[SOLUTION] Dice Rolling Game
Consider a dice game with the following rules All players start with 10 points A dice is rolled, and if the number on the dice is 1, 2, 3, 4 or 5, this number is added to each players score. If the number is 6, the score of all players is reduced to zero Before the dice is rolled each player is given the choice of continuing or taking their current score as their final score. This process is repeated until a 6 is rolled and the game ends. All players still playing at this point receive zero as their final score.Now suppose that a 6 was not rolled and you choose to continue playing(v) On average, do you do worse or better than someone who chooses to stop playing after 1 dice roll?(vi) Is there an optimal number of dice rolls you should continue playing for? Explain your reasoning.(vii) If the rules are changed such that when the number is 2, 3, 4, 5 or 6, this number is added to your score. While if the number is 1, your score is reduced to zero. Discuss how this affects the optimal number of dice rolls you should continue playing for.
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