Player Must In the Delaware Play 3 lottery game, to place a "straight bet" a player must choose a 3-digit number....
In the Delaware Play 3 lottery game, to place a "straight bet" a player must choose a 3-digit number (with zeros allowed for any of the digits). To win the prize of $500, the player's number must match the winning number with all digits in the correct order. It costs $1 to play the game. What is your expected gain or loss when you play this game?
If you buy n tickets, then
n/1000 times you will win (500 - n) dollars
and (1000 - n)/1000 times you will lose n dollars.
Ignoring the denominator of 1000 for the moment:
n (500 - n) - (1000 -n ) n =
500 n - n² - 1000 n + n² =
500n - 1000n = -500n.
-500n / 1000 = -1/2 n
You expect to lose half your money.
Several examples are shown below:
If you bought tickets with every possible number,
they would cost you $1000.
You would get back $500.
Net, you would be down $500.
Thus each play would cost you -$500/1000 = -50c.
If you bought 500 numbers, you would break even
half the time and lose 500 half the time:
1/2 * -500 + 1/2 * 0 = 250. -250/500 = same return.
If you bought 200 tickets,
1/5 of the time you're up $300,
4/5 of the time you're down $200.
1/5 * 300 + 4/5 (-200) = 60 - 160 = -100.
-100/200 = -500/1000.
If you bought 1 ticket, then
999/1000 you're down $1,
1/1000 your up $499
999/1000 * -1 + 1/1000 * 499 = -999/1000 + 499/1000 = -500/1000
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Referee hits player: then he must run for his life
