News: GTO Poker Theories: Marginal Utility

Does every pot won mean less than the previous, or do they set you up to win even more pots?

One of the real gifts poker has given me is that it has been a great jumping off point to learn things from other disciplines like economics, AI, psychology and Game Theory. So here is a series of articles where I bring some of the most interesting things I have learned from other subjects outside of poker which are applicable in this game we know and love.

I once interviewed British poker player Roy Brindley who famously has had massive winning and losing days as a sports bettor, but he told me when he was asked what the most he ever lost was, he said £10. The true figure is thousands times more than that, but he says £10 because of a time when £10 was all he had in the world, so it really felt like he lost everything.

This is what is known in economics as the marginal utility of money. That is, for every dollar you make, you get less utility than the dollar before it. By utility that usually means satisfaction or happiness, but it can also mean function or use.

So simply put, if you have zero dollars and I gave you $50, that money would mean the world to you. But if you have $500 and I give you $50, that is still tremendously appreciated but not to same degree. Then if you have $5 billion and I give you $50, you might call your security on me and sue me later on for wasting your time.

This should make perfect sense to anybody who has been working for a long time. That first ever paycheck probably made you feel like Dan Bilzerian, but now getting a pay rise barely registers once you factor in tax.

Marginal Utility is a valuable lesson when you consider just how hard you want to work in life, because extra money shows diminishing returns. This is perhaps why so many entrepreneurs continue working well after they never need to work again. A much cited paper by Daniel Kahneman (who we featured last week) showed that after earning $75,000 a year, any extra money does not really make people happy. $75,000 seems to be that ideal number where all your major needs are taken care of and you also have the freedom and flexibility to enjoy the finer things in life (but not too much).

ICM

While marginal utility is mostly used to discuss satisfaction and is to a large degree a behavioural economics theory, it is a useful theory to understand Independent Chip Models (ICM) in poker. ICM is all about understanding what the real money value of your stack is in a tournament. It also shows how the more chips you have in a tournament, the less each one is worth. That is because you do not win 100% of the prize money in a tournament, it is spread out across the money finishers

Let’s take a simple example, let’s say we are on the bubble of a Six Max SNG with $400 going to the winner and $200 to the runner-up. The chip leader has 1000 chips and the other two players have 500 chips each, so the leader has half the chips in play. Punch this spot into ICMIZER and the chipleaders stack is currently worth $266 and the other two stacks are worth $166 each, or to put it another way each chip is worth $0.26 to the leader, but $0.33 to the other two players.

Now if this were a cash game then each chip would be worth exactly the same no matter what, but in a tournament the pay jumps influence the profitability of decisions based on their real money implications (especially on the bubble).

Chip Utility Theory

matthew principle — More chips = more means to win chips

There is a counter theory to marginal utility and ICM put forward by Arnold Synder called the Chip Utility Theory. This states that each chip won is worth more than what you previously had because they increase your chance of winning more chips. This is especially true if you are a skilful player. The more chips you win, the more you can bluff, the more your opponents will fear you busting them, the more you can gamble and the more you can call risk free.

I think this is more applicable in cash games and tournaments with top heavy payout structures (where coming in the top three is much more important than min cashing). However, marginal utility and ICM are much more applicable in games with flatter payout structures like SNGs, DoNs and especially satellites.

In satellites in particular there reaches a point where accumulating more chips not only has diminished returns, it might actually lead to negative marginal utility. One of the biggest errors people make in satellites is playing for the win when all the prizes are of equal value, and splashing around even with very strong hands is a recipe for disaster when you already have a seat locked up (folding Aces preflop is a necessary skill in satellites).

Of course one area where marginal utility does not apply is your actual poker bankroll. Adding $5 to a $500 bankroll is indeed not as important as adding $5 to a $50 bankroll, but looking at it from a longer term perspective, the more money you accrue in poker, the more money you can reinvest in poker and eventually start playing bigger games. This is where the Matthew Principle becomes important, success begets more success, and Chip Utility Theory makes a lot of sense.

What theories from outside of poker have really helped you with your game? Let us know in the comments:

ICM

Chip Utility Theory

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