# Algebra 2

posted by Jackie

Game Theory: Consider a game in which each of two people simultaneously chooses an integer: 1 or 2. Find the expected value for player A and the expected value for player B. Is each game fair.

Question: If the numbers are the same, then player A wins 1 point from player B. If the numbers are different, then player B wins 1 point from player A.

1. MathMate

Find probability of numbers matching (2/4) and not matching (2/4).

Construct table for A:
Outcome value,x P(outcome) x.P(x)
Win..... +1 ...... 0.5 ....... 0.5
Lose.....-1 ...... -0.5 .......-0.5

Sum(x.P(x))=0, so game is fair.

2. MathMate

oops
The probability on the second line should read 0.5 (not negative).

3. Jackie

what if player A wins 2 points from player B, and if the numbers are different, than player B wins 1 point from player A?

4. MathMate

Games are random processes.
All we can say is that if he wins, he gets one point, and if he loses, he loses one point. We also know (or believe) that the probability of winning or losing is each 50%.
The actual outcomes depends naturally on chance. But in the long run, the number of points won or loses will be relatively close to zero, which is our calculated expectation.

## Similar Questions

1. ### math-i have another question

Player A and B invented a new game. The probability for Player A to win a round is 1/3 and the probability that Player B will win a round is 2/3. To make the game fair, Player A will score 3 points when he/she winds a round and Player …
2. ### Statistics

The local lottery sets up a game wherein a player has a chance of collecting \$750. The player must choose a 3-digit number and if it matches, the player receives \$750 It costs \$1 to play the game. What is the expected profit (or loss) …
3. ### Stats

The local lottery sets up a game wherein a player has a chance of collecting \$750. The player must choose a 3-digit number and if it matches, the player receives \$750 It costs \$1 to play the game. What is the expected profit (or loss) …
4. ### PLEASE SOMEBODY Answer this Statistics question!

The local lottery sets up a game wherein a player has a chance of collecting \$750. The player must choose a 3-digit number and if it matches, the player receives \$750 It costs \$1 to play the game. What is the expected profit (or loss) …
5. ### math

Students at Euler Middle School are talking about ways to raise money for a school party. One student suggests a game called Heads or Tails. In this game, a player pays 50 cents and chooses heads or tails. The player then tosses a …
6. ### math

A game consists of tossing a coin and rolling an ordinary die. If the player tosses a head and rolls an even number, the player wins \$3. Otherwise, the player loses \$1. What is the expected value of this game?
7. ### Stats

A game is played where a biased coin is flipped. A head is twice as likely as a tail. It costs \$5 to plat the game and if a head occurs you win &7 but if a tail occurs you pay \$3 which of the following is correct?
8. ### Math

A game is played using one dice. If the dice is rolled and shows 1, the player wins \$1; if it shows 2, the player wins \$2; if it shows a 3, the player wins \$3. If the die shows 4,5,or 6 the player wins nothing. a.) If there is a charge …
9. ### Statistics

In a game of dice, the probability of rolling a 12 is 1/36. The probability of rolling a 9, 10, or 11 is 9/36. The probability of rolling any other number is 26/36. If the player rolls a 12, the player wins \$5. If the player rolls …
10. ### statistics

In a game of dice, the probability of rolling a 12 is 1/36. The probability of rolling a 9, 10, or 11 is 9/36. The probability of rolling any other number is 26/36. If the player rolls a 12, the player wins \$5. If the player rolls …

More Similar Questions