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Correct Chip Value Theory and Implications for Winning (and Losing) Poker Tournament Strategy

Universally, purple poker chips are worth $500. Chips with an orange hue have a value of $1,000, and grey ones $5,000. Different states and poker rooms may not adhere to these guidelines standards. Poker Tournament Chip Values. If you decide to play a poker tournament and want to be able to play more than 5 or 6 blind levels, then you will need at least 4 chip colors. Most chip sets now come with at least red, white, green, and black. Here is a simple and flexible chip value system commonly used in live poker tournaments: Red – $25. If you're playing for big money, it's probably a good idea to invest a little more and buy some professional-grade poker chips. Clay chips are often used in high stakes cash games. The Spruce When playing Texas Hold 'Em Poker, Omaha Hold 'Em Poker, or any game that involves chips as currency, it's vital to know what each chip is worth. Unless you are at a casino, most chipsets are unmarked. While there is no official rule for how chip values are assigned, there are common standards used for most poker events.

By Arnold Snyder
(From Blackjack Forum , Fall 2006)
© Arnold Snyder 2006

In my recent article “The Implied Discount”, I addressed a theory (first proposed by Mason Malmuth in his 1987 Gambling Theory and Other Topics) that linked the dollar value of chips in a tournament to the size of a player’s chip stack. Specifically, the theory states that individual chips in a small stack have greater value than individual chips in a larger stack. For convenience, I am going to refer to this theory as the 'reverse chip value theory' throughout this article.

The reverse chip value theory, which has also been embraced by David Sklansky in his 2002 Tournament Poker for Advanced Players, is important because, as I will show in this article, it has led to tournament strategies that are potentially very costly to players. In “The Implied Discount,” I contested this theory based on chip utility value during the portion of tournaments where skill determines results. In this article, I will show why the reverse chip value theory is invalid even later in a tournament, including at a final table, and even when skill and chip utility are not a factor in results.

At the time I wrote “The Implied Discount,” my intuition told me that this reverse chip value theory was incorrect, even in a tournament where skill is not a factor, but I didn’t pin down the source of the error in this theory until shortly after that article had been posted. In this article, I’ll explain the errors behind the theory, show the correct way to calculate the value of chips in a tournament, and discuss the implications of correct chip value theory for winning poker tournament strategy.

The Erroneous Chip Value Theory

To refresh your memories on the reverse chip value theory itself, let’s return briefly to an example I used in “The Implied Discount” to explain it:

One of the most widely held and erroneous concepts of poker tournament logic is the concept that the fewer chips you have, the more each of your chips are worth, and the more chips you have the less each of your chips are worth…

Let’s say a small buy-in tournament is down to the last two players, who are heads up at the final table. The remaining prizes are $3,500 for the winner, and $1,800 for second place.

The player who is the chip leader at this point has $70,000 in chips, while the player in second place has only $10,000. Clearly, the value of each of the chips of the second place player is much greater than the value of each of the chips of the chip leader.

Assuming the blinds are so high at this point that both players are simply all-in before every flop regardless of cards (making this a coin-flip situation for all intents and purposes), the player in second place has an 87.5% chance of taking the second place prize, and a 12.5% chance of doubling up enough times to take first place. This makes his $10,000 in chips worth more than $2,000 in prize money. So, the short-stacked player’s chips are worth more than 20 cents each.

The chip leader, however, will find that his $70,000 in chips have a prize value of less than $3,300. The chip leader’s chips are worth less than 5 cents each. And ultimately, the more chips the second place player loses to the first place player, the greater the value of each of his individual chips. In fact, if he gets’ down to a single chip, that chip will have a value of more than $1,800, while the chip leader’s chips ain’t worth even a nickel each.

The example above does appear to illustrate that the chips in a larger stack have less dollar value than the chips in a smaller stack, assuming that two players are at a final table where no skill advantage is possible for either player. But this logic is based on a false assumption about how chips are awarded in percentage-payout tournaments.

The false logic can be found on pages 220 and 221 of Gambling Theory and Other Topic, in an essay written by Mark Weitzman. In this essay, Weitzman provides a method for players to chop up a prize pool, based on their respective chip stacks, in a percentage payout tournament where the players decide to quit the tournament before the finish. In his example, one player has 70% of the chips while his heads-up opponent has 30% of the chips. Essentially, Weitzman assigns 70% of the first place prize, plus 30% of the second place prize, to the player with 70% of the chips.

Weitzman’s method of chopping the prize pool does provide a fair distribution based on each player’s expected value with his respective chip stack. Unfortunately, Weitzman then leaps to a very wrong conclusion about tournament chip values. He says: “This example also illustrates a general point: If you are behind in a percentage payback tournament, your chips are worth more than their face value, and if you are ahead, your chips are worth less than their face value. For similar reasons, Mason Malmuth has pointed out that the winner of a percentage-payback tournament has in a sense suffered a ‘bad beat’—he has just won all of the chips, but he gets to keep only a percentage of his winnings.”

If you look at the chip distributions Weitzman comes up with for the players in his example, it is obvious that he is saying that you can determine the value of individual chips by dividing a player’s expected win by the number of chips in his stack (which is exactly the method I used in my example above).

But it is not true that you can determine of value of individual chips in this way. In a percentage payout tournament, there are always one or more payouts that players receive for having zero chips, meaning for having busted out before first place (the payout for the player who has won all the chips). In other words, because there is a specific dollar value to having zero chips, this value must be taken into account when calculating tournament chip value. Specifically, to correctly calculate the value of the chips in your stack, you must calculate their value based on what they add to the value of having zero chips.

What Weitzman is doing wrong is assuming that all payout value is derived from your chip stack. He is failing to take into account the portion of each payout’s value that is due to having zero chips. To return to the example above, if a player expects a payout of $3500 for having all the chips (or taking first place), and $1800 for zero chips (or going out in second place), Weitzman would be incorrectly dividing the full $3500 of the first place prize by the number of chips in the first place player’s stack in order to come up with the value of an individual chip. What he should be doing to come up with the value of a chip is dividing $1700 (the amount added to the $1800 payout for zero chips) by the number of chips in the first place player’s stack.

I can see how Weitzman made this error, and why Malmuth and Sklansky accepted the error. I accepted the error myself in my initial analysis in 'The Implied Discount'. Unfortunately, Weitzman’s mistake causes the individual chips in a big stack to appear to be wort

Are Poker Chips Worth Money