Two Plus Two Older Archives A Rebuy ? for Math Majors
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#21
12-27-2005, 05:43 PM
 BPA234 Junior Member Join Date: Jan 2005 Posts: 21
Can Anyone write the math?

Apparently, rebuy strategy is a hot topic. FWIW, I call multi allins with suited connectors. Unfortunately, my post is not a strat. post.

Can anyone wirte a math formula that would use the factors in my initial post and any other relevant factors I left out?

Thanks!
#22
12-27-2005, 05:48 PM
 A_PLUS Member Join Date: Aug 2004 Posts: 44
Re: A Rebuy ? for Math Majors

[ QUOTE ]
Again, you have to stop thinking of it as a collective investment.

If you drop 100 in a \$10 rebuy, that's not a \$100 investment, it's 5 seperate \$20 investments (counting double rebuys). The outcome of one has no impact on the outcome of the others.

If you're +EV playing it once, you're +EV playing it a second time.

[/ QUOTE ]

What he said...Actually, I find myself thinking that about a lot of your recent posts. Now if I could only start getting your results.
#23
12-27-2005, 07:06 PM
 Copernicus Senior Member Join Date: Jun 2003 Posts: 1,018
Re: A Rebuy ? for Math Majors

BPA..I think the results of your request wouldnt be worth the effort.

Lets say in a freezeout with n runners, a starting stack of S per runner and a buy in (excluding vig) of b, your equity is (S/nS) x nb = b because everyones skill is equal. This is essentially an ICM value of the total prize pool, where your chances of each prize happens to be equal to everyone elses.

Now lets say because of your skill, you historical equity happens to be 3 buy ins.

The problem is that you can get to that increased equity in a lot of different ways...eg one player may be a survivalist who has an unusually high number of cashes where they are in the middle prize areas and never wins a first prize, or there may be a "win it all" player who has a small incremental advantage for the big prize, but never make it into the money if he doesnt win.

Now when you look at the equity of a rebuy for these 2 players the answers will be very different depending on the situation, despite their "equivalent skill" of 3b equity.

If the redistribution of chips is fairly even and the average is less than 3b, both players probably still have +EV.

However if the redistibution of chips is skewed, so that the majority are in a few players hands the "win it all" player will have a lower EV than the survivalist, because the ratio of the top stacks (that he has to surpass) to his new buyin is greater than the ratio of the average of the other stacks to the survivalists buyin.

In fact the survivalist may actually have increased EV in that situation...in the extreme say the top stack is equal to all of the rebuys plus his original stack plus the buy ins of 1/2 the field that have dropped out. The remaining players have exactly their original stack. The survivalist has 1/2 the field to get through to get to the same prizes he was contending for before, and a rebuy should be very +EV for him.

The win it all player on the other hand has more ground to cover to get to the same chip ratio to the other tcontenders.
#24
12-27-2005, 07:18 PM
 BPA234 Junior Member Join Date: Jan 2005 Posts: 21
Re: A Rebuy ? for Math Majors

I am disappointed. But, I respect your position. Thank you for replying.
#25
12-28-2005, 02:53 AM
 M.B.E. Senior Member Join Date: Sep 2002 Location: Vancouver, B.C. Posts: 1,552
Re: A Rebuy ? for Math Majors

[ QUOTE ]
I think logically you maximize your ROI

[/ QUOTE ]
#26
12-28-2005, 03:10 AM
 Exitonly Junior Member Join Date: Dec 2004 Location: New Jersey Posts: 3
Re: A Rebuy ? for Math Majors

well, he's right in a way.

the first time you buy in to the tournament is when it's most profitable, because you're stack will be average (or above if you double rebuy) and you'll have the entire first hour to accumulate. The longer you wait the shorrter the stack your buying is. So, if you treated it as a freezeout (well, a double rebuy + an addon, but no extra rebuying) it makes sense that you'd have a higher ROI. Since you're playing only in the most favorable conditions.

BUT it's not in a vacuum there are a million things factored in, so it's all pointless. AND the ROI increase from never rebuying woudl be miniscule, and the hourly wage would be retarded.
---
#27
12-28-2005, 05:26 AM
 M.B.E. Senior Member Join Date: Sep 2002 Location: Vancouver, B.C. Posts: 1,552
Re: A Rebuy ? for Math Majors

You should make the decisions that maximize EV, not ROI.
#28
12-28-2005, 05:37 AM
 Exitonly Junior Member Join Date: Dec 2004 Location: New Jersey Posts: 3
Re: A Rebuy ? for Math Majors

uh?

EV = ROI
#29
12-28-2005, 06:39 AM
 M.B.E. Senior Member Join Date: Sep 2002 Location: Vancouver, B.C. Posts: 1,552
Re: A Rebuy ? for Math Majors

Suppose you have a choice between two poker tournaments in different cities (your bankroll is easily large enough to enter either one).

The first is a \$3,000 buyin and you estimate your ROI would be 75%.

The other is a \$10,000 buyin but the field is a bit tougher so you estimate your ROI in that tournament as 60%.

The first one has higher ROI, but the second has much higher EV. Which would you enter?
#30
12-28-2005, 06:42 AM
 DWarrior Member Join Date: Mar 2005 Posts: 85
Re: A Rebuy ? for Math Majors

Stacked rebuys (as in, being able to rebuy when you still have chips in front of you at or below starting chip amount) and addons aside, I think you're misunderstanding ROI calculation of rebuys.

If there was a \$10+1 tournament where your only option was to rebuy if you went broke (no stacked rebuys or addons) and the rebuy would also be \$10+1, rebuying would be the same as putting money down for a different tournament (your \$10 added to the prize pool wouldn't make any real difference in a large enough field)

There would, however, be one significant difference: you'd be starting with a stack that's below the average. In that instance it would be a better idea to go into a different tournament instead. However, you wouldn't take the rebuy not because your ROI is based off a \$22 investment as opposed to an \$11 investment, but because it is -EV to spend the second \$11 rebuying as opposed to spending \$11 on another tournament.

What affects the EV of rebuys are the fact that sometimes you don't have to pay rake on rebuys and all the strategy changes: starting with a bigger stack, being able to add onto your stack during the tournament, being able to play a tournament where you normally wouldn't be able to (as in, if this was the only tournament around), the psychological effect of having the rebuy cushion for other players, and hte fact that most of the early chips lost will be going to the lucky bad players.

Basically, if you are going to come up with a formula for how much to spend on a tournament, it shouldn't compute a total amount of money you can spend. Instead, it should analyze each time you have to rebuy to calculate the EV of spending the money on the rebuy versus playing another tournament for the same money instead. If it shows that taking the rebuy is outright -EV, or if you're higher EV going to another tournament, then you should quit; otherwise take the rebuy.

It's more or less a general consensus that you should rebuy all the time. Besides, even if such formula were to be created, the values you'll be inputting into it will not be precise, so the results will have to be calculated with a certain degree of error and I suspect the highest expected value of that error would always be positive.

EDIT: I think ROI is a pretty useless statistic when calculating profitability, it's all about EV and SD.

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