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

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The game involves rolling two dice, with payouts based on the sum: winning $2 for sums of 8 or higher, $1 for sums of 5-7, and losing for sums of 2-4, all for a $10 entry fee. To determine if playing is advisable, one must calculate the probability distribution and the expected value of the game. The discussion emphasizes that the question "Should you play?" is subjective and depends on individual financial circumstances and risk tolerance. A more objective approach is to assess whether the mathematical expectation is positive. Ultimately, the game can be adjusted to favor the player by altering the payout structure or entry fee.
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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.
 
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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?"
 
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