Plan B Here’s another attempt at developing a good strategy for the dice game in Exercise 33. Instead of stopping after a certain number of rolls, you could decide to stop when your score reaches a certain number of points.
a) How many points would you expect a roll to add to your score?
b) In terms of your current score, how many points would you expect a roll to subtract from your score?
c) Based on your answers in parts a and b, at what score will another roll “break even”?
d) Describe the strategy this result suggests.
Exercise 33
When to stop? In Exercise 27 of the Review Exercises for Part, we posed this question: You play a game that involves rolling a die. You can roll as many times as you want, and your score is the total for all the rolls. But … if you roll a 6, your score is 0 and your turn is over. What might be a good strategy for a game like this? You attempted to devise a good strategy by simulating several plays to see what might happen. Let’s try calculating a strategy.
a) On what roll would you expect to get a 6 for the first time?
b) So, roll one time less than that. Assuming all those rolls were not 6’s, what’s your expected score?
c) What’s the probability that you can roll that many times without getting a 6?