[Pensive Gerbil]

Thank you for contributing...sorry I missed the fun! I have not yet read any of the posts that follow yours. I thought it was common knowledge among well-read tournament players that if everyone is equally skilled, then the chance of taking first place is generally proportional to the percentage of the total chips that are in your stack.

As you point out, this simple principle does not hold for players whose skills are above average or below average. To elaborate by addressing your question: The probability that an above-average player with 20K will double to 40K before going broke is greater than 50% (except perhaps if he is so short-stacked that he is in danger of being blinded off). Therefore, his chances of winning with 40K must be less than twice what it would be with 20K. To further illustrate, suppose our above-average hero has a 55% chance of doubling-up. If the total chips in play were 80K, then 40K would give our hero a 55% chance of victory. If our hero controlled 20K in chips, his chance of doubling to 40K would be 55% and his chance of doubling again to 80K would be 55%. Therefore, 20K would give our hero a .55 x. 55 or 30.25% chance of victory. As you can see, 55% is less than twice as much as 30.25%. [Due to rising blinds, our hero's chance of doubling up may decline over time. As long as it does not fall below 50%, however, this principle remains valid.]

It is easy to see that in the case of a below-average player, 40K will provide more than twice the chance to win the tournament as 20K in chips.

I'm afraid I won't have time to read or respond to more posts until possibly Sunday.

Regards,

PG