1. ## 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.

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:

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

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

Plug these values into

$\displaystyle EV=pX+qY$

Then we have

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

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

Is that correct?

2. You can make it simplier by saying

$\displaystyle \displaystyle EV=\frac{1}{6} \times 60 + \frac{5}{6} \times -12$

3. 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:
$\displaystyle X = \text{Gain } \$60\displaystyle p = \frac{1}{6} \times 100\displaystyle Y = \text{Lose } \$12$
$\displaystyle q = \frac{5}{6} \times 100$
$\displaystyle EV=pX+qY$
Then we have
$\displaystyle EV=\frac{1}{6} \times 100 \times 60 + \frac{5}{6} \times 100 \times -12$
$\displaystyle EV=1000 - 1000$
$\displaystyle EV=0$
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.

4. 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.

5. 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”.