Re: Conjecture and Question
1. Your equity has an upper bound of the 1st place prize. Your expectation cannot increase linearily when there is an upper bound. I am too far out of 9th grade math, but this is called an S-curve? Your equity cannot increase to infinity.
2. First place isn't worth the sum of all the chips: Win you win the 1000 man tourney, you will have 10,000,000 chips. However, 1st place is a mere 25% or $2.5M. Even though chips were issued at a 1chip = $1 scale, they don't pay that way.
3. Part of your equity comes from your seat, part of it comes from your chips. The part that comes from your seat does not change at the same rate as your chip stack. Seat eq is based on #of players left, chip eq is based on %of total chips.
4. Part of your equity comes from the opportunity present at the table. If you have 20K chips, but no one else at your table has more than 10K, 10K of your chips have no opportunity attached to them. The shortest stack at the table has the most opportunity equity.
5. You are expected to quadruple your buy-in. While it is uncommon to start with a double up, it is, to some degree expected. You have a 4X edge because you find ways to double up. Your equity does go up (obviously) but because you're expected to increase your chip stack, it cannot double. If you were expected to half your buy in, doubling your chips would have a greater effect? This doesn't sound right.
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