3. How to play
• The player names a card out of a shuffled
standard deck of 52 cards. Then cards are
flipped from the top of the deck until the
named card is flipped. The number of flipped
cards determines the payout. The payout is
calculated by adding $1 to every card pulled
that is not the named card, as well as $1 for
the named card being pulled. The game is $30
to play.
4. Theoretical Expected Value and
Standard Deviation
Expected Value:
(1/52)(1)+(1/52)(2)+(1/52)(3)…(1/52)(52)=$26.50
Variance:
(1/52)(26.5-1)^2+(1/52)(26.5-2)^2+(1/52)(26.5-
3)^2…(1/52)(26.5-52)^2=$225.249
Taking the square root of the variance gives us a
standard deviation of $15.01
5. Simulation Expected Value and
Standard Deviation
• For our simulation we used a random number
generator on a calculator to randomly
generate 500 numbers from 1-52. The
numbers would represent the placement of
the chosen card. When we calculated the
mean and standard deviation this is what we
got:
Actual mean payout: $27.26
Standard Deviation: $14.60
6. The results
• The theoretical calculations and simulation
provided expected values and standard
deviations that were very close to each other.
Both the simulated expected value and the
simulated standard deviation came within a
dollar to the theoretical amounts, with an
expected value 71 cents above the theoretical
and the standard deviation was 41 cents lower
than the theoretical. Because the mean was
still lower than the $30.00 fee to play the
game, the game still generated a profit.
7. Improvements
• An improvement that could be made is by
offering a bonus for if the player’s named card is
the 52nd drawn. Instead of getting 52 dollars, we
would increase the pay out to 100 dollars. This
would make the game more enticing to play, even
though it would happen rarely. This change would
make the expected value $27.42, keeping it less
than the $30 pay fee. We also acknowledge that
$30.00 dollars is a lot to pay for this game, so we
would also lower the cost to $28.00 in order to
stay above the expected value and generate a
profit, but also make the game more affordable
(even if we are only saving them $2.00)
