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(I haven't been able to find information elsewhere, so I'm asking here.)

What is the typical graph of chips vs. proportion of tournament lifetime for players who did very well in a tournament (perhaps finishing in the top 1%), but didn't win? (For pacing/format information, I'm basing this off of the WSOP Main Event. For scaling information, the domain of number of hands played is mapped to the interval [0,1] for every player. The range is scaled differently based on whether the chips are measured in number or in big blinds.)

When measured in absolute chips (range scaled to where 1 represents either all chips in play or the maximum of each individual graph), it's fairly straightforward to say that the graph starts with exponential growth to keep pace with exponentially-increasing blinds, and must be zero at the end, but how steep is the decline to zero? When measured in big blinds, I have much less idea on the graph's shape, except that it's probably relatively flat on average. (The sudden-jumping nature of blind sizes introduces some discontinuities, but given that some players are eliminated closer to the beginning of a blind level, whereas others are eliminated closer to the end of a level, these should smooth out.)

Is there any research on this subject that is available, or guidelines to performing a very basic simulation of the process behind such tournaments? (I may split this part off into its own question; I'll link it here if/when I do.)

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Tournaments are interesting because players can gain/lose chips in so many ways. Having more chips does not mean that a player will be guaranteed to last longer in the tournament than a player that has less chips.

Players can double up 3 times in a row and have a very steep increase in chips, or they can win average sized pots every now and then and have a slower increase in chips.

Players can also lose chips very slowly by not playing any hands and blinding down, or they could lose all of their chips in one hand if they get into a cooler situation against a bigger stack.

For this reason, I do not think it is fair to make the assumption that the growth in chips (in BB) is exponential. The average stack in a tournament often decreases in BB as blind levels increase, especially in faster structures. Keep in mind that almost anything is possible in terms of the rate that a player gains/loses chips, and more often than not a player will gain and lose chips in big jumps rather than gradually over the course of the tournament.

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