There seems to be a strong belief that playing poker teaches people how to invest or run a business. This is of course nonsense. The mathematics behind poker is complex and needs years of formal study to understand the game. The more appropriate notion is that a strong understanding of game playing is extremely useful to investing and business.
The branch of mathematics relevant to game playing is not, as most believe, probability but is called, not surprisingly, game theory. Game theory was made famous by the film A Beautiful Mind, depicting the life of one of the main developers of this mathematical field.
In this article I’d like to address just one facet of a successful poker strategy and that is bluffing. Somehow bluffing has taken on the connotation of lying or otherwise being dishonest. Many of the proponents of “poker as a substitute for an education” believe that this gives them license to be dishonest in their business dealing, in particular in negotiations. Their interpretation is wrong both mathematically and ethically. They might not care about the ethics, but from a mathematical point of view, lying is extremely sub-optimal and completely misses the point.
First, let’s dispel the myth that bluffing is lying and afterwards we’ll look at what it really is. A lie is when you say something that isn’t true. “The sun sets in the East.” A wider definition, what I call dishonesty, is when everything you say is true but the picture that you present is false. “She punched him” when the full picture is “He tried to steal her phone and then she punched him.”
Why isn’t this the same as a bluff in poker? A bluff certainly isn’t a lie since it is not a factual statement, it is a declaration of how much a player wishes to bet. Is a bluff dishonest? Well, the only other relevant information is what cards the player is holding, but the game rules dictate that not only does the player not have to disclose that, he is not permitted to disclose it. So bluffing is not dishonest.
There is much debate on the ethics of bluffing in poker and in business. In poker, bluffing is a clearly understood element of game strategy so I do not see how it is unethical. In business the situation is a little different. There are no pre-agreed rules (other than the law). So I’ll answer in two parts.
Part one is haggling. Have you been to the souk and haggled with a vendor on the price of a piece of jewelry? Then you accept bluffing as ethical.
Have you asked a hotel if the room rate that they were offering you was the best rate they could give you? Then you accept bluffing as ethical.
Have you asked a car salesman if what he offered you was the final price? Then you accept bluffing as ethical.
Part two is due diligence. Have you ever listened to a CEO speech but still insisted on analysing the financials before investing? Have you been presented information on a private equity acquisition but insisted on further due diligence? You might not accept bluffing as ethical, but you understand it as a normal part of business.
Now that we have the ethics behind us, let’s focus on the mathematics. In game theory there are, broadly speaking, two types of strategy. The first is called a pure strategy. This is a strategy that is executed in a deterministic manner, each decision known in advance. Tic-tac-toe is a perfect example of when a pure strategy is useful. The optimal next move is completely determined by what has happened so far. In this case, the pure strategy is called a dominating strategy. For a refresher, watch WarGames. Yes, game theory made it into the movies as early as 1983.
A simple game that has a mixed strategy as the optimal solution is odds — evens. Two players decide that one will be “odds” and the other will be “evens.” They then simultaneously show a fist to the other, extending either one finger or two (keep it clean). The total number of fingers shown therefore ranges from 2 to 4. If the number of fingers shown is 2 or 4 then the “evens” player wins. If the number of fingers shown is 3 then the “odds” player wins.
In this game, if one of the players always plays the same hand, say “odds” always plays one finger, then “evens” can always win by also playing one finger. This shows the case that when there is no single dominating strategy, as there is in tic-tac-toe, then playing a pure strategy is sub-optimal. You need to mix it up by randomly changing your strategy. Who knew Seinfeld wasn’t just a show about nothing.
Some more familiar examples for the need of a mixed strategy. A football player who takes penalties. Keep shooting to the same spot and the goal keeper will always get the save. A team that always passes the ball to the same striker will never score. The striker will always be heavily defended.
A boxer who always bobs and weaves right. The followup left cross to the initial jab will knock him out.
A tennis player who always plays to their opponent’s weak backhand will fare worse than one who adds a little randomness by also occasionally serving to his opponent’s forehand.
One for my American readers: Pass on every down, and you will get blitzed and sacked on every down. Switching between a passing game and a running game is classic game theory.
A less clear cut example is Saudi’s decision to shift from an oil price defender to a market share defender. After decades of acting as the swing producer, the rest of the world learned to play against the Saudi historically pure strategy. The proof is the acrimonious accusations from nearly everybody when Saudi refused to continue to play the pure strategy last year.
This isn’t the first time that Saudi changes strategy switching from a price focus to a market share focus. The difference this time though is that Saudi seems to have understood the value of a mixed strategy, and keeping the exporters on their toes. If OPEC is dead then Saudi’s primacy in the global energy markets certainly isn’t. Quite the opposite, the Saudi application of a game theoretic strategy catapults them into a league of their own.
Bluffing, as understood by poker players, is simply a randomisation, or mixed, strategy. People unaware of this facet of game theory might misunderstand an optimal mixed strategy as a confused response by the player. Could you imagine someone saying “That boxer, the one who has been bobbing and weaving right for the past decade, has now decided to go left. Clearly the boxer is confused!” Maybe the boxer is sick and tired of meeting the left cross every time he moved right.
Game theory, and in particular mixed strategies, are essential for players with fewer resources to beat players with greater resources. What many miss is that it is an important strategy for well resourced players as well, as famously promoted by Machiavelli. Nixon’s madman strategy is a perfect example: Nixon felt that playing the rational pure strategy was too predictable and therefore he introduced a mix of rational and madman strategies to achieve his goals. Indeed, politics is an even more detail ground for game theory than finance, but that is for someone else to cover.
Running a business is not all art, marketing and charisma. Sometimes a little mathematics developed by clever people can come in handy.
Management sincerely hopes that learning to look at your favourite sport through the lens of game theory does not decrease your appreciation of the sport, but enhances it.
- The second post in the series, Game Theory’s Relevance to Investing: The Basics is self descriptive. The link will go hot on 25/1/2015 @ 1515h Abu Dhabi time.
- The third post in the series, Gotham Game Theory: The Joker’s Dilemma, uses an example from the Batman film The Dark Knight to further describe game theory and its uses. The link will go hot on 26/1/2015 @ 0840h Abu Dhabi time.
- The last post in the series, The Pirate Code is behind Pay Inequality, proves, using game theory, that pirates are the real reason behind compensation differentials. The link will go hot on 28/1/2015 @ 0840h Abu Dhabi time.