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No because of the declining value of chips in a tournament.

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This is a pretty vague statement. For instance, it's easy to come up with an example where, in a single hand, your chips have increased AND your tournament $ EV per chip has increased, i.e. the average value of your chips has gone up as your stack has increased. (My example is an all-in where you are short-stacked, win the main pot while the big stack busts several others out.) Can you define "value" and "declining value" precisely? (Even better would be a reference that has a proof.)

In the context of the OP, I think I can now show that $EV can only go down in tournaments that pay up to 4 palces. The jump from 3 to 4 wasn't as easy as I had hoped at the time of my earlier posts.