#1
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Math Problem Been Bugging Me
I thought of this the other day and its been on my mind since.
Lets say you have a wheel that is divided into four sections. The sections are 1, 2, 3, and double. When you land on double you spin it again and now 1, 2 and 3 are worth double. You can keep doubling infinitly. What is each spin of the wheel worth on average? It looks like a calculus problem to me, but being the college dropout I am I have no idea how to solve this. |
#2
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Re: Math Problem Been Bugging Me
Here's my try.
1/4 * (1 + 2 + 3) + 1/4 * (1/4 * 2 * (1 + 2 + 3)) + 1/4 * (1/4 * (1/4 * 2^2 * (1 + 2 + 3))) + ... I think it ends up looking like (1 + 2 + 3) * (1/4 + 1/8 + 1/16 + ...) = 6 * 1/2 = 3 Not 100% sure this is right, but this is what I came up with. -RMJ |
#3
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Re: Math Problem Been Bugging Me
[ QUOTE ]
Here's my try. 1/4 * (1 + 2 + 3) + 1/4 * (1/4 * 2 * (1 + 2 + 3)) + 1/4 * (1/4 * (1/4 * 2^2 * (1 + 2 + 3))) + ... I think it ends up looking like (1 + 2 + 3) * (1/4 + 1/8 + 1/16 + ...) = 6 * 1/2 = 3 Not 100% sure this is right, but this is what I came up with. -RMJ [/ QUOTE ] Right. Or more simply: EV = (1/4)*1 + (1/4)*2 + (1/4)*3 + (1/4)*2*EV (1/2)*EV = 3/2 EV = 3. |
#4
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Re: Math Problem Been Bugging Me
I guess I was along the right track. After thinking about it I figured that it is 1+2+3+what a double is worth / 4.
I'm still not sure I exactly understand it, but I'm closer now. thanks. |
#5
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Re: Math Problem Been Bugging Me
[ QUOTE ]
I guess I was along the right track. After thinking about it I figured that it is 1+2+3+what a double is worth / 4. I'm still not sure I exactly understand it, but I'm closer now. thanks. [/ QUOTE ] A double is worth twice what the whole game is worth, since when you get a double, the game starts over with everything being worth twice as much (2,4,6,double). |
#6
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Re: Math Problem Been Bugging Me
So its like infinitly recursive (reggresive?), how do you get a number for it?
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#7
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Re: Math Problem Been Bugging Me
[ QUOTE ]
So its like infinitly recursive (reggresive?), how do you get a number for it? [/ QUOTE ] Right, it's a recursive equation for EV in the sense that EV appears on both sides of the equation. Just solve for EV like I did above. |
#8
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Re: Math Problem Been Bugging Me
[ QUOTE ]
Right. Or more simply: EV = (1/4)*1 + (1/4)*2 + (1/4)*3 + (1/4)*2*EV (1/2)*EV = 3/2 EV = 3. [/ QUOTE ] Very elegant solution. Are you a mathematician? |
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