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I posted this thread in the 2+2 forums, hopefully it generates some good discussion here:
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I made a post on the High Stakes forum about this topic but didn't have any luck (no replies, too theoretical?, non-important topic?). So I decided to post it on the Poker Theory forum and have better luck, I got one reply
by Dr. Zebra.
My question was:
Lets suppose you have an average stack on the Sunday Million with 18 people left, and you're a winner player, lets say 50% ROI.
A break even player (0% ROI) is the chip leader, with about 1/4 of the chips in play.
Now a good player, lets say one with a 100% ROI buys the account of the mediocre break even player and starts playing the last 2 tables.
Using numbers from the last Sunday million
1st $185,760
2nd $96,755
3rd $69,628
9th $8,009
10-18th $5,942
How this transaction affects your equity? How much money do you lose because of the transaction?
Here is his answer :
ok. let's start off with a few unrealistic assumptions:
1. let's simplify some of the numbers: payouts are
200k, 100k, 70k, 50k, 40k, 30k, 20k, 12k, 8k, and 9 spots at 6k each.
2. the 18 players have equal chips
3. 17 people average 50% ROI and one person averaged 0% ROI and now is someone who averages 100% ROI
4. There are exactly 2000 entrants for 500+30 and 200 pay
the results should be nearly obvious because of the oversimplification, but i think the scratch work below is correct in case you want to loosen the assumptions (ie make the field more diverse...)
this is the pre-deal equity for a random 50% ROI player with these assumptions:
584k*[(1.5)(530)-E(416k/182))/(584k/18+530)]/
[17*((1.5)(530)-E(416k/182))/(584k/18+530))+(1)(530)-F(416k/182))/(584k/18+530)]
where E and F are the expressions = (1+ROI)(Buyin)/(TotalPrizePool/entrants + Buyin)
your new equity is:
584k*[(1.5)(530)-E(416k/182))/(584k/18+530)]/
[17*((1.5)(530)-E(416k/182))/(584k/18+530))+(2)(530)-F(416k/182))/(584k/18+530)]
which simplifies to:
pre-deal: 33,056.70
postdeal: 31,854.30
Hopefully this generates some good discussion between the community
David
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whaaaa???
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I think Your equity gap would be even Larger now that you have someone that will not chop, (I would think HU would be your only chopping point with a sold account).
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i wonder what the worst account purchase was...
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