Algebra 2

posted by .

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.

  • Algebra 2 -

    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.

  • Algebra 2 -

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

  • Algebra 2 -

    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?

  • Algebra 2 -

    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.
    Hope that answers your query.

Respond to this Question

First Name
School Subject
Your Answer

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. 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) …
  4. 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?
  5. Math

    Roulette is a well known game in which a mechanical device randomly selects one of 38 equally likely numbers. IF a player decides to play by choosing a number, he gains $35 if his number is selected by the device. If any other number …
  6. 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 …
  7. math

    A game is defined by the rules that two dice are rolled and the  player wins varying amounts depending on the sum of the two dice rolled based  on the following table: Sum 2 3 4 5 6 7 8 9 10 11 12 Winnings …
  8. data management gr.12

    A game is defined by the rules that the die is rolled and the player wins varying amounts depending on the number on the upper face according to the following table: sum 1 2 3 4 5 6 Winnings $10 $9 $8 $7 $6 $5 The cost to play the …
  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