to determine whether a 'best' strategy for a given game exists and to find that strategy. Game Theory Poker Example.The following game is played with Rose and Colin. Each player antes $50 for a $100 pot. Rose looks at a card from a full deck. Rose will win the pot at showdown if the card is a Spade, otherwise she will lose.Rose can decide to bet $100 or check.If Rose bets, Colin may decide to call $100 or fold. That occur in the game of poker. The analysis of models of poker has a long and distin-guished existence in the game theory literature. Chapter 5 of the book of Emile Borel,´ Applications aux jeux de hasard (1938), and Chapter 19 of the seminal book on game theory by von Neumann and Morgenstern (1944) are devoted to the topic.

You may have heard of this style of poker: It’s called game-theory optimal, or GTO for short. The idea is to make yourself as unexploitable as possible, rather than exploit your opponents, and it really started gaining traction sometime around 2015, when computer programs are known as “solvers” gained the power to quickly (and cheaply) analyze billions of hands. GTO solvers are even more powerful now. They can recommend the right balance of value bets and bluffs to frustrate your opponents, and the closer you can get to striking that balance, the more money you can win at the poker table.

When to Play Balanced in Hold’em

Achieving this balance is easier said than done. GTO solvers, and advanced poker bots like Libratus, use complex strategies that are virtually impossible for humans to mimic. A lot of good work has been done recently in coming up with simplified Hold’em strategies that are near-optimal in many situations. These are much easier strategies to implement; they aren’t perfect, but they’ll keep you from making the kind of big mistakes that many players make trying to play perfectly balanced poker.

Instead of trying to memorize and replicate these strategies at Bovada Poker, consider taking the time to think about why balance is important. We already know that deception is a vital element in Hold’em; when you make a bet, for example, you want your opponents to be confused about whether you’re betting for value or as a bluff. Balance takes this one step further, by using the best ratio of bluffs to value bets for your situation. Too many value bets will allow your opponent to exploit you by folding. Too many bluffs will allow your opponent to exploit you by calling.

Once you understand the concept of balance in poker, the next step is to know when to play unbalanced poker. Think of GTO like a defensive shell that you leave whenever there’s a large enough opening to exploit your fellow players. You’ll “drop your guard” by making a certain move more or less often than optimal play would suggest, hoping to land a big punch and extract more value from your opponent. But beware: When you’re unbalanced, you’re vulnerable to getting hit yourself.

EmileBorel: The Forgotten Father of Game Theory?

In 1921, Emile Borel, a French mathematician, published several papers onthe theory of games. He used poker as an example and addressed the problemof bluffing and second-guessing the opponent in a game of imperfectinformation. Borel envisioned game theory as being used in economic andmilitary applications.Borel's ultimate goal was to determine whether a 'best' strategy for agiven game exists and to find that strategy. While Borel could be arguablycalled as the first mathematician to envision an organized system forplaying games, he did not develop his ideas very far. For that reason,most historians give the credit for developing and popularizing gametheory to John Von Neumann, who published his first paper on game theoryin 1928, seven years after Borel.

John Von Neumann

Born in Budapest, Hungary, in 1903, Von Neumann distinguished himself fromhis peers in childhood for having a photographic memory, being able tomemorize and recite back a page out of a phone book in a few minutes.Science, history, and psychology were among his many interests; hesucceeded in every academic subject in school.

He published his first mathematical paper in collaboration with his tutorat the age of eighteen, and resolved to study mathematics in college. Heenrolled in the University of Budapest in 1921, and over the next fewyears attended the University of Berlin and the Swiss Federal Instituteof Technology in Zurich as well. By 1926, he received his Ph.D. inmathematics with minors in physics and chemistry.

By his mid-twenties, von Neumann was known as a young mathematical genius and his fame had spread worldwide in the academic community. In 1929, hewas offered a job at Princeton. Upon marrying his fiancee, Mariette,Neumann moved to the U.S. (Agnostic most of his life, Von Neumann acceptedhis wife's Catholic faith for the marriage, though not taking it veryseriously.)

In 1935, Mariette gave birth to Von Neumann's daughter, Marina. Two yearslater, Mariette left Von Neumann for J. B. Kuper, a physicist. Within ayear of his divorce, Von Neumann began an affair with Klara Dan,his childhood sweetheart, who was willing to leave her husband for him.

Von Neumann is commonly described as a practical joker and always the lifeof the party. John and Klara held a party every week or so, creating akind of salon at their house. Von Neumann used his phenomenal memory tocompile an immense library of jokes which he used to liven up aconversation. Von Neumann loved games and toys, which probably contributedin great part to his work in Game Theory.

An occasional heavy drinker, Von Neumann was an aggressive and recklessdriver, supposedly totaling a car every year or so. According to WilliamPoundstone's Prisoner's Dilemma, 'an intersection in Princeton wasnicknamed 'Von Neumann Corner' for all the auto accidents he had there.'(p.25)

His colleagues found it 'disconcerting' that upon entering an office wherea pretty secretary worked, von Neumann habitually would 'bend way wayover, more or less trying to look up her dress.' (Steve J. Heims, JohnVon Neumann and Norbert Wiener: From Mathematics to the Technologies ofLife and Death, 1980, quoted in Prisoner's Dilemma, p.26) Somesecretaries were so bothered by Von Neumann that they put cardboard partitions at thefront of their desks to block his view.

Despite his personality quirks, no one could dispute that Von Neumann wasbrilliant. Beginning in 1927, Von Neumann applied new mathematical methodsto quantum theory. His work was instrumental in subsequent 'philosophical'interpretations of the theory.

For Von Neumann, the inspiration for game theory was poker, a game heplayed occasionally and not terribly well. Von Neumann realized that pokerwas not guided by probability theory alone, as an unfortunate player whowould use only probability theory would find out. Von Neumann wanted toformalize the idea of 'bluffing,' a strategy that is meant to deceive theother players and hide information from them.

In his 1928 article, 'Theory of Parlor Games,' Von Neumann firstapproached the discussion of game theory, and proved the famous Minimaxtheorem. From the outset, Von Neumann knew that game theory would proveinvaluable to economists. He teamed up with Oskar Morgenstern, an Austrianeconomist at Princeton, to develop his theory.

Their book, Theory of Games and Economic Behavior, revolutionizedthe field of economics. Although the work itself was intended solely foreconomists, its applications to psychology, sociology, politics, warfare,recreational games, and many other fields soon became apparent.

Although Von Neumann appreciated Game Theory's applications toeconomics, he was most interested in applying his methods to politics andwarfare, perhaps stemming from his favorite childhood game, Kriegspiel, achess-like military simulation. He used his methods to model the Cold Warinteraction between the U.S. and the USSR, viewing them as two players ina zero-sum game.

From the very beginning of World War II, Von Neumann was confident of theAllies' victory. He sketched out a mathematical model of the conflictfrom which he deduced that the Allies would win, applying some of themethods of game theory to his predictions.

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In 1943, Von Neumann was invited to work on the Manhattan Project. VonNeumann did crucial calculations on the implosion design of the atomicbomb, allowing for a more efficient, and more deadly, weapon. VonNeumann's mathematical models were also used to plan out the path thebombers carrying the bombs would take to minimize their chances of beingshot down. The mathematician helped select the location in Japan to bomb.Among the potential targets he examined was Kyoto, Yokohama, and Kokura.

'Of all of Von Neumann's postwar work, his development of the digitalcomputer looms the largest today.' (Poundstone 76) After examining theArmy's ENIAC during the war, Von Neumann came up with ideas for a bettercomputer, using his mathematical abilities to improve the computer's logicdesign. Once the war had ended, the U.S. Navy and other sources providedfunds for Von Neumann's machine, which he claimed would be able toaccurately predict weather patterns.

Capable of 2,000 operations a second, the computer did notpredict weather very well, but became quite useful doing a set ofcalculations necessary for the design of the hydrogen bomb. Von Neumann is also credited with coming up with the idea of basing computercalculations on binary numbers, having programs stored in computer'smemory in coded form as opposed to punchcards, and several othercrucial developments. Von Neumann's wife, Klara, became one of the firstcomputer programmers.

Von Neumann later helped design the SAGE computer system designed todetect a Soviet nuclear attack

In 1948, Von Neumann became a consultant for the RAND Corporation. RAND(Research ANd Development) was founded by defense contractors and theAir Force as a 'think tank' to 'think about the unthinkable.' Their mainfocus was exploring the possibilities of nuclear war and the possiblestrategies for such a possibility.

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Von Neumann was, at the time, a strong supporter of 'preventive war.'Confident even during World War II that the Russian spy network hadobtained many of the details ofthe atom bomb design, Von Neumann knew that it was only a matter of timebefore the Soviet Union became a nuclear power. He predicted that wereRussia allowed to build a nuclear arsenal, a war against the U.S. would beinevitable. He therefore recommended that the U.S. launch a nuclear strikeat Moscow, destroying its enemy and becoming a dominant world power, so asto avoid a more destructive nuclear war later on. 'With the Russians it isnot a question of whether but of when,' he would say. An oft-quoted remarkof his is, 'If you say why not bomb them tomorrow, I say why not today? Ifyou say today at 5 o'clock, I say why not one o'clock?'

Just a few years after 'preventive war' was first advocated, it became animpossibility. By 1953, the Soviets had 300-400 warheads, meaning that anynuclear strike would be effectively retaliated.

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In 1954, Von Neumann was appointed to the Atomic Energy Commission. A yearlater, he was diagnosed with bone cancer. William Poundstone'sPrisoner's Dilemma suggests that the disease resulted from the radiation VonNeumann received as a witness to the atomic tests on Bikini atoll. 'A number ofphysicists associated with the bomb succumbed to cancer at relativelyearly ages.' (p. 189)

Von Neumann maintained a busy schedule throughout his sickness, even whenhe became confined to a wheelchair. It has been claimed by some that thewheelchair-bound mathematician was the inspiration for the character ofDr. Strangelove in the 1963 film Dr. Strangelove or: How I Learned to StopWorrying and Love the Bomb.

Von Neumann's last public appearance was in February 1956, when PresidentEisenhower presented him with the Medal of Freedom at the White House. InApril, Von Neumann checked into Walter Reed Hospital. He set up office inhis room, and constantly received visitors from the Air Force and theSecretary of Defense office, still performing his duties as a consultantto many top political figures.

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John von Neumann died February 8, 1957.

His wife, Klara von Neumann, committed suicide six years later.

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Dr. Marina von Neumann Whitman, John's daughter from his first marriage,was invited by President Nixon to become the first woman to serve on thecouncil of economic advisers.