Question

A player tosses three coins. He wins $3 if 3 tails occur. $2 if 2 tails occur. $1 if 1 tail occur and loses if 0 tail occur. Adjust the cost of game to make it fair. Find theoretical mean and variance.

Answer 1

Help please

Answer 2

i have calculated a bit

Answer 3

how do i make the game fair what on earth is that?

Answer 4

where is everyone help please!!

Answer 5

Note, the game would be fair if it costs $1 to play.

Answer 6

How did you determine that $1 per play is fair?

Answer 7

it says in a similar question in my notes wait let me post it

Answer 8

Because $1 per player would definitely favor the player.

Answer 9

I mean $1 per PLAY

Answer 10

how do i make the game fair the average should equal zero when summed

Answer 11

I'm working on that. I'm looking up the game of Chuck-A-Luck on Wikipedia.
It works with 3 dice (as opposed to 3 coins).

Answer 12

these are my notes where it is shown what is fair and what isnt

Answer 13

and i have to make a question myself and adjust it to fair. so i created this one

Answer 14

So, am I right in thinking that the winning probabilities add up to 12/8?

Answer 15

i dont know about this

Answer 16

can u tell me how did u think winning prob. adds to 12/8

Answer 17

I looked at column Xp (X=x) 3rd column over

Answer 18

the column which i draw adds to 1, the third one

Answer 19

I was only adding up the positive numbers.
Okay, adding all four, it adds to 1
Maybe it should add to zero to be a fair game?
So, should each play cost $12?

Answer 20

yea it should add zero to be fair

Answer 21

*add to zero

Answer 22

1 out of 8 times you win $3 plus the bet
2 out of 8 times you win $2 plus the bet
3 out of 8 times you win $1 plus the bet.

Answer 23

yep

Answer 24

this is a project i got and i have to create a game, these are the things it says
1. Calculate the probabilities of winning at least three different amounts of money and the probability of losing the game
2. Decide on how much you will charge to play the game and the amount each player will gain/lose for each outcome
3. By using the probabilities, calculate the expected gain/loss per game and the theoretical standard deviation over a period of time
4. Adjust the cost of the game needed to make the game fair and state your new amounts gained/lost.

Answer 25

so i came up with this question

Answer 26

but i am lost

Answer 27

As I said, Wikipedia has the "house advantage" (AND how to calculate it) for "Chuck A Luck" (a casino game with 3 dice). I don't know if it would complicate things but it might be worth discussing it.

Answer 28

i want to make things simple, i clearly get the idea of 3 coins but i am lost in the adjustments to make it fair

Answer 29

Well at least for Chuck A Luck ypu can see the house advantage calculated (AND for 3 different winning payouts).

Answer 30

brb