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?