On buying accounts and equity

[sirio11]

I posted this on the tournament (HS MTT) forum with no luck.

Probably somebody would be interested in this forum.

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?

[DrZebra]

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

[sirio11]

I posted your answer on the MTT Community, hopefully it generates some discussion.