short stack final table - what's the math?

[mizzle243]

When EXTREMELY short stacked, is it not mathematically correct that the short stacker's chips are more valuable than everyone else's relative to the payout earned by moving up a spot or two. That is, if a short stack finds his way to making a final table, if the stack is extremely low at $30K ($4/$8K blinds, $1K ante) relative to everyone else ($380K, $270K, $250K, $210, $190K, $180K, $160K, $85K), when does it make sense NOT TO GAMBLE?

In this scenario, the small stack is seated to left of the button, but is seated out first hand when moved to final table. The 2nd biggest stack is in the Big Blind, and 3rd stack is in Small Blind, 8th chip stack is on button.

Is it proper for ultra low stacker to not get involved, with the theory being that there is no fold equity with such a low stack, and that value of additional chips earned by gambling with no fold equity is low relative to the additional payout earned by moving a couple of spots.

Estimated Payouts
1st - $3900
2nd - $2500
3rd - $1850
4th - $1400
5th - $1050
6th - $750
7th - $500
8th - $400
9th - $275

I watched a player (shellgame) work a short stack of less than 5XBB from the money line - 63 players (and probably earlier than that) throughout the entire duration of the tournament, to a 5th place finish and $1045.

I thought you should always gamble with that short a stack at that stage of a tourney, but when the stack is EXTREMELY LOW (zero fold equity), is it proper to try and move up some spots, rather than throw caution to the wind only to finish 9th?

[nicepair111]

Research ICM, that will answer your question. There is a good ICM article on p5s right now that I think will really help you out here.

[Sherman]

I've thought about this a bit. Technically, at some point it must be +$EV to fold every hand. Take this extreme 4 player example.

Blinds: t10,000/t20,000 (No antes for simplicity)

Player A - t200,000
Player B - t500,000
Player C - t350,000
Player D - t1

Prize payouts
1st - $1 Million
2nd - $500,000
3rd - $200,000
4th - $100,000

You are player D on the button and are dealt AA. Player C folds. What do you do?

Clearly the best option is to fold until you are forced into the blind. Your probability of doubling enough to actually compete for an improved prize is sooooo tiny that it is actually smaller than the probability that one of the other players will knock each other out.

Therefore, I am sure there is a point where the probability of doubling enough to move up in the prize pool is equal to the probability of another player knocking someone else out before you blind out.

Determining where this point is depends a lot on your opponents IMO though.

Sherman

[nicepair111]

I have seen a much more realistic example of this at a live tourny.

Blinds were something like 4k-8k (doubling every 15 mins) with no ante. All stacks were very short. Chipleader had 16kish with most players under 8k. Shortstack had 1 $500 chip and was lucky enough to start with the button. Everybody was in the money and the payouts increased at a pretty standard rate.

It is 100% correct for the shortstack to fold AA prefolp here.