On buying accounts and why you should care

[sirio11]

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 [img]/images/graemlins/laugh.gif[/img] by Dr. Zebra.


<font color="green"> My question was: </font>

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?


<font color="green"> Here is his answer </font> :

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