A Rebuy ? for Math Majors

[Copernicus]

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.

[BPA234]

I am disappointed. But, I respect your position. Thank you for replying.

[M.B.E.]

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I think logically you maximize your ROI

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That's where I stopped reading this thread.

[Exitonly]

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.
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[M.B.E.]

You shouldn't even consider ROI when thinking about poker tournaments: that just leads to bad decisions.

You should make the decisions that maximize EV, not ROI.

[Exitonly]

uh?

EV = ROI

[jcm4ccc]

[ QUOTE ]
[ QUOTE ]
I think logically you maximize your ROI

[/ QUOTE ]
That's where I stopped reading this thread.

[/ QUOTE ] That's too bad. Because eventually you would have come to this sentence:

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if you are trying to maximize your amount of winnings per day (as opposed to maximizing your ROI), then of course you will want to rebuy when you go broke.

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My main point was to refute the notion that you should only enter rebuy tournaments if you are planning on rebuying if you go broke. Which I think is just silly and illogical.

[REL18]

The problem with rebuying after a certain amount of time has passed in my opinion any more then 30 minutes is that even though your edge no matter how big it is can not make up for the fact that the donkies u face now have a good size chip stack why not save the money and play well again when people do not have that larger chip stack

[BPA234]

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!