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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.
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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.