I am really interested in hearing from winning tournaments players on how they feel about Chip Utility Theory. This is brought up in "Poker Tournament Formula 2" by Arnold Snyder (the book for higher buy-ins that have more 30 minute+ levels).

In the beginning of the book he lays out this Chip Utility Theory which is basically the opposite of everything I have learned about the value of chips in tournaments. However, the way he explains it makes intuitive sense to me but the old (lets call it Skalansky way) also makes sense to me and I am having a hard time reconciling the two.

I have heard many pro's and authors talk about how: The value of a chip won in a poker tournament is less than the value of that same chip lost. To put it another way, each marginal chip gained has less and less value. People say this all the time, and I thought it was a poker fact - but now I am not so sure.

Chip Utility Theory is exact opposite and it says that each marginal chip gained actually has MORE value, and each chip you win has MORE value than each chip you lose because you get to USE (utility) those chips with your skill.

The author actually takes a few shots at Skalansky and explains why his mathematical examples to prove that each chip won is worth less is wrong.

Can someone, who is familiar with BOTH THEORIES and a winning tournament player, please explain which theory they think is correct. Or if possible, are both theories correct.

Specifically, I thought that in tournament you should pass up on a 51% favorite even though you would take it in a cash game if you feel you have a skill edge in the tournament. Chip Utility Theory claims you should actually be more inclined to take this, in-fact you should even take a 45% shot if you can, assuming you have a skill edge in the tournament.

Yeah this is commonly known as the Independent Chip Model

It is my understanding that ICM is the opposite of Chip Utility Theory. Assuming you have read the book I am referring to, please correct me if I am wrong. I think the point the author is making is that ICM was developed by mathematicians who didn't take into account the Utility of those chips. He also says that even Bill Chen's book they point out it would be necessary to calculate this utility, but since its relatively unquantifiable they ignore it. The author makes the point that ignoring it basically means that ICM is based on faulty logic.

what? icm is the opposite of this theory

I apologize, i obviously have no idea what I'm talking about. Teaches me to read properly before replying.

One obvious factor to be considered is the type of game. Can you easily bully people with a big stack, or do small stacks actually have an advantage?

'A chip and a chair' (non-mathematicians' version of ICM logic) applies much more to limit games and all kinds of O8 than it applies to no-limit holdem IMO. I think the chip utility theory probably has its merits when applied to the latter.

Steepness of the payout curve is probably relevant too. Small fields and flatter payouts favour hanging in there (i.e. ICM) a lot more.

I play the sorts of tournaments I think favour ICM, and I have a good ROI. I'm pretty sure I'm too nitty to do well in large NLHE tournaments.

Do the proponents of this theory propose some sort of curve shape for marginal chip values or some kind of model describing the manner in which marginal chip values change throughout the tournament? I mean, it is obvious that chip #2 is worth less than chip #1, so the derivative must slope down near zero. But then they claim that marginal chips are worth more, so there is a positive derivative for a while. And then it is obvious that chips #99-100% are worth less than chips 10-11%, for example, so there are at least three local extrema.

To my knowledge it is not as structured as ICM, so there isn't a quantifiable number you can determine. A lot of it has to do with how you perceive your edge to be, the stack sizes at your table, the skill level at your table, and the structure of the tournament. It seems like you have to estimate your "utility factor". It also appears there is no specific formula, like for example if you have KJ in the CO and the blind are 2,000/4,000, then you should do ____. I think the point the the author makes is that ICM leads you to play too conservative because it doesn't take into account how you can use those chips with your skill to gain more chips (= utility). I might have explained it wrong, I am not sure if they specifically claim each marginal chip is worth more...

One example they bring up is that say a person HU has 12.5% of the chips, his equity in the tournament is far less than 12.5% because the 12.5% assumes both players are going all in every hand with random hands .. where in fact the bigger stack has the luxury of being more selective/using his skill and he should, on average, win much more than 87.5%

I am not a math guy, so I was hoping someone who read it could explain it better than me. I wish I could explain it more clearly, sorry - but I do appreciate you're response Jarrod.

Here is an article by the author:

Reverse Chip Value Theory vs. Chip Utility Value Theory for No-Limit Hold'em Poker Tournaments

http://www.blackjackforumonline.com/...lue_theory.htm

Except that ICM doesn't assume that at all. It merely assumes equal skill. Take two equally skilled players, give one of them nine times more chips than the other, and he's going to win 90% of the time.

I don't think Reverse Utility Theory is mathematically justifiable. But if it helps you as a player to not be quite so nitty and take some chances on speculative hands that might pay off big, it's something to think about.

Overall, my opinion of Snyder is that his theories work well against players who play too tight. I think that there are fewer of those players than there were when he was writing his books.

Well said, and I agree. I have been trying to switch from a Harrington style to this Snyder style, and although my sample size is too small one thing I noticed is that I cash less but when I do I cash higher. My ITM% has gone down but my ROI has improved slightly, and I am finding I win more often. But this is a small sample size, so I don't want to draw any conclusions yet.

Appreciate the feedback.

I haven't read Snyder's stuff of this in any great detail, but my cursory reading of it echoes what I have long thought. My general belief is that chips have diminishing marginal utility late in tournaments (close to the bubble and thereafter), as explained by ICM. However, precisely because of this diminishing marginal utility late in tournaments, chips have increasing marginal utility early in tournaments.

When you are able to accumulate a big stack early you are much better able to put your opponents in spots where ICM dictates a fold later on. You are able to call your opponents off lighter, while your opponents can only call you off very tightly, because these call cost you less in terms of tournament equity when you have a big stack, even though it may cost the same in terms of chips.

If Snyder's claim is that chips always have increasing marginal utility, this implies that it is always profitable to get involved in coin flips. This is clearly not true given how tournaments payout. However, it can be profitable to get into a coin flip if both (a) winning will make it easier for you to gain future chips than it is for your opponents and (b) you are far enough away from the money (or far enough away from a significant payout jump) that ICM dictates a relatively flat value of chips. There's a nice graph of when this is true in "Kill Everyone" IIRC.

Of course, if a tournament is winner-take-all, neither of these is true and chips constant marginal value at all points given equal skill.

Perhaps another way to look at it would be to infer theoretical winrates for a given winner player based on certain stack sizes in the midgame of an MTT where the average stack hovers between 20-35bb. It would seem intuitive that the winrate (measured in bb/orbit) for that player would increase steadily up to a certain stack size (perhaps 35bb in the absence of multiple large stacks at the table), then taper off and completely flatten out somewhere not too far above this.

interesting thread, I've always intuitively felt this to be true before I ever heard of this theory...

I agree also but would maintain theres an inflection point which occurs at certain points- IE most obviously on the bubble when you`re a short-stack- also if your ROI in a tourney is below zero then surely every chip lost is worth more, since your losing rate with a short-stack would be expected to be lower.