Operations Research 12A: Zero-Sum Game & Pure Strategy
Texas Holdem Game Theory As new depths of poker strategy continued to be discovered, Texas holdem tables sound more like science labs than the scene of a simple card game.
Perhaps more than any other advanced strategy concept, the notion of game theory optimal play — better known as GTO — has seeped into the mainstream poker consciousness.
The steady advancement in the way players tackle Texas holdem problems is only natural, as the Poker Boom of 2003 to 2006 prompted millions of thoughtful, intelligent, and analytical individuals to take their talents from the classroom to the card room.
According to Roger B.
Additionally, the ideas put forth by game theory experts have also been co opted for use by economists, political scientists, biologists, and several other fields of study.
Thus, while the study of game theory is predicated on the various rules and procedures used to govern classic games like Texas holdem, the ideas that emerge from game theory investigation are widely applicable across a diverse range of subjects.
Throughout the 20th century, mathematicians and logicians like John von Neumann, Oskar Morgenstern, Merrill M.
Flood, Melvin Dresher, and John Nash each contributed fundamental theories and postulations to the field of game theory study.
For poker players with an educational background in advanced mathematics — of whom there seemed to be an endless supply during the Poker Boom — learning the lingo of game theory and applying it to their favorite game proved to be a highly beneficial proposition.
These players were able to expand their lines of thinking beyond the most basic constructs — what do I have or need, what does my opponent have or need, etc.
The average person can only take so many abbreviations and hypotheticals before their head begins to ache, so breaking things down to their basic meaning is a helpful way to begin.
Take a look below for a comprehensive glossary of essential terms and concepts used within the world of game theory: Exploitable Strategy Strip blackjack online hacked strategy that offers a reduced expected value EV, compared to GTO strategy, when playing against an exploitive strategy.
Any non game theory optimal GTO strategy is, by definition, an exploitable strategy.
Exploitive Strategy Any strategy that offers an increased expected value EV than a game theory optimal GTO strategy, when playing against any particular strategy.
Any non GTO strategy that counters an exploitable strategy better than a strictly GTO approach is, by definition, and exploitive strategy.
Game Theory Optimal GTO The strategy that offers the highest possible expected value EV when an opponent always applies an optimal counter strategy.
This strategy provides the highest level of EV, at 0.
Optimal Exploitive Strategy The strategy that offers the highest possible expected value EV against any opponent strategy.
Suboptimal Strategy Any strategy that offers a lower expected value EV than the optimal exploitive strategy.
A game like Monopoly, in which players can negotiate the price of a mortgage on property deeds among other agreements, is a classic cooperative game.
A non chips 3d model free poker game, on the other hand, forbids players from making similar arrangements among themselves.
Technically speaking, poker variants like Texas holdem are non cooperative games, because the rules preclude collusion and other forms of explicit cooperation.
Infinitely Long Games From a practical standpoint, any game involving human players must be a finitely long game — or one that has a fixed endpoint.
Whether that means attaining a certain score, satisfying a series of conditions, or otherwise defeating your opponent, a finitely long game has a beginning — and a definitive end.
And even in a game designed to stretch on into perpetuity, the limits of human endurance, and indeed lifespan, prevent it from being truly infinite.
For poker players, every cash game or tournament session has a start and an end.
But as any experienced poker pro knows quite well, judging the results of any particular session provides an inconsistent appraisal, and the truth is best discovered by examining results over the long run.
These factors can span the spectrum from personal history between join seminole hard rock tampa blackjack tournament words players, the relative importance of pending prize money to opponents of different means, the impact of physical fatigue and diminished stamina, and even the presence of television cameras or a similar spotlight.
Some players can dominate a large tournament field until reaching the final table, where the change of setting from anonymous area on the floor to ringed off feature table can jar their nerves.
Experienced players use their knowledge of this meta game to apply increased pressure and make things uncomfortable for less experienced foes.
Perhaps the other player has shown a propensity for checking back strong hands in position, so you may begin using flop checks more often to clarify his range.
The classic example of a perfect information game is chess, as both players begin with identical piece alignments and witness all subsequent moves.
An imperfect information game is one in which both players are limited to an obscured view of the full game conditions.
In blackjack, for example, you know your own hole cards, but not that of the dealer, leading to a situation in which making educated guesses is the click way to proceed.
Texas holdem is another imperfect information game, because even though all players can see the same community cards on board, and their own hole cards, the hole cards of every other opponent remain concealed until the showdown round is reached.
If you win 12,000 chips in a pot, a player or players at the table must have lost 12,000 chips as a result.
Conversely, a non zero sum game is one in which the amount of available resources in play can be changed.
They can, and they already do.
Strategies that rely on unspoken acknowledgement of certain factors, deviations from the norm decided on when competing against certain players — these plays that seem instinctual are actually demonstrations of game theory in action.
You wind up playing your way into the final four out of nine players — but only three players will earn a payout.
You sit with 7,000 chips, another has 6,800, while two short stacks are clinging to 1,200 and 1,000 respectively.
In the big is blackjack a zero sum game position, with 400 chips already committed, you watch the shortest stack shove all in for his last 1,000.
The small blind player, who is your fellow big stack, makes the call to put the shorty at risk.
You look down at Kc 10c — a decent hand to try and bust the next player with — so you call as well, creating casino blackjack automatic heads up side pot while the all in player sweats the action.
The flop comes down 10s 9h 7h, and the small blind checks it over to you.
In most spots, firing out with top pair on a textured flop would be advisable, as to prevent opponents from backing into a straight or flush on the turn.
But you shoot your heads up opponent a quick look and knock the felt with your fist, signaling a check.
The turn comes a blank with the 2d, but this time the small blind is checking as the baby card falls.
You check back quickly, and the process repeats itself on the Kh river.
But the small blind turns his 5h 3h face up on the felt, and the flush is good enough to bust the short stacked player in fourth place.
In this case, even though poker is a non cooperative game by rule, you and the small blind recognized a prime opportunity to cooperate.
By checking down through all three streets, you and the small blind effectively ensured that two hands, rather than one, would have a chance to eliminate the fourth place player and burst the bubble.
In the game of Texas holdem, communicating your intent to join forces with the small blind would represent a violation of the rules against collusion.
Players know this all too well, so when a check down situation like the one described here presents is blackjack a zero sum game and it invariably will on any tournament bubble or pay jump, the agreement to check it down remains unspoken.
In this case, you have a stack of 850,000 when the click at this page is only 300,000 — and 29 players remain with the final 27 getting paid.
A look around your table presents a beautiful sight, as four of the six opponents across from you are riding short stacks of 100,000 or under.
You begin raising several hands in a row, hoping to get involved with a short stacked player and take your chances on a gamble.
The four short stacks are playing it snug, each hoping to keep enough chips in hand to sneak into the money.
As for the two bigger stacks, they remain fearful of entering pots against you — the only player who can bust them.
As you relentlessly raise, and the table keeps passively folding, you keep dragging seemingly small pots which contain the 5,000 chip small blind, 10,000 chips in the big blind, and another 7,000 in antes at 1,000 chips each.
Then, a funny thought occurs to you: having this particular dynamic at the table may actually be better than bursting the bubble.
In pure cash terms, knocking out two more players from the tournament will return double your buy in amount at the least.
But in terms of chips, keeping the field at 29 players — and out of the money — presents the best opportunity to build an even bigger stack.
And as we all know, tournament chips equate to cash on an escalating level, so as you progress later in a tournament, having more chips can mean the difference between a min cash or winning life changing money.
Suddenly, a short stacked player shoves all in from the hijack position and the action folds around to you in the big blind.
A look over at the other table confirms that only 28 players remain, so this is your shot to burst the bubble and ensure a cash.
You peek down to see Ad 9d, certainly is blackjack a zero sum game enough to warrant a call, and probably the better hand against a short shover.
The short stacked player lives to fight another day, and you go back to raising on the very next hand — and many more after that — ravaging your fearful opponents for every last chip before the money bubble finally does break.
But by folding, and keeping them in the game for a few more orbits, you were able to use the raise and take method to add another 120,000 or so without facing any serious fight.
Those extra chips prove to be quite useful too, and instead of the usual 8th or 9th place exit you wind up with on deep runs, you go on to win the entire tournament for your first big time score.
Given a normal tournament scenario, calling with a huge chip advantage to bust a short stacked player from the field would be the proverbial no brainer.
The average stack at the moment sits at 175,000, and while you have more than seven players at the table, one actually has you covered with a 600,000 stack.
The field has dwindled to 39 players and the final 36 will make the money.
The other big stack is on the small blind and next to act, and rather than keep the pot small, he splashes three of the pink 5,000 chips into the middle for a three bet to 15,000.
The issue here was simple, as most players late in tournaments prefer to survive rather than exploit fine edges.
From a game theory perspective, this example illustrates a suboptimal strategy, because a purely GTO approach to flopping a big ace on a dry board would be to call or raise often, while folding almost never.
Big stacks at the table late in tournaments often operate under an unspoken assumption, taking turns bullying the smaller stacks, but seldom engaging in outright aggression against one another.
And to take the game theory implications one step further, poker experts generally agree that the optimal strategy as a big stack in this situation should be based on exploitative play.
Everyone gets creative with funky suited connectors and baby is blackjack a zero sum game hands of course, but at the lower stakes, playing a snug game which incorporates premiums and top tier hands from early and middle position will prove to be profitable.
But every poker game is a different animal entirely, consisting of unique playing styles and personalities, along with constantly fluctuating variables like stack size, positions, and indeed, hole cards.
In certain situations, you may find yourself expanding your range drastically, playing basically every hand in an attempt to exploit your post flop advantages over a weaker opponent.
The lowly 2d 4c.
She flopped nothing but a deuce on the Kc 6s 2h flop, called a bet to see the 3d fall on the turn, and called an even bigger wager to find her 5d gin card on the river.
Just like she drew it up.
At this point, your radar is blaring alarm bells and you realize that an opponent demonstrating an extremely exploitable strategy has just arrived on the scene.
It takes an orbit or two, and you bleed a few chips along the way while she continues to act as the table card rack, but eventually you call her opening raise with the 10d 8d and catch a nice Jd 9c 2c flop.
The woman suddenly slows down with a tap of the table, checking it over to you.
You fire out a wager and she comes over the top with a big all in is blackjack a zero sum game, which you happily snap off with your nut straight.
She shows the Qd 2h for a ragged two pair, having flopped bottom pair and made two pair on the river.
Against most opponents, hands like 10 8 may not be the most profitable holding over the long run, but here you correctly identified an opponent who would allow you to take the low risk, high reward shot.
The excitement of running deep is counterbalanced by the desperation of needing a quick double up.
In this spot, most recreational players, and quite a few professionals, are plagued by the problem of patience.
To help solve this dilemma, poker focused game theorists have crunched the various probabilities based on hand strength relative to current big blind volume.
These charts function just like the basic strategy charts used by blackjack players, providing clear and defined guidelines on the optimal way to approach close situations.
Essential Texts and Resources As we mentioned earlier, the author of this page in no way, shape, or form claims to be an expert in Texas holdem game theory.
These resources were written, or otherwise created, by experienced experts who have spent the long hours in the classroom which are required to wield advanced game theory knowledge.
With that said, everybody learns differently, so a dense textbook style treatise on game theory may not work as well for you as it does for others.
Conversely, visual aids and interactive features are perfect for some students who need a tangible grasp on abstractions, while more mathematically inclined learners will have no need for the added clutter.
Dixi and Barry J.
The best players use game theory whether they realize it or not, so why not basics casino blackjack more about it and maximize your chances to win?
The information found on Blackjack magazine />It is a purely informational website that does is blackjack a zero sum game accept wagers of any kind.
Although certain pages within Gamblingsites.
If you believe you have a gambling problem, please visit BeGambleAware or GAMCARE for information and help.
Is Stock Market a Zero Sum Game?
A zero sum game, in simple terms, is a game with only one winner. Craps and blackjack are zero sum games. Either you win or the casino wins. However, there is a hurdle for players which is the house advantage.
It above my understanding!
This valuable message
It still that?
It is remarkable, very amusing opinion
It is a pity, that now I can not express - it is compelled to leave. But I will return - I will necessarily write that I think.
I congratulate, what necessary words..., a remarkable idea
Precisely in the purpose :)
I consider, that the theme is rather interesting. I suggest all to take part in discussion more actively.
Not in it an essence.
It is necessary to try all
It was specially registered at a forum to tell to you thanks for support.
It agree, this magnificent idea is necessary just by the way
What charming answer
I consider, that you are mistaken. Write to me in PM, we will talk.
In it something is. Thanks for the help in this question.