In a simple competition / raffle where you buy tickets for $3, and the prize is $1,000.
Assume 200 tickets have been sold to other people, and nobody else will buy more in future.
How many tickets should you buy (b) to get the maximum expected value? And what is the formula to work this out?
Expected value = $1,000 * b / (200+b) - b*$3
I can see through trial and error that b = 58 is the correct answer, giving an expected value of $50.81 (1,000 * 58/258 - 58*3). But how can you work out the optimum value of b using a formula (or spreadsheet formula), not using trial and error.
Guess it is to stop at the point at which the increase in probability * prize is still greater than the cost of the extra ticket.
Assume 200 tickets have been sold to other people, and nobody else will buy more in future.
How many tickets should you buy (b) to get the maximum expected value? And what is the formula to work this out?
Expected value = $1,000 * b / (200+b) - b*$3
I can see through trial and error that b = 58 is the correct answer, giving an expected value of $50.81 (1,000 * 58/258 - 58*3). But how can you work out the optimum value of b using a formula (or spreadsheet formula), not using trial and error.
Guess it is to stop at the point at which the increase in probability * prize is still greater than the cost of the extra ticket.
