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Poker Probability Essay

By Jennifer Ouellette

Last week, a federal judge in Brooklyn overturned the indictment of a Staten Island man who ran poker games in the back room of a warehouse, on the grounds that poker is a game of skill, not chance — and hence, such games cannot be prosecuted under federal laws prohibiting illegal gambling businesses.

It’s just the latest sally in the ongoing debate over poker that’s been raging for more than years. And it comes on the heels of a ruling last year by the Justice Department that ′s Wire Act applied only to sports betting, not poker. This is kind of ironic, since the Justice Department also shut down online poker in the spring of , charging the men behind the three most popular online sites with fraud and money laundering.

Clearly, the issue is far from resolved, but John Pappas, executive director of the Poker Player’s Alliance, is encouraged by the latest ruling by Judge Jack B. Weinstein. “Today’s federal court ruling is a major victory for the game of poker and the millions of Americans who enjoy playing it,” he said in a statement. (The alliance is dedicated to decriminalizing poker.)

But wait! Via @Chemjobber on Twitter, I learned of a spanking new study by German researchers concluding that winning at poker is basically all about luck. They recruited poker players, half self-defined “experts” and half “average,” sat them down at tables of six, evenly divided between expert and average players, and then had them all play 60 hands of Texas Hold ‘Em. Oh, and they fixed the deals, the better to measure the effects of luck.

Their conclusion, per Neuroskeptic: “Luck, rather than skill, was key in determining final balance, with experts taking no more, on average, than novices. Experts did play differently, on various measures, and seemed better able to cope with bad luck, losing less; but they also won less when given good cards.”

So are the German researchers correct that poker should thus be classified as gambling? Not necessarily. A study concluded that poker is a skill — students who received some basic pointers performed better while playing hands of poker than those who received no training at all. Still other studies support the German conclusion. Who are we to believe?

Neuroskeptic rightly points out a major flaw in the study, namely, the classification of “expert” players was based on self-reports. I would argue further that playing a mere 60 or hands of poker is an insufficient sample size, given the statistical complexities of the game. There are 52 cards, with more than million possible five-card combinations. Texas Hold ‘Em uses seven cards so there are around million combinations. Plus, you know, fixing the deals really messes with those probabilities.

Compare this to the sample size of the expert witness cited by Judge Weinstein in his massive page ruling. Randal D. Heeb is an economist and statistician (and avid poker player) who analyzed million hands online of no-limit Texas Hold ‘Em and found that the skill of a player “had a statistically significant effect on the amount of money won or lost.”

The many mathematicians and physicists who are aficionados of poker would agree with Heeb. I wrote a feature for Discoverin November on poker-playing physicists, which included the Time Lord (a.k.a. Caltech physicist Sean Carroll, a.k.a. my Better Half), as well as string theorist Jeff Harvey, particle physicists Michael Binger and Marcel Vonk (both of whom have done extremely well on the professional circuit), and a former grad student of Harvey’s named Eduard Antonyan. It spawned an NPR piece for good measure. And I gathered all the material cut from the article into a massive blog post, which dealt explicitly with this question of whether poker is a game of chance or skill.

If poker is a game of chance, and hence gambling, why do physicists love it so much? Physicists hate to gamble. “I don’t like gambling at all,” Antonyan told me. “I don’t enjoy it and there’s nothing in it for me to compensate for the clear negative EV decision of gambling.”

Harvey’s not a fan, either: “Personally I don’t like to gamble on games where the house has the odds, but I’m not critical of people who do.” And while the Time Lord gamely learned craps with me while I was writing The Calculus Diaries (it was research, people!), he hasn’t been tempted to play craps since.

Binger doesn’t mind gambling, per se, but he learned the pitfalls of blackjack as an undergraduate, when he wrote a computer program to beat the game through card-counting (or, as the casinos like to call it, “cheating”) for his senior project. Then he tried to put his strategy into practice. He lost a pile of cash playing blackjack on an ill-fated trip to Reno, and was barred from six casinos in one day for card-counting in a desperate attempt to recoup his losses. “I realized I wasn’t going to get rich playing blackjack,” he recalled.

But poker was different: as he studied the game and pondered the underlying mathematics, Binger realized that poker could be a “beatable game.”

Fundamentally, poker is a game of skill and strategy, not a game of pure chance (although luck plays a role). Vonk has always loved games, but his love for poker rests on the combination of “math skills” and “people skills,” as he put it. “Good poker requires that you make sound game-theoretic decisions but there is still plenty of freedom to try and outsmart your opponents,” he said. “Other casino games miss that second element. All you can do in blackjack or roulette is make the best possible mathematical decisions, and even then, you will still lose in the long run. I have never been attracted to those games. It’s the fact that you play against other people that makes poker so interesting, and that makes it possible to actually be a winner at the game.”

"A Waterloo" by Cassius Marcellus Coolidge, circa Public domain.

Math skills help, but that’s not all it takes to be a poker badass. Binger said the probability and equity calculations and statistical analysis he applies give him an edge in the game. Vonk finds that his post-game analysis of how he played specific hands benefits from his mathematical skills.

But both Vonk and Binger admit that there are also plenty of other players who really don’t know much about the underlying math; they have a good feel, or instinct, for how to play the game.

“There are many people who hate math but are great poker players, but there are hardly any players who lack the people reading abilities and still manage to be good poker players,” said Vonk. “Mathematical knowledge can to a large extent be replaced by intuition and experience. After a player has played a million hands of poker, even if he does not know the math at all, he will have a decent feeling about when it is profitable to draw to a flush and when it is not.”

That said, knowing the math means you can acquire this kind of knowledge much more quickly, and those skills can give an edge in very rare situations that don’t often occur in a poker game. “To be a great player, you need both!” Vonk insisted. Chris “Jesus” Ferguson is one of the best players in the world, and definitely relies on math and game theory when he plays (his father is a UCLA mathematician, and the two men have written several papers together):

Antonyan estimated that the game of poker is “90% simple math/general strategy, and 10% understanding the dynamics of the table and/or the attitudes of one or more players towards you as they develop.” The math part rests on basic probability theory, and the probabilities of poker are a bit more complicated because there are many more possible combinations of hands — plus you’re working with incomplete information.

Vonk broke down the process to a few basic questions: What cards do I have? What range of cards do I think my opponent has? Given these, what is the probability I will win the hand after all cards have been dealt? And most important: given that probability, will I make money in the long run when I pay the bet? The best one can do, most of the time, is “make a very broad guess,” he says. Per the Time Lord (blogging way back in ):

“Texas Hold ‘Em is so popular because it manages to accurately hit the mark between ‘enough information to devise a consistently winning strategy’ and ‘not enough information to do much more than guess.’ The charm in such games is that there is no perfect strategy, in the sense that there is no algorithm guaranteed to win in the long run against any other algorithm. The best poker players are able to use different algorithms against different opponents as the situation warrants.”

To get a sense for how the probabilities can play out, consider the following three possible pairs of hole cards:

Jack suited

Ace-7 unsuited

Pair of sixes

A game of Texas Hold 'Em in progress. Photo by Todd Klassy. woaknb.wz.sk

Sean posed this question on Cosmic Variance back in Which hand is most likely to win if you choose to stay in the pot all the way to the showdown, against other pairs of randomly chosen hole cards? The answer took a whole ‘nother blog post to delineate.

Mathematically, it depends on the number of opponents. The probability that you will win goes down as the number of opponents goes up, because there are more ways for you to be beaten. Some hands play well against very few opponents, while others play well against many opponents. It all depends on the circumstances.

Against one opponent, the sixes will win % of the time, versus % for Ace-7 and % for Jack suited. Against four opponents, those odds are reversed: Jack suited will win % of the time, versus % for Ace-7 and % for the pair of sixes.

Why does this happen? “Against only one randomly-chosen pair of hole cards, there is a substantial chance that the sixes won’t need to improve; likewise the ace can often come out on top just by itself, so the Ace-7 is second-best,” Sean explained. “But against four randomly-chosen pairs of hole cards, chances are excellent that someone will improve, and Jack suited has the best chance.”

The probabilistic outcomes change again if we pit these three hands against each other, two at a time. In that case, sixes are slightly more likely to beat Ace-7, and Ace-7 is likely to beat Jack suited, but Jack suited is likely to beat a pair of sixes.

The sixes are the best starting hand all by themselves. For one of the latter two to win, favorable community cards must appear on the flop, turn, or river. The only way for the Ace-7 to beat paired sixes is for either an ace or a seven to turn up — or, less likely, for just the right combination of four cards to land on the board to make a straight or flush.

Pit those same sixes against Jack suited, and the situation is reversed. In that scenario, there are more ways for Jack suited to improve. The cards are “connectors,” so there are more possible cards that would give low straights () and high straights (Q-K-A), plus the hole cards are suited, making it much easier to make a flush.

So Jack suited will usually beat a pair of sixes. But it won’t usually beat Ace-7 if the ace is of the same suit. For instance, if four more suited cards come up, the Jack suited will have a flush, but the Ace-7 will have a higher flush, and will win the hand.

See? Poker is a very complicated game, even more so once you add in player behavior during the various rounds of betting. If determining the edge and the odds were all it took to succeed at poker, probability theory would suffice, and one could fairly deem it gambling. If it were a purely logical game like chess, it would merely require impressive feats of calculation to determine the winning series of moves.

But poker is a game of limited information, where players must deduce what cards their opponents are likely to have based on their knowledge of the odds and clues from other players’ behavior. There may not be a single answer. As Harvey put it in the Discover article: “Chess is like classical mechanics. Poker is like quantum mechanics. In chess, there is only one right move. In poker, there is a probability distribution of right moves.”

Like Poker for Chocolate: playing for Hershey's minis at Science Online in Raleigh, NC.

Harvey admitted that one of his classic errors is “calling when I think I am beat for other reasons (betting patterns, tells),” but he calls anyway because “the math says I should. At times like that, I need to pay less attention to the math.”

Human beings aren’t always predictably rational, particularly when it comes to poker: if you assume your opponent is skilled and rational, and he isn’t, your strategy could backfire and fall victim to “beginner’s luck.”

I found this enlightening analysis over at woaknb.wz.sk, outlining the different between an optimal strategy and an exploitive strategy (Ferguson’s favorite) in No-Limit Texas Hold ‘Em. (Note the very specific circumstances described throughout: change even one element and it might call for a different strategy.)

“Let’s say you’re playing no-limit hold ‘em against a calling station who never folds pre-flop no matter what the bet is, but will sometimes fold after the flop if he misses completely. He just insists on seeing the flop. Now say you’re dealt two aces and you each have a few thousand blinds in front of you. The optimal strategy is probably to make a small raise, both building a pot and disguising your hand. But with this player in the game, a much better play is to move all in, knowing he’ll call you.”

“To take maximum advantage of this terrible opponent, you need to employ an exploitive strategy. The optimal strategy would still win you money but against bad players, other strategies might win you more money. … An optimal strategy is designed to protect you against opponents who play well. But when we can find ways to do better than optimal strategy against certain players, we do it.”

The article also mentions mathematical/computational giant John von Neumann, who with Oskar Morgenstern (an economist) wrote the definitive treatise on game theory and poker in Theory of Games and Economic Behavior. It offered an intriguing insight into the art of the bluff: you should always bluff with your worst hand, not a mediocre “bubble” hand.

If betting is slow, it might be worth calling, or “limping” into the game, with a mediocre hand, because your chances of winning are pretty good against other mediocre hands (assuming someone isn’t “slow-playing” pocket aces). A bad hand won’t win unless everyone else folds, so an aggressive raise is the best strategy.

Indeed, there are rare cases where game theory dictates you should fold pocket aces before the flop when playing a tournament. In non-tournament play, the goal is not just to win the hand but to make the most money. In a tournament, you want to outlast your opponents to win it all. That might entail intentionally opting not to maximize your monetary gains on one specific hand to remain competitive in the tournament. You sacrifice short-term gain to achieve the long-term goal.

It doesn’t pay to be too consistent, either. I once played poker with a group that included Harvey. I consistently bet when I had a strong hand, checked when I had a “bubble” hand, and folded when I had a bad hand. So when I scored with pocket aces and nothing but rags (low cards of varying suits) after the flop, I pushed all-in, going heads-up with Harvey.

He had pocket Queens, a strong hand — unless one’s opponent holds pocket aces. It’s hard to fold pocket Queens but that’s just what Harvey did. He correctly analyzed his chances, based on my all-too-predictable style of play. I won the hand, but didn’t win much money because Harvey folded before he’d committed many chips to the pot.

The optimal strategy can also depend on what type of poker is being played: your strategies will be different for No-Limit Texas Hold-Em, for a No-Limit tournament, a Limit Texas Hold ‘Em “ring game,” and different again for online poker. “The only people playing online are serious,” said Harvey. “They also use software to keep track of their opponents’ statistics, which is consistent with the rules of the site, even if it seems a bit like cheating.”

Here’s the difference: in a live game, you have to remember/keep track of opponents’ style of play yourself, i..e, when they raise and in what position. The online software can analyze thousands of hands being played at the same time, and that larger sample space makes for a more accurate statistical analysis.

“It’s much more about modeling, statistical analysis and game theory at that level,” said Harvey. “I’d have to spend as much time learning and playing poker as I do on physics.” And to date, he’s been unwilling to do that, unlike Binger, who left physics after scoring big in the World Series of Poker. He won $4 million with his third place finish, and more than $2 million since. (You can follow his exploits on Twitter: @mwbinger.)

The mathematicians have had a good run when it comes to analyzing poker, but the Time Lord is (rather cheekily) on record predicting that physicists will prove to be the better poker players in the future. His reasoning? No-Limit Texas Hold ‘Em is such a complex system that “we cannot derive a dominant strategy in a closed form.”

“Game theorists and mathematicians study simplified systems about which they can actually prove theorems,” he explained. This is a decent strategy for two players going heads-up, but for a full table, pre-flop, “it becomes a question of which approximations to make and which models to choose for your opponents.” Physicists, let’s face it, are often pretty adept at choosing the best models.

He also had a corollary: “Phenomenologists and astrophysicists will be better poker players than string theorists.” Take that, Jeff Harvey!

There’s a saying that Texas Hold ‘Em consists of long stretches of boredom punctuated by three minutes of sheer terror. Poker never lacks for suspense: you can play a hand flawlessly from a probabilistic standpoint, but there is still the possibility you’ll lose; statistical anomalies do happen. In poker, they’re known as “bad beats.” Even with pocket aces and a flop of , your chance of winning a heads-up showdown against pocket queens is only 92%. Harvey once faced just that scenario – and a third queen appeared as the very last card. His opponent “sucked out on the river.”

Temperament matters too. Poker requires nerves of steel, and an emotional equilibrium that Harvey, for one, admitted he does not possess. “You need to be unflappable. Bad luck can’t bother you. It’s too easy to get ‘tilted,’ and start playing looser, more erratic, or too passive.” More often than not, he said, “My emotions get the better of me.”

How can you possibly take into account all those confounding factors in a small study involving players and 60 hands of poker, where the deal is fixed? Quite frankly, you can’t. As Dedonno and Detterman concluded in their paper, “The reason that poker appears to be a game of luck is that the reliability of any short session is low…. [O]btaining accurate estimates of poker ability may not be easy. Luck (random factors) disguises the fact that poker is a game of skill. However…. skill is the determining factor in long-term outcome.”

Having a good poker face won’t hurt your chances either.

Adapted from an October blog post from the archived Cocktail Party Physics blog.


Dedonno, M.A. and Detterman, D.K. () “Poker Is a Skill,” Gaming Law Review 12(1).

Ferguson, Thomas, and Ferguson, Chris. () “On the Borel and von Neumann Poker Models,” Game Theory and Applications 9 (),

Ferguson, Thomas, and Ferguson, Chris. () “The Endgame in Poker,” Optimal Play – Mathematical Studies of Games and Gambling, Stewart Ethier and William R. Eadington, eds. Reno, NV: Institute for the Study of Gambling and Commercial Gaming.

Ferguson, Thomas, Ferguson, Chris, and Garwargy, Cephas. () “U(0,1) Two-Person Poker Models,” Game Theory and Applications 12,

Fiedler, Ingo C. and Rock, Jan-Philipp. () “Quantifying Skill in Games—Theory and Empirical Evidence for Poker,” Gaming Law Review and Economics 13(1):

Meyer, G., von Meduna, M., Brosowski, T., and Hayer, T. () “Is Poker a Game of Skill or Chance? A Quasi-Experimental Study,” Journal of Gambling Studies, Online First, August 15,

von Neumann, John and Morgenstern, Oskar. Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press,

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Poker is a game. So is corporate strategy, in some ways at least. Of course you can’t equal the two. But you can compare them. I think there are some interesting thoughts by looking at corporate strategy through the lens of poker. In poker as in corporate strategy, luck determines the outcome of a battle, but strategy the outcome of the game.

The importance of having deep enough pockets (bankroll management)

In poker the bankroll is the total amount of money that you are able to invest into playing poker. It’s the question of how deep your pockets are in case you are loosing, because you will be loosing at times, sometimes over long stretches. When you enter a game you pay the &#;buy in&#;, which is the the total amount of money that you can lose playing that particular session (e.g. a tournament or cash table). Prepare to often lose your full buy-in. When it happens, you need to be able to afford to buy in again. And again. But once you are winning, you will be winning a multiple of your buy in, compensating for all the lost games before.

The rule of thumb in poker says that your bankroll should be at least times the buy-in for no-limit games. So, if you want to play high stakes with say a $50’ buy in, you need to have at the very least one million dollars in cash that you are willing to invest into poker. However if you have $50’ dollar on your bank account and you do play a $50’ game, you are acting irresponsibly by exposing your substance to luck. Additionally, you put yourself into a stressed position: Besides psychological effects due to which you will probably play badly, others with deeper pockets will also attack you with expensive moves, that you can’t afford to counter, unless you put your whole substance into one single bet.

Parallels to corporate strategy:

Diversify your options and assure deep pockets

You need to consider each session as an option where you have a high upside (the potential win) and only a limited downside (the buy in). In other words, the prize of one option is the cost of a buy in. You need to have many options in order for your portfolio to be winning overall. This is the basics of diversification. Whether it’s your own company&#;s money or the money of committed investors; you need to have deep enough pockets in case you need to buy another option. In poker times the cost of one option is considered a realistic bank roll. For a business portfolio this would mean that you need to afford different investments with a high upside each.

Options can also be exercised over time

Contrary to a fund’s portfolio, which is invested in parallel into all it’s investments (options), you may also exercise your options over time, one after the other. It may even be a bettter idea than spreading your options over too many areas (i.e. too many different types of games/markets), because you will inevitably not be equally good in all of them. It may be better to invest your money into similar strategies within the same market, one after the other, to see which one yields most.

Choose your battles (game and table selection)

In poker, the first question you have to ask yourself is which game you are going to play and against whom.

Game selection is primarily a question of individual risk preferences and skills. There are fixed limit games (where the maximum bet size is capped) and unlimited ones (where players can bet up to the total of their disposable chips, the infamous &#;all in&#; move). Playing a new game, players usually start out playing free variants with purely virtual chips known as &#;freerolls&#; or small stake games with e.g. a 5$ buy in until they are familiar with the rules and dynamics of the particular game.

Table selection then is very simple: You look out for the tables with the worst players. Poker isn’t about proving you can beat the best players in the world (unless you are among them fighting for multi-million dollar prizes). Poker is very simply about earning money while having fun. To do so you definitely want to fight the easiest targets, know as &#;fishes&#;, not the hard-to-beat &#;sharks&#;.

Parallels to corporate strategy:

Simulate and get familiar with the rules of a new game as cheaply as possible

For corporate strategy this could mean trying out new product/market strategies in test or even purely virtual markets. This is pure MVP thinking. E.g. if a project can get funding on kickstarter, chances are you can also sell the product afterwards.

Increase your bets continually

Make substantial investments only once you are sure you can make them grow, because you have proven so with smaller investments before.

Choose environments with bad players

What goes for table selection also goes for market selection: It is so much easier to make money if your competitors are really bad. Maybe the best markets are then not the one with the biggest pots (i.e. large and for that very reason highly competitive markets such as the US or Germany) but rather smaller countries where the pots are easier to grab (e.g. in Eastern Europe).

Where and when you start makes a big difference (position)

When you enter a game, the first thing that will influence your strategy is your position: You have an absolute position, which is simply the question which players sit left and right from you. Players at the right are the ones that will make their moves just before you. They are preferably the lose and aggressive players at the table, i.e. those who bet a lot. As they are much more difficult to deal with, it’s an advantage if you know their moves before you act yourself, so you gain an information advantage over them.

Then there is the relative position: Each time a new hand is dealt the &#;dealer button&#; along with the big and small blinds (the forced bets), moves one player further. If you are &#;sitting on the button&#; you will be the last one to make your call. This is a substantial advantage in terms of the information you have available to make your decision: As you know how all the other ones have behaved (i.e. betted), you can take direct advantage out of this knowledge. For instance, if all of the players before you have showed reluctant betting behaviour, a strong bet of yours might bring them to fold, even if they might have better cards than you.

Parallels to corporate strategy:

Attack the weak

One obvious parallel is how you position yourself against your competitors: You should closely observe and react to the good and the aggressive players. You should at the same time try to squeeze the weak, predictable and risk-averse players (i.e. grab market shares from them).

First mover or follower: Be the first, or be the best?

In poker, position is a temporal concept: It implies that being a follower is better than being the first mover. I don’t argue that this is a universal lesson for corporate strategy, however…

The follower&#;s advantage: Information

Poker lets you feel the core advantage of a follower position: You can deal with much more information. By analyzing the first movers’ actions you can use this knowledge to your advantage. And indeed in the real world, the winners are rarely the ones who did something first, but the ones who did it best. Facebook was not the first social network, Google was not the first search engine and Apple wasn’t the first computer maker. All of them learned from earlier players&#; and then played their own game.

Deal with real options rather than all-in scenarios under uncertainty

Each game session for which you paid the buy-in (which you can consider as options to multiply your buy-in) is composed of many &#;hands&#;, that is individual games that are played until one (or sometimes several players) have won the game’s pot (the &#;profit pools&#; in strategy language). And within each hand, you have again to deal with many options, which is the actions you can take.

If you are not familiar with poker, see the appendix at the end of this article on how the available information and the real options unfold in the course of a session of No limit Texas hold&#;em.

If you look at a poker round as a temporal process in which the available information increases, it becomes crystal clear why &#;all in&#; moves at an early stage are usually not a good idea: You put all your assets at full risk, although you have almost no clue about how the round will turn out. In the example above, even with two aces – the best starting hand possible – your odds are still more than against you! So better wait and nurture the pot according to your chances to win it, and if the hand turns out in your favor, you can still go all in at a later stage.

If you want to succeed in poker in the long run, you need to get hold of as much information as possible and process it to estimate your current winning odds. Information is not only quantitative about the probabilities of how a hand can develop, it&#;s also qualitative. The latter is namely any information you can get about your competitors, such as their previous and current behaviour, their call/raise-frequency and also &#;tells&#;, i.e. unconscious behaviours that may reveal a lot. You need to add all those small pieces of qualitative information to complete the picture. Very often you will overrule the statistically correct call or bet size because of those pieces of additional information. But don&#;t mistake this for gambling: This is still a purely rational decision.

Parallels to corporate strategy:

No move without the analysis homework

Just because your information is incomplete, it’s absolutely crucial to do the number crunching to get the probabilities as exact as possible. Only then you can take a rational decision. Your winning probability will never be %, but if you don’t know how high it is, you will take bad decisions by either investing too much or not enough. And always remember that the numbers are just one side of the story; qualitative information is the other and often the much more important one.

Know your outs (scenarios)

To calculate your odds of winning, you need to know what possible outcomes in the future will be beneficial to you and in what way. The actual outcomes may develop in completely different directions (say you have a pair in your hand and end up with a straight, for which the fact of having a pair is useless, as you only need one the cards). In corporate strategy, this is why the development of scenarios is so important: Not because you want to know how the future looks like, but because you need to know how it could look like and what actions you would take depending on different developments.

Use your intuition

Despite all number crunching and information processing you nevertheless need to apply your intuition in the end. There are just too many factors that cannot be nailed down however hard you try, sometimes not even qualitatively. You need to judge the total picture in your head correctly in order to make the correct call. However, without analysis, intuition is useless. And without intuition, the analysis is useless, too.

Consider your choices as real options

Every good poker player is dealing with real options. He adjusts his bet sizes based on the probability of a certain outcome. Increasing the bet increases the upside as other players have to call him, if they want to compete. It also cleans out the competitive field as more and more players with weak hands will fold, i.e. he is raising barriers to entry. But still you&#;re rarely in for a sure win, however good your hand is at a particular point in time, it still remains only an option to win. In the end you may lose everything that you’ve invested. This is why it is so crucial to manage your investments wisely, to spread them over many different hands, even within one game and to manage your options correctly.

Sometimes you need to go all-in (but you still should not gamble)

At occasions, you will want or be forced to move all-in. These are exactly the moments of truth where you will see whether or not you will win the game. However, as soon as you do it, you are not able anymore to do anything: You put your fate up for luck. You may be &#;the winner who takes it all&#; or the challenger who went bust trying to beat the &#;big stack&#;. Moving &#;all-in&#; in every hand would obviously be a very dumb approach (that you see in freerolls some times). Others would slowly ripp you off, because you expose your assets way too much. But when it’s necessary, you also need to be willing to literally &#;bet everything on one card&#;.

Let sunk cost be sunk

One of the prime psychological mistakes both poker players and corporate leaders make is considering sunk costs for decisions, i.e. how much you have already invested. However to calculate how much you should invest into a particular decision, the only parameters that matter are the current size of the pot (how much can you win) and the probability to actually win it. How much of your own money you have already thrown in is just plainly irrelevant. The little devil inside your head will tell you otherwise however: He tells you that because you&#;ve already put in so much, you should keep trying your luck.
So if a game turns out unfavourable and you think your hand is weaker than your competitor&#;s, you just need to give up the investment immediately. The single biggest mistake in such situations is investing more money, into mere hope.

It&#;s just a game: Be a good loser

In the end, it’s just a game. If you lose, you need to regain your strength, and just go for the pot again. And again.

Luck vs. merit

What is very essential to both poker and the corporate world is that without tactics (how you behave) and strategy (your game plan), you are destined to lose in the long run. Without tactics and strategy, poker as well as strategy and management is just gambling.

On the other hand, you will be winning big money in the long run if you are doing your strategy work correctly. You need to be getting the stats right to know what would be the rationally correct action every single time, you need to have your individual tactics and strategy in place, and you need to be letting your intuition make the final calls.

Parallels to corporate strategy:

Luck is of great importance

You should never attribute a particular win to your skills, but to coincidence. Because that’s what is: The question is not whether luck or skill was responsible for a particular win, because the world is usually too complex to judge this anyway. The real question is how you are dealing with luck (i.e. uncertainty), in the long run.

Take the long term view

Going for the quick win will always be a matter of luck. Going for the long term win will always be a matter of brains: It’s the results of a sequence of myriads of decisions that you take over time. This is the game that you can win without exposing it to luck. But you need to make the stats work for you. If your statistical probability to win is 10% and you can increase it to 12% through skilled playing, your return in the long run will be 20%! Put variance into the equation and the only thing you need is a long enough breath to realize the expected returns.

Strategy and tactics are essential to have a positive return

If you take the long term view, the only way to improve your odds is smartness, i.e. tactics and strategy. Here, consistency is of the essence. You need to execute your play consistently over time in order to materialize wins.

Someone needs to lose

Obviously, if you win, someone needs to lose. In the long run, I argue that in both poker and the real world, strategy is what makes the difference. Strategy makes winners win and the lack of it is what makes the losers lose.

Dealing with frustration: Bad luck can last for long

You won’t find this in any text book neither for corporate strategy nor for poker, but I would argue that the capacity to tolerate frustration really is the most difficult piece in both disciplines. If you lose a game, you will feel bad. You need to resist the immediate urge to &#;fight back&#;, because with such emotions you will ultimately play badly and only lose even more money. You better calm down, reflect your mistakes, and give it another try another day.
Loosing phases can also last for long and if they do, frustration joins the game. You need to master negative emotions in order to win again.

The importance of an image (table image)

In poker, as in real life, who you think you really are is not nearly as important as who others think you are. Let’s take the example of aggression: If others perceive you as an aggressive player, they will fear that you might fight them in expensive and stressful confrontations. The truth is, most people do not like to fight, because it’s emotionally difficult to deal with. For that reason, aggressive players can be very successful, simply because other players will give up a hand a bit more often than statistically appropriate in order to avoid a fight. On the other hand, &#;tight&#; players can be also very successful, because every time they enter a fight, people expect they have got some serious weapon in their hand, even if they don’t.

And then there is the somewhat strange phenomenon of the winner image: You get it by chance, by having one or two monster hands in a short time and winning a couple of hands in a row, which of course is luck. But if you acquired such an image, it becomes a self-fulfilling prophecy: However rational they may be, others will start to fear your hands and avoid confrontations more often than appropriate. This is funny, as your chances of getting a good hand are just the same as for all the others. And yet the psychology does a huge trick. Some unconscious believes about fate and coincidence may play a role here, too.

The worst image that you can have in poker by the way, is the one of someone who is undecided. Such players are dubbed &#;calling stations&#;: It’s someone who throws his money into the game and then folds often. It’s someone who does not have the guts to claim a pot. This is a sure strategy to lose your money.

Interestingly, image is not only something that is attached to you. It’s also something that is very occasional: If you are the first one to raise in a round, you take the &#;initiative&#;. People almost inevitably think that you have a good hand. If you keep up the initiative in the next betting round, that image in the heads will only strengthen. Even if your hand turns out to not be that good in subsequent betting rounds, this is the moment where a bluff may work.

Parallels to corporate strategy:

Don’t underestimate image

The really important part of poker psychology is not bluffing (over-promising), as many assume: It’s who people think you are. In corporate life, this is what you build up with a multitude of activities, such as PR, marketing, product design, marketing messages, commercial strategies, etc.

Dare something

Often you can go further than what you think was possible, just by daring. Lean yourself a bit out of the window and feel how fast the wind is blowing. If the wind is going too fast, i.e. there is too much resistance, you can still change strategy. Take this blog post for example: I’m a senior strategist writing about poker in the context of corporate strategy… a bit crazy, isn&#;t it? I would claim however, that if you have read that far, I successfully managed to get your attention, which was my goal in the first place. So to say, I won this hand by daring something unconventional 😉

Don’t bluff

Contrary to popular belief, bluffing with absolutely no good cards doesn’t work for long in poker. You might succeed once or twice, but the first time you get caught running such a bluff, people will keep calling you in the future. Bluffing without having good content actually reduces your options, because future bluffs become next to impossible. In German there is a saying: &#;Wer einmal lügt, dem glaubt man nicht, und wenn er auch die Wahrheit spricht&#; (Someone who lies once is not believed, even though he may speak the truth). In the corporate world, this is the parallel to meaningless marketing campaigns or over-promising on products in sales. People will very soon make it transparent.


Learnings from poker for corporate strategy

In poker, strategy in the narrow sense of the word (i.e. a plan for how to go forward) is not all that important. Poker is much more about the concept of tactics, i.e. the rules, values and behaviours that you apply in a consistent way in order to play your game. I personally think that for many businesses these days, in particular digital ones, this holds true as well: Tactics have become much more important than traditional long term strategies (although you need them, too).

In other words, it&#;s about what governs your decision making. This is the very essence of tactics. Good tactics define the values and rules that allow you to take effective decisions in any given situation (e.g. your business principles, your long term vision, your mission, recruiting policies and so on). I would also add behaviours to the tactics concept; it&#;s the corporate equivalent of character.

The reason why tactics are more important than strategy in poker is that is very essentially a game of incomplete information. As such, it is very similar to most decisions in corporate strategy and management. Poker suggests that in such situations,

Real options should become the instrument of choice to manage uncertainty.

In poker, it would be just plain non-sense to predict future events. Strangely though in the business world, most business planning exercises still seem to pretend to predict the future to make their long term plans. I would argue, this is just as meaningless in the corporate world as it is in poker.

Poker essentially requires that you identify your options, the possible future outcomes, calculate their probability, give the options a price and make your call. Everything else is gambling.

I think it would be very appropriate for corporate strategy as well to see any given situation as a portfolio of options into which you can invest a bit more to see how they turn out in the next round. As such, I would go as far as to say that the poker image actually strongly suggests to let go concepts such as net present value analysis. The underlying assumption of uncertainty decreasing the value of your investments is just plain wrong in most cases: Uncertainty usually increases the value of your investments (given that you treat them not as destiny, but as options that you are willing to let go, or re-invest into).

If I would go for one single analogy of how a poker strategy would look like in the real world, I would say it is the lean management approach.

This approach is essentially based on the same reflections of cheaply creating options, validating them, re-iterating, and once something works, re-investing and growing it big. That&#;s exactly how poker works as well.

Applicability of the poker image for corporate strategy

  • The poker analogy applies neatly to winner-take-it-all markets, namely anything that is driven by network economies. If this is the case, any no-limit poker variant simulates the possibility of gaining everything, i.e. total market dominance, by eliminating your opponents (rather than cooperating with them). In the light of a potential total win your assessment of risk automatically changes. And as poker teaches: Not only the probability side changes over time, also the psychology. Things will pick up momentum at some point, purely for psychological reasons.
  • Poker is played against opponents. As such, you can’t apply it to products and customer relationships. But in my opinion it does simulate neatly how competitors interact with each other. It’s actually a pretty sophisticated application of game theory.
  • The way how other players are eliminated also resembles to tender processes, where a field of competitors is narrowed down in subsequent offer (betting) rounds. In the course of a tender process the actual needs of the client become clearer so the information increases (just as you see more and more cards in the course of a betting round). Whether or not your products fit depends largely on this development. Also your boldness plays a role in the sense of how much you improve your offer (how aggressively you bet) and of course the psychology.
  • Poker also resembles in many ways to negotiations in general (although negotiation trainers would jump off the roof over such a statement). But I experienced that the way negotiations often unfold has many parallels with poker: The uncertainty of the outcome, a power play between the parties, the building up of a &#;table image&#;, and the fact that there are several (betting) rounds where new information and new proposals come on the table. Of course, successful negotiations need compromising at some point, and poker teaches you nothing about that. So be careful with transferring the learnings nevertheless.

Limits of the poker image

Although poker is one of the most complex games there is (contrary to chess even the best computers still struggle to beat humans), it&#;s still just a game. Although you could argue the corporate world is just a game, too, it certainly is an even much more complex one. Poker doesn’t share some essential characteristics of the corporate world, namely:

  • The real world obviously has no clear set of rules. The rules themselves are part of the game and as such, they are often negotiable.
  • In poker, your options are limited to call, raise or fold. In the real world, you have much more possible actions to take. The most notable difference is that in the real world, you can design your options in the first place and change them on the way. Poker is not a creative game, but the real world is: The more effort you put into creativeness, the more options you can create out of thin air and the better you can adapt them over time, the more likely it is for you to win.
  • And lastly, in reality, you can engage in parallel activities/options, in poker you can’t (besides the possibility to play several online games in parallel). Essentially, in poker your options are sequential. The image therefore rather resembles to a sequence of projects or business ventures, not to the portfolios of such that you would find in most organizations.


Play a round of poker. See for yourself if you can learn anything applicable for your business. And even if you can&#;t: Enjoy the fun!


&#;Images of strategy&#; is an essay in the form of a series of blog posts looking each at an analogy that has nothing to do with management and (corporate) strategy in the first place. What unites the images is that they all have highly strategic aspects. Looking at them may provide transferable ideas for corporate strategy.



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Appendix) Example of how real options unfold in no-limit Texas hold’em

Taking the example of the popular no-limit Texas hold’em, you start off each hand holding only two cards out of the seven that will be there in the end. Therefore you have less than 30% of the information needed even to complete the picture of how good your own hand is(and you know very little about what your competitors have at this point). Nevertheless you have to take the decision whether or not you &#;play the hand&#;. If you play the hand, you need to decide how much money you invest into the options that the two cards you are holding provide.

You have the following possible actions:

  • Fold: You give up the hand because you estimate your chances of winning too low
  • Call the big blind: Hereby you engage in the minimal bet required to potentially &#;see the flop&#;, i.e. the next 3 cards that will form the final hand
  • Increase the bet: If you do so, you increase the stake the other players need to call, if they want to play this hand against you

Let’s assume there are 10 players at the table: The probability for each player to win a hand is 10%. Now depending on how good your starting hand is, your true winning probability ranges from about 5% (a 2 and a 3 of different colors) to about 30% (two aces). But even though two aces are 6 times more likely to win over 2 and 3, it&#;s still possible to win the pot with a 2 and a 3.

By taking your decision to bet, you will take into consideration not only the statistical odds, but also many other factors, such as the behaviour of the other players, the size of your chip stack at the table (i.e. disposable money for the project) and the strategy you are taking (e.g. even if you have two aces, making an all-in move would scare off other players and it&#;s not a sure win neither; you would win the hand only in less than 1 out of 3 cases).

Then comes the &#;flop&#;, i.e. the next three cards of the hand. Now you dispose of significantly more information: You know now 70% of the cards of your final hand. Using them, you can again calculate your winning probability or equity in the pot, because again, you have to take the same three possible actions. Knowing how likely it is at this point of the game to win the pot in the end is again crucial to take your next decisions.

Another card is laid (the &#;turn&#;) increasing the total information to 85%. You decide again whether to fold, call or increase.

Only after the last card (the &#;river&#;) you dispose of the full information about your final hand strength. And again there is a betting round. Although you know all your cards, you still can only take assumptions about your competitors’, i.e. even now your information is limited. However, during the hand, the information about your competitors has also greatly increased: The way they have behaved will have revealed a lot about what they are up to. But still, only after seeing the hands of all the players still in the game you dispose of % of the information. But then it&#;s too late as at this point you have already won or lost.


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