Say we have a $1 million raffle that has only two tickets: a winner and a loser.
I give you a random ticket and tell you that you MUST sell it. How much money should you sell it for? (I.e. how much is it worth?)
A. $1 million?
No, because it could just as easily be worth $0.
No, because it could just as easily be worth $1 million.
C. $0.5 million?
Yes. This is the expected value of the ticket.
Notice that the holder of the winning ticket will never actually get $0.5 million. They will either get $0 or $1 million. We just use $0.5M as the expected value. If you sell it for more than $0.5M, you made money on the deal. If you sell it for less than $0.5M, you lost money on the deal.
Note: We got $0.5 million by multiplying the odds of winning (0.5) by the amount of money you would win ($1 million).
You would use the same strategy in poker, where the "value of the winning raffle ticket" is the money in the pot, and the "odds of winning the raffle" are the odds of your poker hand winning.
Another way to think about this is from the point of view of the raffle creator.
Say I am giving away $1 million in my raffle again with two tickets. How much should I sell each ticket in order to break even?
Well, if I am giving away $1 million, I want to make sure that I am getting $1 million back, otherwise I will be losing money (if I sell it for less), or making money (if I sell it for more).
A. $1 million per ticket?
No, because then I will take in $2 million total (2 tickets * $1 million each).
I would make money in this case.
B. $0 per ticket?
No, because then I will take in $0 total (2 tickets * $0 each).
I would lose money in this case.
C. $0.5 million per ticket?
Yes, because now I will break even by getting back $1 million (2 tickets * $0.5 each).