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May 5th, 2008, 01:12 AM   #1
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Complex probability calculation

Hi,

it is required of me to write a math formula that will do the following...

I have 5 values (2,3,4,8,12).
A user can bet on those values. (has 20 units on start)
One value will be selected and user will depending on his bet win a number of new units he bet on or lose the units he bet.

Through a certain number of plays - (1000 for example) he should be on 90 % of what he started with.

Now there is quite a few variables to be considered here...

Can somebody at least point me to a formula or theorem that could be useful?

Thank you,

Dani
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May 14th, 2008, 07:30 PM   #2
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This post is a little dated, but it caught my attention. I am a bit confused by what is being asked. You have some random variable let's call it X defined on the set {2,3,4,8,12}

I think what you are asking is what probabilities do we need such that through a certain number of plays, the player should have 90% of what he started with ie we need to define 0<=pi<=1 for i = 1,2,3,4,5 such that

p1 + p2 + p3 + p4 + p5 = 1
P(X = 2) = p1
P(X = 3) = p2
P(X = 4) = p3
P(X = 8) = p4
P(X = 12) = p5

Let Y be the random variable which represents the number of units the player has at any given time. Now when you say that through a certain number of plays he should have 90% of what he started with do you mean

E[Y] = 0.9 * 20 = 18

I am a bit perplexed by the formulation of the question since for instance I could bet all 20 units on 2 and it come up 3 and lose. Clearly, I will never return to 20 units or 18. Can we define any strategy and betting behavior of the player to achieve the desired expectation?

I am also confused by the payout structure. I assume that you intend to convey that let's say if I bet 2 units on 2 and it comes up 2 I win 4 units. Is this correct?

I have some ideas on how to proceed, but I will wait for clarification provided the answer is still meaningful to you.
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