Conjecture and Question

[DonT77]

Well, I think you make a good case that doubling-up early in a 10-player, winner-take-all tournament won't double your $EV; but I don't think this line of thinking carries forward to say a 1000-player tournament with escalating, non-linear payouts.

In a 1000-player tournament, if a player repeatedly doubles-up until he has let's say half of the chips in play, then obviously his $EV won't double-up each time - but we (Mason's conjecture) are only concerned about what happens when the player doubles-up the first time.

Let's say there is an $EV multiplier associated with each double-up. Now, according to this:

"Everyone has a stack of chips. If you double through to 2 stacks, you might think your expectation becomes $40. Another double through to 4 stacks and it becomes $80. A third double through to 8 stacks and it becomes $160, and you still haven’t won the tournament. But that cannot be correct, since the total prize pool is only $100 (add to that the fact that for a MTT, the maximum prize is significantly less than the total prize pool)"

each time you double your chips the $EV multiplier should be less each time, However in larger MTTs sometimes (like once in the money where the money is flat but then escalates rapidly) doubling-up more than triples your $EV.

Clearly there is a complex, non-linear relationship between cEV and $EV throughout the course of a large MTT that can not be explained by simple examples given the complexity of the variables involved (including payout structure and the accumulating benefits of a big stack).

[Slow Play Ray]

[ QUOTE ]
Well, I think you make a good case that doubling-up early in a 10-player, winner-take-all tournament won't double your $EV; but I don't think this line of thinking carries forward to say a 1000-player tournament with escalating, non-linear payouts.

[/ QUOTE ]

I disagree - by the same logic, since the $EV of your starting stack is greater, then everyone else's must be worth (slightly) less on average. It works the same way - what was your argument against it? It was unclear to me what you were trying to say.

I don't think anyone is disagreeing that it is a completely different situation (far greater increase in $EV) when you double-up in the money - but we are talking about doubling up on the 1st hand.

[ZeroPointMachine]

Couldn't it be argued that when you double up on the first hand you have picked up the chip equity from the eliminated player but his seat equity is split between the remaining players? Therefore your equity cannot have doubled.

[DonT77]

Who's to say that when you double your stack to 20K on the first hand your $EV isn't 80K+? Maybe you've reduced the value of your opponent's chips more than 40K as a whole. Until somebody shows me the exact cEV/$EV curve over an large MTT with varying chips stacks, varying payout structures, etc. I'm going to go with with Shane (Shaniac) on this one based on empirical results that when I double up early I tend to finish ITM and finish deep at least 2x more often than if I don't double-up early.

[Slow Play Ray]

Doubling up early could be a psychological thing for you too, but we are not addressing that - just the stats.

Haha - I certainly won't be the one generating that data for you, but anyway Eric's example makes it intuitively clear to me...I just wanted to know your logic behind that statement. And now I know.

[ZootMurph]

I think there are two competing factors here. First is the fact that chip values diminish as your stack increases. Everyone seems to understand this theory, so no more needs to be said. However, the second is that a great tournament player can play a 'big stack' game now, and that will increase his/her equity. As the great player's stack increases, not only does his equity increase but also his ability to either splash around in more pots and outplay his opponents or push people around and pick up even more chips.

All this being said, a double up on the first hand doesn't really make the player's stack SO big that they can go hog wild with big stack play, so in the example given I'd have to say less than double the starting equity. However, let's say the next hand the player takes someone else's stack. Now he has 30k to the average 10k... Not only has his equity increased, but so to has his leverage. So, another thing to consider besides the player's stack and the average stack is the player's stack compared to the total chips in play. As that ratio increases, the player's leverage within the tournament increases, and thus adds to his equity.

So, in the example given... at a 3 table tournament, his relative equity after doubling up on the first hand is obviously higher than in a 500 person tournament.

[gergery]

What if you are Sammy Farha, and you double thru Danny Negreanu, knocking out someone else who is a 2x par competitor and leaving just the fish left at your table?

then clearly its possible to more than double, it just wouldn't be the typical result.

very nice post, wotmog.

-g

[AtticusFinch]

I've posted a couple of threads recently trying to come up with a model to illustrate this.

The most recent is this: http://forumserver.twoplustwo.com/sh...3452&page=

In a nutshell, my theory is that your expectation is based not just on your stack size, but your ability to grow it over time, which has some limiting factors constraining it.

For example, you can never win more in any one hand than the lower of your stack and your opponent's stack. And you can never win more than all the chips in the tourney.

More concretely, if you have more chips than anyone else at your table, you can't "invest" all of your chips in a good hand, so not all of them are "working." Thus your potential growth rate decreases as you get farther and farther ahead of the field, no matter how good you are.

Thus I think the key to estimating your expectation is finding a weighted expected growth rate based on your relative skill, and the constraints of the tourney format.

To estimate your growth rate, I took a formula from biostatistics that's used to measure growth rates of species in environments with limited resources. The parameters are quite analogous to a poker tourney.

I need data to test it, but I have high hopes for it.

I have a lot more to say about this, but I'm at work, so I'll have to add more later.

[AtticusFinch]

[ QUOTE ]
this is not provable without data.


[/ QUOTE ]

Agreed.

[ QUOTE ]

one side is the TPFAP/ICM chips decrease in value. the other is most associated with gigabet - if i have 2x chips, my chip-generating potential goes way up.


[/ QUOTE ]

This misstates Gigabet's position. He believes the value of your chips accelerates for a while after you pass the middle of the field, but once you are way past the field, it slows down significantly. My recent threads on this topic were in part an attempt to quantify Gigabet's theory.

[ QUOTE ]

it will vary by person and situation and you can't make a blanket statement one way or the other.

[/ QUOTE ]

Certainly, but you can estimate it based on relative skill level. I think that's what we're attempting here.

[DonT77]

Okay, so what if by winning the first coin-flip your advantage becomes .61 instead of .60 and after the second coin flip it becomes .62 and so on. Can we then say how winning the first coin-flip affected your expected outcome after n coin-flips (which will be a factor of the size of the field)?