Expected Value of Rolling a Pair of Dice - Fair Price to Play

  • Context: MHB 
  • Thread starter Thread starter rymatson406
  • Start date Start date
  • Tags Tags
    Expected value Value
Click For Summary
SUMMARY

The discussion centers on calculating the fair price to play a game involving rolling a pair of dice. If the sum of the dice equals 7, the player pays $28; otherwise, they receive a payout equal to the sum of the dice. The expected payout for the opponent is approximately $5.83, while the player's expected win is about $4.67. To ensure fairness, the player should pay $35 to participate in the game.

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with expected value calculations
  • Knowledge of the outcomes of rolling two six-sided dice
  • Ability to perform simple arithmetic operations
NEXT STEPS
  • Study the concept of expected value in probability theory
  • Learn about combinatorial outcomes in rolling dice
  • Explore variations of dice games and their fair pricing
  • Investigate advanced probability topics, such as game theory
USEFUL FOR

This discussion is beneficial for mathematicians, game theorists, and anyone interested in probability calculations and fair game pricing strategies.

rymatson406
Messages
3
Reaction score
0
We roll a pair of dice. If the sum of the dice is 7, you pay me $28. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is the price that you should pay to play the game that would make the game fair?
 
Physics news on Phys.org
I deleted the duplicate of this thread in the Advanced Probability subforum. We ask that you post a question only once, as doing otherwise can lead to duplication of effort on the part of our helpers. I'm sure you can understand that the time and effort of our helpers is valuable, and we don't want to see it wasted. :D

edit: I did the same with your other question.
 
rymatson406 said:
We roll a pair of dice. If the sum of the dice is 7, you pay me $28. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is the price that you should pay to play the game that would make the game fair?

Among the 36 possible results of the roll of two dice, those whose sum is k are k-1 for k ranging from 2 to 7 and 12 - (k-1) for k ranging from 8 to 12. The expected win your opponent is ...

$\displaystyle E\ \{ O \} = \frac{(1 + 2 + 3 + 4 + 5)\ 14}{36} = 5.833... \text{dollars}$

Your expected win is...

$\displaystyle E\ \{ Y \} = \frac{28}{6} = 4.666... \text{dollars}$

... and it is lower. For a fair game You should ask 35 dollars...

Kind regards

$\chi$ $\sigma$
 

Similar threads

Undergrad Probability to get a certain number or less by throwing two 6-faced die
  • · Replies 6 ·
Replies
6
Views
2K
MHB Should You Play? Analyzing a Game with Probability & Strategies to Fix it
  • · Replies 1 ·
Replies
1
Views
2K
MHB How Do You Calculate Expected Value in a Dice Game?
  • · Replies 2 ·
Replies
2
Views
8K
MHB Understanding Dice Throwing Probabilities: A Layman's Guide
  • · Replies 8 ·
Replies
8
Views
5K
MHB Pr of exactly one dice showing 2
  • · Replies 9 ·
Replies
9
Views
3K
High School Probability in a dice game
  • · Replies 41 ·
2
Replies
41
Views
6K
Undergrad What Is the Probability of Rolling Pairs That Sum to Seven with n Dice?
  • · Replies 5 ·
Replies
5
Views
2K
High School What would you pay to play (or avoid) a finite St Petersburg game?
  • · Replies 6 ·
Replies
6
Views
2K
High School Dice calculation of p(7), two different values?
  • · Replies 32 ·
2
Replies
32
Views
3K
Graduate PDF of open ended double dice rolls
  • · Replies 6 ·
Replies
6
Views
3K