Question on Stack Sizes

[baggins]

ok. let's say you are in a tournament. the one i had in mind is the PokerStars Freeroll, which usually gets more than 2000 players.

let's say you know the Chip Leader's stack size, you know the average stack size, and you know the smallest stack size. is there a way to predict with any reliability what place you are in?

say chip leader has ~140K, you have 120K average stack is 30K and shortest stack is <100.

intuitively it seems there should be a way to crunch these numbers and figure out how many stacks whould be bigger than yours, thus telling you where you stand on the ladder. am i off here?

[Bozeman]

A few rules of thumb I use:

Average stack is usually 5~10% ahead of median stack

Smallest stack is usually irrelevant to your place

If you are within 10% of big stack, you are probably in 2nd (unless there are more than 100-200 people left)

If you are close to the chip leader, you might as well be the chip leader, unless you are playing a pot against him

Average stack at PS is about (starting stack)*2^(time played/1 hour) (exception: PLO tourneys elinimate more players in the first hour)

The big stack is usually ~4 times the average

If you have >1/2 of average final table stack, you will probably make the final table

With two table left, 1/2 of an average final table stack usually puts you in about 18-n place out of n

Average stack at final table is usually in third place

Though the distribution may start normal, it soon becomes a strictly decreasing function (not certain of this, it may maintain a peak below the average for a significant time)

Craig

[baggins]

thanks! that's really helpful.

[thylacine]

That's good info. Some more comments and questions.

Pokerstars actually tells you your position, though not all sites do.

I asked a question a while back about distribution of stack sizes, which includes the question in this thread. It also includes the question: at various stages, how many big blinds is the average stack? I got little response. Ray Zee suggested it depends a lot on the game. Perhaps the average stack in NLHE is more BB's than is the average stack in LHE.

Any statistical or theoretical answers?

[Copernicus]

Average stack is just the total starting chips divided by number of players remaining, so the relationship of average stack to blinds is a function of how quickly players are eliminated and how quickly blinds increase. Assuming that blinds follow the same pattern (increase the same amount at the same time or after the same number of hands) then that factor is gone, so how quickly are players eliminated?

Certainly in NL players are eliminated faster earlier in the tournament than they are at Limit, so the average stack will be higher in terms of big blinds. That relationship should continue throughout the tournament, and you would eventually get heads up with a higher average stack relative to the blinds. That, in turn, should result in luck being a little less of a factor in the late stages in NL than L, and that is certainly my experience.

As noted earlier, though, position is usually a more important consideration than size of the stack, and that is better estimated from median stacks than average. Unfortunately sites post average not median, except for Stars, where you always know where you stand, with exact chip counts, another reason I like it best. (Although with my bank recently changing its policy on using credit cards at poker sites, funding/withdrawing at Stars is quite a bit more difficult than some other sites.)