In this version of “dice blackjack,” you toss a single die repeatedly and add up the sum of your dice tosses. Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the “house” then tosses the die repeatedly. The house stops as soon as its total is 4 or more. If the house totals 8 or more, you win. Otherwise, the higher total wins. If there is a tie, the house wins. Consider the following strategies:

■ Keep tossing until your total is 3 or more.

■ Keep tossing until your total is 4 or more.

■ Keep tossing until your total is 5 or more.

■ Keep tossing until your total is 6 or more.

■ Keep tossing until your total is 7 or more.

For example, suppose you keep tossing until your total is 4 or more. Here are some examples of how the game might go:

■ You toss a 2 and then a 3 and stop for total of 5. The house tosses a 3 and then a 2. You lose because a tie goes to the house.

■ You toss a 3 and then a 6. You lose.

■ You toss a 6 and stop. The house tosses a 3 and then a 2. You win.

■ You toss a 3 and then a 4 for total of 7. The house tosses a 3 and then a 5. You win.

Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values so that you are 95% sure that your probability of winning is between these two values? Which of the five strategies appears to be best?