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 05-12-2018, 07:14 AM #1 sfetaz adept   Join Date: Jan 2007 Posts: 858 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?
 05-12-2018, 10:32 AM #2 StuckinARutt (╯°□°）╯︵ ┻━┻     Join Date: Nov 2008 Location: 3rd rock from the sun Posts: 35,852 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
 05-12-2018, 02:07 PM #3 statmanhal Pooh-Bah   Join Date: Jan 2009 Posts: 4,103 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.
 05-13-2018, 07:59 PM #4 StuckinARutt (╯°□°）╯︵ ┻━┻     Join Date: Nov 2008 Location: 3rd rock from the sun Posts: 35,852 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
 05-15-2018, 03:37 PM #5 statmanhal Pooh-Bah   Join Date: Jan 2009 Posts: 4,103 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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