You can roll a 5-side dice up to 2 times. After the first roll, if you get a number, you can decide either to get dollars or to choose to continue rolling. But once you decide to continue, you forgot the number you just rolled. If you get to the second roll, you'll just get dollars if the second number is and the game stops. Here are two examples: (i) If you get number 2 in the first roll and decide to stop, you will get 2 dollars. (ii) If you get number 2 in the first roll, decide to continue for the second roll, and get number 1 in the second roll, you will only get 1 dollar. Then the questions are: (1) What is your strategy for deciding whether to continue for the second roll? The expected value for the first roll is three ( chance for each value (1 - 5)). The best strategy is to re-roll if you get a value less than 3. (My Answer) (2) What is the game worth (expected profit if we follow the best strategy in (1)) ?

• 1. (1) Continue rolling if the first roll is 1, 2, or 3 (2) 3.6
• 2. (1) Continue rolling if the first roll is 4 (2) 4.75
• 3. (1) Continue rolling if the first roll is 1, 2, 3, or 4 (2) 4.4
• 4. (1) Continue rolling if the first roll is 1 or 2 (2) 4