A Rebuy ? for Math Majors

[BPA234]

Basically, what I am visualizing in my head is a line graph that shows entry/rebuy purchases intersecting with cashes. At some point the number of purchases exceeds the likely cash return. Finding a way to invest optimally for each set of conditions would be very helpful.

[ZBTHorton]

If you see it in your head, what is the answer?

[jcm4ccc]

[ QUOTE ]
Basically, what I am visualizing in my head is a line graph that shows entry/rebuy purchases intersecting with cashes. At some point the number of purchases exceeds the likely cash return. Finding a way to invest optimally for each set of conditions would be very helpful.

[/ QUOTE ] You can't get that kind of graph, because you are thinking about this in the wrong way.

Your question is (or should be): Is it profitable for me to invest $20 in rebuying 3000 chips?

Here are 2 situations: You push 4 of your first 20 hands and lose everytime (let's say that every push was +EV--you are just having a bad run of cards). 10 minutes has passed. Should you invest $20 to rebuy another 3000 chips?

OR

You push only one hand--the 20th you are dealt. 10 minutes has passed. should you invest $20 to rebuy another 3000 chips?

You should see that the answer is the same. It doesn't matter that you invested $80 in one situation and $20 in the other. That is completely irrelevant to the question. You are faced with the question as to whether you should invest another $20, and you have 50 minutes to rebuild your bankroll.

The better way to approach this question is to determine beforehand how much you can invest in the rebuy, and to stick to that.

[BPA234]

Please understand, this is not about a specific rebuy scenario or a strategy request. Simply a request to see if there is a way to input some relevant data into a model that will produce a result that can be used to guide decisions on investment that yield over an annual period.

Since the factors can be expressed numerically, and since this is about results over time, I know this is possible. I just do not know how to write the math.

[Exitonly]

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.
--

jcm made points about the time remaining, but in the bigger rebuys that we're used to (like the 45k) if you're a winning player w/ 3000 chips to start, then you will be w/ 5000 and an hour in. So i don't think time remaining plays a significant role.

[jcm4ccc]

[ QUOTE ]
jcm made points about the time remaining, but in the bigger rebuys that we're used to (like the 45k) if you're a winning player w/ 3000 chips to start, then you will be w/ 5000 and an hour in. So i don't think time remaining plays a significant role.

[/ QUOTE ] I probably am making too much of the time factor, for most winning players. But if you have a somewhat limited bankroll, then I think time is an important factor. If you have only 100X buy-ins, the smart thing if you bust out 30 minutes into the tournament is to come back the next day.

Actually sleep is the important factor for me. If I bust out with 10 minutes remaining, I'm giving it up and going to bed.

[A_PLUS]

[ 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.

[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.