Chip EV, Cash EV, and "Flexibility": a Possibly Naive Question

[Nate tha' Great]

The blinds are 50/100 in a typical NLHE MTT. A middle position player who is a bit on the loose side has T3000 behind and raises to T250. It's folded to me on the Button with 55.

Now, if I have T1500, I probably need to fold this. But if I have T3000 myself, I can probably expect some profit from a call, hoping to stack him if I flop a set. Also, I have enough of a stack to do something like reraise preflop and fold to a push, or raise on a ragged flop and fold to a push, which might be attractive if my table image is strong and he plays predictably.

This might or might not be a good example; I am far from a NLHE tournament expert. But it seems pretty indisputable that a proportionately larger stack gives you proportionately more options, necessarily including proportionately more +EV options. Another very obvious example is the ability to steal blinds during the bubble period. We can refer to this as "flexibility".

My question is how much this flexibility is worth, and how much it offsets the general principle that tournament chips decline in marginal utility.

[woodguy]

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My question is how much this flexibility is worth, and how much it offsets the general principle that tournament chips decline in marginal utility.

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Its funny that you post this, as I was going to post something similar.

We all take for granted that the more chips you have, the less each individual chip is worth.

You mention marginal utility and I think that is the correct approach to this question. It helps that economics isn't afraid of variables that can change with individuals.

I was thinking of it this way:

When we assume that chips ALWAYS decline in value as the amount you accumulate increases, we ignore the ability of a chip to generate more chips.

At some point the next chip is worth more than a current chip as the next chips adds greater ability to generate more chips.

I am not saying that Mason is entirely wrong, but that the function of chip values is not a constant delcine as your stack increases, but rather increases at some point, which is probably a function of:

a) blinds size

b) your stack size

c) stack size of opponents (opponents at your table, not the "average for the tourney") I can only bully those at my table, not the entire tourney. If the tourney average is 15BB's and I have a 30BB stack and everyone else at my table has 60BB then my 30BB isn't worth nearly as much as it would be if everyone at my table had 10BB's. Tourney average stack is a useless stat.

d) your ability to gains chips as a result of having more chips.

e) motivation for opponents to play weak-tight (bubble considerations, etc)

Taking all of this into account is best served with economic models that can quantify such nebulous variables.

Unfortunately I am over 10 years removed from any senior level undergrad economics/stats/finance and am woefully underequipped to take on that task.

I do think it starts down the right path though.

Regards,
Woodguy

[slickpoppa]

[ QUOTE ]
The blinds are 50/100 in a typical NLHE MTT. A middle position player who is a bit on the loose side has T3000 behind and raises to T250. It's folded to me on the Button with 55.

Now, if I have T1500, I probably need to fold this. But if I have T3000 myself, I can probably expect some profit from a call, hoping to stack him if I flop a set. Also, I have enough of a stack to do something like reraise preflop and fold to a push, or raise on a ragged flop and fold to a push, which might be attractive if my table image is strong and he plays predictably.

This might or might not be a good example; I am far from a NLHE tournament expert. But it seems pretty indisputable that a proportionately larger stack gives you proportionately more options, necessarily including proportionately more +EV options. Another very obvious example is the ability to steal blinds during the bubble period. We can refer to this as "flexibility".

My question is how much this flexibility is worth, and how much it offsets the general principle that tournament chips decline in marginal utility.

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I think you are confusing what is meant by diminishing marginal utility. Diminishing marginal utility means that each chip you gain is worth slightly less than the previous chip. Early in a tournament, increasing your stack from 1,000 to 2,000 approximately doubles your EV, but increasing your stack from 10,000 to 11,000 only increases your EV by 10%. So 1000 chips are worth much less to the player with 10,000 than the player with 1,000. That is what is meant by diminishing marginal utility. You seem to be asking about the value of doubling your stack, not the value of a adding a fixed amount of chips to different sized stacks.

I do see what you are trying to get at about flexibility, but it does not undermine the concept of diminishing marginal utility. Going from T1,500 to T3,000 with 50/100 blinds greatly increases your flexibility, but going from T20,000 to T21,500 does not.

[fnord_too]

This is something I think about a lot. I started a thread a while back about it, but it did not really go anywhere.

Stack size definitely affords you more options, and I think that definitely translates into higher cashing EV than just a straight chip count model gives you. I think the greater variace in stack sizes amongst the other player influences the cashing bonus of your stack size.

One minor nit, options don't go up proportionally, they go up considerably less due to the exponentional nature of bets in NL. (That would suggest some sort of log function, but it is even less than that because your options are limited by your opponents' stack sizes. It does no good to have 100BB in a hand against someone with 7BB, since the hand will be entirely played pre flop except possibly in blind situations).

[fnord_too]

[ QUOTE ]
[ QUOTE ]
The blinds are 50/100 in a typical NLHE MTT. A middle position player who is a bit on the loose side has T3000 behind and raises to T250. It's folded to me on the Button with 55.

Now, if I have T1500, I probably need to fold this. But if I have T3000 myself, I can probably expect some profit from a call, hoping to stack him if I flop a set. Also, I have enough of a stack to do something like reraise preflop and fold to a push, or raise on a ragged flop and fold to a push, which might be attractive if my table image is strong and he plays predictably.

This might or might not be a good example; I am far from a NLHE tournament expert. But it seems pretty indisputable that a proportionately larger stack gives you proportionately more options, necessarily including proportionately more +EV options. Another very obvious example is the ability to steal blinds during the bubble period. We can refer to this as "flexibility".

My question is how much this flexibility is worth, and how much it offsets the general principle that tournament chips decline in marginal utility.

[/ QUOTE ]

I think you are confusing what is meant by diminishing marginal utility. Diminishing marginal utility means that each chip you gain is worth slightly less than the previous chip. Early in a tournament, increasing your stack from 1,000 to 2,000 approximately doubles your EV, but increasing your stack from 10,000 to 11,000 only increases your EV by 10%. So 1000 chips are worth much less to the player with 10,000 than the player with 1,000. That is what is meant by diminishing marginal utility. You seem to be asking about the value of doubling your stack, not the value of a adding a fixed amount of chips to different sized stacks.

I do see what you are trying to get at about flexibility, but it does not undermine the concept of diminishing marginal utility. Going from T1,500 to T3,000 with 50/100 blinds greatly increases your flexibility, but going from T20,000 to T21,500 does not.

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A key point: Doubling your stack on the first approximately doubles your cashing EV. It actually is less than double, and doubling again increases your cashing EV still less.

For example: 256 person tourney that pays 30 spots. You have to double up 8 times to win. Say the entry (w/o juice) is $100, so your cashing EV when you start is $100. Your cashing EV after you have doubled up 8 times is not $25,600, it is about $7,500 since 2-29 ate most of the prize pool.

What Nate is (I think) talking about with the flexibility portion is that when you have more chips you have more tactical and strategic advantages open to you. If you are playing someone with a fair amount of chips, the play of the hand can involve multiple bets, giving you more opportunities to exploit any advantage in skill or position you have. A bigger stack also allows you to survive losing a hand or two.

I had a post on specifically stack size advantages about 3 months ago I think. It was kind of rough though, I just cut and pasted it from a rough bit of analysis I was doing for something else. I'll see if I can find it in search....

Here it is

Forgive the grammar, I did not edidt it beyond a couple of bold tags.

Edit -- "strategic" seems to be bolded everywhere. I think that is because that is the key word I used to find the post. Odd.

[MLG]

What makes the concept of flexibility difficult to quantify is that its value changes as the tournament progresses. Lets take the WSOP for example. Even if you lose 3/4 of your starting chips on the first hand of the tournament that still leaves you with 50BBs (2500 with the blinds at 25/50) and doesnt really decrease your flexibility, so while there is an added benefit to flexibility here (perhaps the ability to semi-bluff all-in without the risk of going broke) its relatively small. However, if we look at typical online tournaments, say the Stars sunday tourney, having 25BBs will usually put you in the top 5-10 in chips with 200 people left. Having that stack gives you a huge advantage, mainly that you aren't in all-in or fold mode. So, the added benefit of flexibility changes as the average stack depth changes. Also there is a large threshhold effect when looking at flexibility. There isnt that much difference between 35x and 45x when it comes to flexibility, but there is a rather large difference between 9x and 13x.

There are pracitical applications that we can take from this idea even if we can't quantify it. It pays to take close gambles if winning the gamble will give you a lot more flexibility (it will move you above a threshold) while losing the gamble will not drop you below another threshold. Likewise, it might be right to pass a small edge if winning the gamble will not take you above a higher threshold, but losing will drop you below a threshold and drastically reduce your flexability. I would think that those thresholds are, in fact, inflection points.

[woodguy]

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There are pracitical applications that we can take from this idea even if we can't quantify it. It pays to take close gambles if winning the gamble will give you a lot more flexibility (it will move you above a threshold) while losing the gamble will not drop you below another threshold. Likewise, it might be right to pass a small edge if winning the gamble will not take you above a higher threshold, but losing will drop you below a threshold and drastically reduce your flexability. I would think that those thresholds are, in fact, inflection points.

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Well put.

I was thinking that this rehases some of your inflection points post.

In regards to online tourneys, do you argree that if you are at 15BB that its worth taking even money or a bit worse for your whole stack to get to 300BB's, if getting to 30BB's represents a significant advantage?

You can substitute 15 and 30 for another threshold number, but you get my drift....

Regards,
Woodguy

[DireWolf]

[ QUOTE ]

There are pracitical applications that we can take from this idea even if we can't quantify it. It pays to take close gambles if winning the gamble will give you a lot more flexibility (it will move you above a threshold) while losing the gamble will not drop you below another threshold. Likewise, it might be right to pass a small edge if winning the gamble will not take you above a higher threshold, but losing will drop you below a threshold and drastically reduce your flexability. I would think that those thresholds are, in fact, inflection points.



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This seems like Gigabets recent post. Though, im not sure i fully understood it.

[MLG]

yeah, I think its in the same area, although I couldn't really unpack all of what gigabet said.

[gergery]

[ QUOTE ]
Likewise, it might be right to pass a small edge if winning the gamble will not take you above a higher threshold, but losing will drop you below a threshold and drastically reduce your flexability. I would think that those thresholds are, in fact, inflection points.

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Well put, very concise. This is what Gigabet meant to say, if he hadn't have been smoked that funny weed.

As an aside, one of the things i find most interesting about NL tourneys is how the correct play changes with your stack size. Consider in this example what you should do with different chip stacks.

With 100 chips, easy call. You’re getting lots of odds on your money and with no fold equity must win a showdown soon.

With 400 chips, probably call/push. You won’t have fold equity by waiting for another hand and this one is decent.

With 700 chips, fold. You have no fold equity if you play this hand, but should have some next hand if you’re first in.

With 1000 chips. Push or fold both could work depending on how likely it is he’ll fold, as you now have fold equity.

With 1500. Probably fold. You have enough chips to wait for better spot, and can’t put in a portion of your chips without all of them, but have enough chips where pushing risks too much.

With 2500 Probably call. You now have some implied odds and enough of a stack to hurt him that your position could move him off a hand, and you have position.

Cool stuff, huh!

--Greg