# Calculating the expected value of free tickets in a paytable?

Lets says I have a lottery game where the ticket costs $1 and has the following probability/prize distribution: • 0.3 -> \$1
• 0.2 -> X
• 0.5 -> \$0 If X = \$1, then the expected value is: 0.3(\$1) + 0.2(\$1) = \$0.50 If X = FREE_TICKET, then I've calculated (and confirmed) via sampling that the EV is either: • 0.3(\$1) / (0.3+0.5) = 0.375
• 0.3(\$1) + 0.2 * \$1 * 0.3/(0.3+0.5) = 0.375

Obviously, a FREE_TICKET isn't the same as \$1, the price of a ticket. However, I'm stumped when calculating the EV of the table for the following two cases: • X = 2 FREE_TICKETS • X = \$5 + FREE_TICKET

How do I calculate them?

-
You have the expected value as $Y = 0.3\cdot 1 + 0.2\cdot X + 0.5\cdot 0$. If, in addition, $X = 2Y$, or $X = 5 + Y$, you can solve for $X$ and $Y$ simultaneously. – mjqxxxx Nov 28 '12 at 18:24
Thanks, you're right, it's just basic algebra. – AlexD Nov 29 '12 at 14:31