Math Problem Been Bugging Me

[antistuff]

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.

[RocketManJames]

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

[BruceZ]

[ 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.

[antistuff]

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.

[BruceZ]

[ 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).

[antistuff]

So its like infinitly recursive (reggresive?), how do you get a number for it?

[BruceZ]

[ 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.

[notmyusername]

[ 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?