Should You Play? Analyzing a Game with Probability & Strategies to Fix it

  • Context: MHB 
  • Thread starter Thread starter UghhHelpp
  • Start date Start date
  • Tags Tags
    Game Probability
Click For Summary
SUMMARY

The discussion centers on a dice game where players roll two dice, with potential winnings based on the sum of the rolls. The payout structure is as follows: winning \$2 for a sum of 8 or higher, winning \$1 for a sum between 5 and 7, and losing the \$10 entry fee for a sum between 2 and 4. To determine if playing is advisable, participants are encouraged to construct a probability distribution and calculate the expected value. The conversation also emphasizes the importance of mathematical expectation over subjective factors when deciding to play.

PREREQUISITES
  • Understanding of probability distributions
  • Basic knowledge of expected value calculations
  • Familiarity with two-dice rolling mechanics
  • Concept of risk versus reward in gambling scenarios
NEXT STEPS
  • Calculate the expected value of rolling two dice in this game
  • Explore strategies to adjust the payout structure to favor the player
  • Learn about variance and its impact on gambling outcomes
  • Investigate other games of chance and their mathematical expectations
USEFUL FOR

Mathematicians, game theorists, gamblers, and anyone interested in understanding probability and risk management in games of chance.

UghhHelpp
Messages
1
Reaction score
0
Part 1: Your friend wants to play a game. You will roll two dice. If the sum of the dice is 8 or higher you win \$2, from 5-7 you win \$1, and from 2-4 you lose. You pay \$10 to play the game. Should you play? Explain. (Hint: Construct a probability distribution and find the mean)

Part 2: Fix the game so that it is in your favor to play.
 
Physics news on Phys.org
UghhHelpp said:
Part 1: Your friend wants to play a game. You will roll two dice. If the sum of the dice is 8 or higher you win \$2, from 5-7 you win \$1, and from 2-4 you lose. You pay \$10 to play the game. Should you play? Explain. (Hint: Construct a probability distribution and find the mean)

Part 2: Fix the game so that it is in your favor to play.

Well, let's see what you have. Produce a mathematical expectation for us.

Note: "Should you play?" is not a good question. This is very subjective and includes your financial goals, your risk aversion, the proximity of your next payday, and lots of other factors. Do you mean, "Is your mathematical expectation greater than zero?"
 

Similar threads

MHB Probabilities of certain events in a lucky wheel game
  • · Replies 2 ·
Replies
2
Views
2K
Graduate A game of seemingly mutually independent events
  • · Replies 7 ·
Replies
7
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 Which probability calculation is "more correct" in Baccarat games?
  • · Replies 9 ·
Replies
9
Views
5K
Undergrad Probability to get a certain number or less by throwing two 6-faced die
  • · Replies 6 ·
Replies
6
Views
2K
High School Probability Distribution with a resettable count to win
  • · Replies 8 ·
Replies
8
Views
2K
MHB How Do You Calculate Expected Value in a Dice Game?
  • · Replies 2 ·
Replies
2
Views
7K
High School What is the probability of breaking a 56 game hitting streak record?
  • · Replies 12 ·
Replies
12
Views
4K
Undergrad How Many Unique Games of Commander Can Be Played?
  • · Replies 4 ·
Replies
4
Views
3K
High School Probability in a dice game
  • · Replies 41 ·
2
Replies
41
Views
6K