21 (Drinking Game)

Transcript

21 (Drinking Game) The Game and its Rules The game is a simple counting game for two players with the following rules: The first player starts by saying a number: 1, 2, or 3. The second player adds 1, 2, or 3 to that number. The players take turns adding 1, 2, or 3 to the previous total. The first player to say the number 21 wins! Let’s play an example game Between you and your friend Turn 1: Player 1 (You) You Say: "1” Turn 2: Player 2 (Friend) Friend adds 3 and says: "4" Turn 3: Player 1 (You) You add 1 and say: "5" Turn 4: Player 2 (Friend) Friend adds 2 and says: "7" Turn 5: Player 1 (You) You add 2 and say: "9" Turn 6: Player 2 (Friend) Friend adds 3 and says: "12" Turn 7: Player 1 (You) You add 1 and say: "13" Turn 8: Player 2 (Friend) Friend adds 3 and says: "16" Turn 9: Player 1 (You) You add 1 and say: "17" Turn 10: Player 2 (Friend) Friend adds 2 and says: "19" Turn 11: Player 1 (You) You add 2 and say: "21" The Winning Strategy The key to winning this game is to work backward from 21 and identify the "magic numbers" you must say to guarantee a win. The Goal: To say 21. The number before 21: To guarantee you can say 21, you must leave your opponent in a position where they cannot reach it. If you say the number 17, your opponent can add 1 (making it 18), 2 (making it 19), or 3 (making it 20). In all of those cases, you can simply add 3, 2, or 1 to reach 21 on your next turn. So, the first magic number before 21 is 17. The number before 17: Using the same logic, to guarantee you can say 17, you must first say 13. If you say 13, your opponent's move will result in 14, 15, or 16, allowing you to say 17. The next magic number is 13. The Winning Sequence If you keep working backward, you'll see a pattern. The magic numbers are all 4 apart. The winning sequence of numbers to say is: 1, 5, 9, 13, 17, 21.