# Expected Value Question

• Apr 12th 2011, 04:35 PM
centenial
Expected Value Question
This problem was presented in a philosophy class. I don't have much prob/stat background, so I want to make sure I understand it correctly.

Quote:

A game at a casino consists of the following:
• You roll a dice.
• If it lands on a 6, then you win $60. • Otherwise, you lose$12.

What is the expected utility of agreeing to play this game?
I did some googling and found this resource on Expected Utility:

Quote:

If there is a $p%$ chance of $X$ and a $q%$ chance of $Y$, then $EV=pX+qY$
Based on that Theorem, here is what I have done:

$X = \text{Gain } \60$
$p = \frac{1}{6} \times 100$
$Y = \text{Lose } \12$
$q = \frac{5}{6} \times 100$

Plug these values into

$EV=pX+qY$

Then we have

$EV=\frac{1}{6} \times 100 \times 60 + \frac{5}{6} \times 100 \times -12$
$EV=1000 - 1000$
$EV=0$

So, based on that formula the expected value would be zero. So you don't stand to gain anything by playing.

Is that correct?
• Apr 12th 2011, 04:38 PM
pickslides
You can make it simplier by saying

$\displaystyle EV=\frac{1}{6} \times 60 + \frac{5}{6} \times -12$
• Apr 12th 2011, 04:48 PM
Plato
Quote:

Originally Posted by centenial
This problem was presented in a philosophy class. I don't have much prob/stat background, so I want to make sure I understand it correctly.
I did some googling and found this resource on Expected Utility:
Based on that Theorem, here is what I have done:
$X = \text{Gain } \60$
$p = \frac{1}{6} \times 100$
$Y = \text{Lose } \12$
$q = \frac{5}{6} \times 100$
$EV=pX+qY$
Then we have
$EV=\frac{1}{6} \times 100 \times 60 + \frac{5}{6} \times 100 \times -12$
$EV=1000 - 1000$
$EV=0$
So, based on that formula the expected value would be zero. So you don't stand to gain anything by playing. Is that correct?

That is absolutely correct.
But I have a question: "Why is this a question in a philosophy class"?
No question that has definite answer is a philosophical question.
• Apr 12th 2011, 05:13 PM
centenial
Quote:

Originally Posted by Plato
That is absolutely correct.
But I have a question: "Why is this a question in a philosophy class"?
No question that has definite answer is a philosophical question.

Thanks! We were talking about Pascal's Wager and the professor brought up some other Expected Utility games.
• Apr 12th 2011, 05:22 PM
Plato
Quote:

Originally Posted by centenial
Thanks! We were talking about Pascal's Wager and the professor brought up some other Expected Utility games.

Oh yes, now I quite well understand.
It is often said “Pascal could have been a great mathematician but religion got in the way”.

Others say “Pascal could have been a great theologian/philosopher but mathematics got in the way”.