Question

4. Create a simple dice, card or spinning wheel game that can be analyzed using expected value.

Discuss what the expected value of the game means in terms of what a player can expect if they

were to play the game over the long run.

Answer 1

Let's consider a game of simple dice in which a player will win if number 6 occurs on the top.

Let us find out out the expected value for player,

As the dice has 6 sides, the probability of occurring of 6 on top is 1/6.

Suppose this game is continued for long run let's take that the dice is rolled 20 times.

Hence expected value is given by,

Number of times dice rolled * probability of occurrence of 6

= 20 * (1/6)

= 3.33

Here this expected value means that the player will win 3.33 times out of 20 times, but here 3.33 is not practical value hence we will approximate it to 3,

Thus it means that player can expect 3 wins out of 20 times dice rolled.

(if we take X : occurrence of 6 on top of dice

Then the distribution of X is Binomial (n=20, P=1/6)

Hence Expected value of X = n*P = 3.33)

Similarly, in cards game,

Assume that a player wins if the chosen card out of 52 cards is King.

There are 4 Kings in the deck of cards.

Probsbikity of occurrence of King = 4/52

Let this game is repeated 30 times

Hence the expected value = 30 * (4/52) = 2.3

Hebce the player can expect that he /she can win the game 2 times out of 30 times.