copernicus
Thursday, December 29th, 2005, 6:06 PM
BTW I just focused on a statement in your original post that "I am aware that a larger stack has less value than a small stack in a tournament".
That is a misstatement of Sklansky's principle that "each additional chip has less value than the ones before it", which, even when stated that way, is misapplied.
What he shows in TPFAP that, since the prize structure is not winner take all, if you wind up with 2 million in TC, and the final prize is only say $800,000, then each chip was only worth 40 cents on the dollar in the end. But at the start of the tourney you had equal equity in all of the prizes (ie your $EV=buyin) so tc1=$1.
Another way to look at it is, what does ICM tell you about your prize equity?
If you have 5% of the chips you have 5% equity in the FIRST PRZE (say 40% of the total prize structure) and some lesser equity, say 3% equity, in the rest of the prizes. That nets out to 3.8% equity in the total prize structure.
If you double up to 10% of the chips you have 10% equity in the FIRST PRIZE...but you are coming in first twice as often, so you are picking up the rest of the prizes half as often, or 1.5% of the time. That nets out to 4.9% of the total prize structure.
Is the larger stack more valuable? absolutely..4.9% vs 3.8%. But it isnt TWICE as valuable.
The steeper the prize strucutre the closer doubling your tc's has to doubling your prize equity.
In addition, there is an "inverse utility curve" for tournament chips. In standard utility theory each incremental $ you have above what meets your minimum needs has diminishing utility...you can only buy so much, and the more you buy the less meaning each thing you acquire has in relation to all your other posessions.
But, everyone knows that a good big stack player can "bully" the rest of the table..ie pick up a lot of small pots with minimal risk. Why?
Because while the surplus chips he has dont have as much prize value as the chips up to his next nearest competitor...they can be used to see a lot of flops and make speculative raises, because losing them doesnt really hurt that badly. They have marginal value in terms of current prize equity, but they have great
utility because they have the potential to pick up a lot of pots that do meaningfully increase your prize equity.
There is a great thread on this in 2+2, but be warned: it is very tough reading.
http://forumserver.twoplustwo.com/showflat...o=&fpart=1&vc=1