Probability distribution game

Question

I want you come up with a game. I want your game to have at least 8 different possible monetary outcomes. You are going to charge people money (you decide how much) to play the game and then you decide how much each outcome is worth (win or lose). Make sure that you are able to find the probability of each outcome (Hint: use dice, deck of cards, etc.) Your goal is to come up with an appealing game that people will want to play, but that you will be the one making money in the end. I want you to create your game so the player’s expected value is between $-2.50 and $0.00.

NO RAFFLES.

There are 40 gnomes in a game. The gnomes will have colored stickers on the bottom. Cost to play is $2 to pick one gnome

Prizes:

Green: Nerf Football

Blue: Candy

Yellow: Necklace

Red: Large Stuffed Animal

Pink: Can of soda

White: Earbuds

Purple: Cotton Candy

Black: Nothing

There are 8 blue stickers, 4 yellow stickers, 2 green sticker, 1 red sticker, and 5 black stickers.

Cost to Me:

Candy: $0.25

Candy valued at $0.25

Soda Valued at $0.50

Earbuds valued at $5.00

Cotton Candy valued at $1.00

Necklace valued at $0.50

Nerf Football valued at $2

Small stuffed animal valued at $5

Large stuffed animal Valued at $10

Outcome	X	P(x)	X*P(x)
Green		2/40
Blue		10/40
Yellow		6/40
Red		1/40
Purple		7/40
Pink		8/40
White		1/40
Black		5/40
		40/40 = 1

Expected Value:

Answer 1

Your goal is to reach the target range for the player's expected winnings, [-2.50, 0] while keeping the game appealing. For instance, you could easily hit your target range for the player's expect value by only giving out cheap prizes, but who would want to play. You also wish to keep your costs low.

So, the trick is to make your most expensive prizes the least likely outcomes.

I would run several scenarios via excel. The X column should be the prize value (cost to you) minus the $2.00 cost to play the game.

Do you remember how to compute an expectation? In column 4, for each outcome, multiple X times the probability of its occurrence, e.g., col 2 x col 3 for each outcome. For instance, if a player would earn $8 dollars from an outcome with a 1/40 probability, the entry in column 4 would read .025.

Sum all your entries for column 4. that would be the expected value for the player's winnings.

Let me know if you have any questions