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Old 05-12-2018, 07:14 AM   #1
sfetaz
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I'm having a brain fart on how to figure out expectation on a single die

It's simple yet I can't remember how to do it.

Roll a single die.

If 1 or 2 comes up, you pay me X amount of money

If 3, 4, 5 or 6 comes up, I pay you Y amount of money

I want my EV for every single roll to be 10 cents.

How do I calculate X and Y?
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Old 05-12-2018, 10:32 AM   #2
StuckinARutt
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Re: I'm having a brain fart on how to figure out expectation on a single die

x/6 + x/6 - y/6 - y/6 - y/6 = $0.10
or basically 1/3x - 2/3y = 0.10

You can't solve for x and y since you only have one equation, but you can plug anything you want in there to make it work.

i.e $0.60 x and $0.15 y
or $3.00 x and $1.35 y
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Old 05-12-2018, 02:07 PM   #3
statmanhal
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Re: I'm having a brain fart on how to figure out expectation on a single die

Well, you can do a little better by solving for one given the other.

Assume baseline is X and Y = KX.

Then you want 1/3*X - 2/3*KX = 0.10

K=(1/3*X – 0.10)*(3/2X) = 0.50- 0.15/X

Therefore, Y = 0.50X – 0.15

So if X = 3, Y= 1.50 - 0.15 = 1.35 as was shown above.
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Old 05-13-2018, 07:59 PM   #4
StuckinARutt
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Re: I'm having a brain fart on how to figure out expectation on a single die

yea, that's the long way of how I did it in my head
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Old 05-15-2018, 03:37 PM   #5
statmanhal
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Re: I'm having a brain fart on how to figure out expectation on a single die

The "long way" was getting this simple equation Y = 0.50X – 0.15 that works for any X.

Bet I can beat you using it vs. your 'in my head way'.
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