A Rebuy ? for Math Majors

[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.