Re: ??
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The CASH value of each individual chip in a tourney is $0. The UTILITY value of each individual chip is a different matter.
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You're playing games with terms trying to define the issue the way that suits your argument. I don't agree that the cash value of an individual chip is zero. If the tournament were stopped prematurely for some reason and payouts were made on remaining chips, they would have value. Any additional value based on skill would be subjective and would have to be ignored. So the chips have value independent of skill.
And I agree that the "utility" value as you use the term is not linear based on stack size. And trying to plot a curve based on stack sizes, and skills of the remaining players would be hard, and such a curve would be complex. And no two curves would ever look the same.
But if you claim that chips added to a stack are worth more than chips already in that stack at any place on such a curve then the burden is on you to prove it. No one has done this. Some have demonstrated that they don't, at least on average.
One place where a chip might be more than a previous chip is when such a chip gives you an additional hand, blind or round of hands.
Example: You are last to act in a heads-up hand on the river. The game is a no-limit holdem tournament and the blinds are 50/100. The next hand the blinds go to 100/200. There is 400 in the pot and you have 650 left. If you check and take the pot you'll have 1050, enough for three rounds plus part of the big blind. If you bet 100 you have 1150 if you are called and win. You'll have enough for three rounds plus the big blind and part of the small blind. But if you bet 200 and are called and win you'll have 1250, enough for four rounds plus. The second 100 you win by betting 200 is probably worth more than the 100 you'd win by betting 100.
But while the second 100 chip that you win may be worth more than the first 100 chip that you win, the second 100 chip you lose if you bet 200 and lose the hand is worth more than the second 100 chip should you win.
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