Anyone read - "Theory of Doubling Up" by Chen and Ankenman?

[MarkD]

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For the purpose of this discussion we will ignore the value of time and assume your goal is simply to increase your equity in the tournament


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This is key. If you get knocked out of the tournament you get something precious, you get some of your life back.

For most people I believe the model needs modification.

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I don't think so. When I play a tournament I'm not thinking about getting my life back. I entered the tournament to win it and thus I want to get the maximum equity from the tournament. The model would apply to me, as well as many other people I think.

[Piers]

Ok For many people I believe the model needs modification.

[MLG]

Interesting stuff, but C shouldn't be a constant number, which makes things more complicated I think. I have a much better chance of doubling up early in a tournament before many of the bad players have been eliminated than later on when there is a higher % of skill players relative to the remaining field.

[maddog2030]

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It's an interesting result, but probably only really important in winner takes all type of tournaments.

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I only quickly glanced at the equations/results. While it initially could only be used for calculating 1st place equity, it seems like it could be used recursively similar to the linear relationship between chips and win% as given by ICM, to calculate equity for other positions (This may be taken into account with the initial equity variable, I'm not sure yet).

If there's some way for me to get my hands on the full article I'd be very appreciative. Once I do that I'm thinking I can write up a calculator and see how the results work out.

[Jerrod Ankenman]

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Interesting stuff, but C shouldn't be a constant number, which makes things more complicated I think. I have a much better chance of doubling up early in a tournament before many of the bad players have been eliminated than later on when there is a higher % of skill players relative to the remaining field.

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So let me just say a couple things about this article:

This isn't all-encompassing, rigorous, "you can arbitrage your house on the things that this model says". This is quick-and-dirty "here's a guide to making decisions in the early to middle stages of tournaments that incorporates your skill appropriately."

Most players overvalue their skill in the early stages of tournaments, and do so in a manner that is provably false; that is, they think that their chance of doubling is such and such early on, but if they did have this higher chance of doubling and they simply did par from some point on, they would have much better tournament results than they do. It's not constant, but Bill and I believe constant is a better approximation than most.

As for needing a winner take all structure, that's wrong, I think. When a lot of people are left in the tournament, it's perfectly reasonable to use your remaining chips/total chips in play as a proxy for your cash equity in the tournament, as long as they're not colossal relative to the field. As you get close to the money, you should stop using this model because it doesn't have anything to do with that part of the tournament.

Jerrod

[maddog2030]

Until I get my hands on the full article and get a better understanding of how the equations were derived I can't deduce it myself, but would it be possible for this model to be applied on the same concept ICM is based on, and calculate payouts for all positions?

Meaning, ICM takes it the you have X of Y total chips, therefore you have (x/y)% of winning 1st place. So it takes this idea and more or less applies it recursively to get probabilities for the remaining positions (given player A gets first and remove his chips from play, what's the probability of B getting 2nd, etc.).

[Jerrod Ankenman]

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Until I get my hands on the full article and get a better understanding of how the equations were derived I can't deduce it myself, but would it be possible for this model to be applied on the same concept ICM is based on, and calculate payouts for all positions?

Meaning, ICM takes it the you have X of Y total chips, therefore you have (x/y)% of winning 1st place. So it takes this idea and more or less applies it recursively to get probabilities for the remaining positions (given player A gets first and remove his chips from play, what's the probability of B getting 2nd, etc.).

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It doesn't sound like these models are doing the same thing. That might be good for joining them together. Or it might make them totally incompatible.

There are two effects it seems like we want to measure here.

1) The effect of the graduated payout structure on the values of chips in the stacks.

2) The effect of skill on the value of chips in the stacks.

Based on your description above, it sounds like your method is complicated and computerized and calculates EV for chip stacks, particularly when those stacks are pretty large compared to the chips in the tournament (like 5%?) I would be very surprised if, say, a 2x starting stack is worth much less than twice a 1x starting stack.

My method could care less about the payout structure; it basically wants to measure the effect of skill on the tournament. So if you are better than your opponents, your chips are worth more than their par value. How much more? That's the question.

But it relies on an abstraction of doubling up N times to get all the chips in the tournament as its value function. So unless you can think of a good way to change that to "finish in these other places," you may be out of luck.

Jerrod

[maddog2030]

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It doesn't sound like these models are doing the same thing.

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To what little I've seen of yours, it seems it does. You calculate 1st place equity by whatever equation you have, ICM uses the (mychips)/(allchips) formula and therefore has no skill bias. ICM takes it the next step and applies this formula to 2nd place, 3rd place, etc. by removing players one at a time.

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That might be good for joining them together. Or it might make them totally incompatible.

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I think they're incompatible, but the ideas from ICM can be carried over to your model.

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1) The effect of the graduated payout structure on the values of chips in the stacks.

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ICM takes care of this. I assumed you knew what ICM was, but if you don't, here's a calculator and a short explanation.

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2) The effect of skill on the value of chips in the stacks.

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ICM doesn't take this into account by its basic linear 1st place equity equation. It has been suggested that you could arbitrarily add a certain % of chips to a good players stack, but it hasn't been well explored as far as I know.

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Based on your description above, it sounds like your method is complicated and computerized and calculates EV for chip stacks, particularly when those stacks are pretty large compared to the chips in the tournament (like 5%?) I would be very surprised if, say, a 2x starting stack is worth much less than twice a 1x starting stack.

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It does get fairly computationally intensive for large numbers of players. However, we use it all the time in the STT forum for 4-5 player situations where the money pays the top 3 and its results seem to make a lot of real world sense. Early in the tournament, I think ICM predicts you need a 53-55% chipEV advantage to call an allin in order to be breakeven $EV wise. This gap widens considerably as your approach the bubble (4 players).

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My method could care less about the payout structure; it basically wants to measure the effect of skill on the tournament. So if you are better than your opponents, your chips are worth more than their par value. How much more? That's the question.

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I think this is why your model as is would break down as you approach the money. But I think this issue can possibly be resolved...

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But it relies on an abstraction of doubling up N times to get all the chips in the tournament as its value function. So unless you can think of a good way to change that to "finish in these other places," you may be out of luck.

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Well let's say you assume you have a 2x buyin equity (this is very high for a STT, but that's irrelevant for now). That means someone else in the tournament has a -2x buyin equity (Edit: This should be: everyone else has a combined total of -2x a buyin, but just assume it's just one really bad player for now). Everyone else can be assumed to be breakeven. Say for the sake of argument it's a single table tournament with 10 people with the standard 50-30-20 payout structure. You can calculate the first place $EV of each player using your model given their stack sizes and their respectable equity variable. Well, to calculate the remaining positions, assume player A got first. Now from there subtract him and his chips out of the tournament. Now you have a "new" tournament. Calculate your equity again there for yourself and everyone, except now its for a 2nd place prize and the probability of it happening is multiplied by the probability of A getting 1st in the first place. Repeat and you solve the equity for all positions and all players.

The main difference between your model and ICM is how you calculate your chances of getting 1st place; yours takes into account a skill advantage, classical ICM does not.

[Jerrod Ankenman]

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It doesn't sound like these models are doing the same thing.

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To what little I've seen of yours, it seems it does. You calculate 1st place equity by whatever equation you have, ICM uses the (mychips)/(allchips) formula and therefore has no skill bias. ICM takes it the next step and applies this formula to 2nd place, 3rd place, etc. by removing players one at a time.

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I should restate that. Both of these models are trying to map chip stacks to equity. One of them is accounting for the payout structure; the other for the skill of the participants. It seems that sufficiently motivated individuals could join the two together in some useful way to gain in accuracy, although it seems there would be better ways of assessing tournament situations close to the money than doubling-up chances.

Jerrod Ankenman