Average stack question

[DOTTT]

I was wondering if there is any way to determine how fast an average stack should rise in a tournament. Suppose you have 500 players that start with 1500 in chips, with blinds starting at 10/20 and moving higher every 15 minutes (15/30, 20/40 25/50). Is there anyway to determine how much the average stack rises in the first hour, or does this just vary based on the players in the game? I hope my question is clear enough to answer, if not just forget it I might be babbling here.

Thanks.

[kerssens]

The way I see it, it just depends on the number of people that get knocked out...every time someone gets knocked out the average stack increases by a little over 3 so if you can estimate the amount knocked out per hour you can get your answer

[Bozeman]

In other words, you are asking about how many people can be expected to bust out in a given time for a particular level of blinds.

This obviously depends on the played involved, but I think a reasonable ballpark rule of thumb is that an average player has a halflife (50% chance of busting out) of about the number of hands you could survive if you folded everything. So if your stack is 1500, and blinds are 50/100, your probability of surviving one hand is ~(1/2)^(.1*blinds/stack)=99.3% for ten handed games. For a round P(survival)~(1/2)^(blinds/stack). In general, tournaments are somewhat looser than this, particularly at the beginning. 2+2 tourneys are the exception to this, in my experience. However, for limit tournaments the probability can be zero, so the one hand numbers aren't valid, only the longer term.

For this ballpark model, if blinds start at 50/100 and stacks at 1000, you will have a smooth progression if the blinds double every 7 rounds (half the people die each 7 rounds). For a p* (NLHE) tourney, typically half the players are eliminated in the first hour, while the ballpark model gives only 25%. This indicates to me that I have underestimated the attrition rate, there is probably closer to P~(1/2)^(2*blinds/stack)=(1/4)^(blinds/stack) chance of survival each round. While the form is good, the exact constant (1 or 2 or ?) which could equivalently be encompassed in the (1/2) part (changing it to 1/4 or ...) may be different (and depend on the players, type of game, etc.). Anyone want to give an estimate for this number from the tourneys they have experience with?

In addition, attrition rate will depend on the distribution of stacks sizes. Though the all stacks the same approximation is not too bad.

Any way, tournaments are typically run so that a larger fraction of the people remaining are eliminated in each level. The blinds start small, and then usually double in less time than 1/2 the remaining players are eliminated. The causes the crapshoot factor at the end, and makes casinos happier since less time is spent shorthanded (and playing tournaments in general), while most players get some play for their money.

Craig