Question

1. extra credit (2 points) snowball game

you (player 1) and 2 other players (players 2 and 3) are playing. goal: player not hit with a snowball is the winner.
sequence of turns: player 1, then player2, then player 3, then player 1, etc: if a player is eliminated, it is the next
non - eliminated players turn. on a players turn, the player can only throw 1 snowball at another non - eliminated
player. unfortunately, you have the worst accuracy of the 3 players at 50%, followed by 75% for player 2, and 90%
for player 3. what is your best strategy (1 point) and why is this the best strategy(1 point)?

Explanation:

• Best Strategy: Miss on purpose (throw the snowball in a non - target direction) on the first turn.
• Why:
• If Player 1 (you) tries to hit Player 2 or 3 on the first turn:
• If you hit Player 2 (with a 50% chance), then Player 3 (with 90% accuracy) will target you on their turn. Your survival chance against Player 3 is low.
• If you hit Player 3 (with a 50% chance), then Player 2 (with 75% accuracy) will target you on their turn. Your survival chance against Player 2 is also relatively low.
• If you miss on purpose:
• Player 2 will then take their turn. Player 2 (75% accuracy) will likely target Player 3 (the more accurate player).
• If Player 2 hits Player 3 (75% chance), then it's your turn again. Now you are up against Player 2. Your 50% accuracy is better than facing Player 3's 90% accuracy.
• If Player 2 misses Player 3 (25% chance), then Player 3 will take their turn. Player 3 (90% accuracy) will likely target Player 2. If Player 3 hits Player 2 (90% chance), then it's your turn against Player 3. But this sequence gives you a better chance compared to directly engaging with the more accurate player first.

Answer:

• Best strategy: Miss on purpose on the first turn.
• Why: By missing, you let the more accurate players (Player 2 and Player 3) potentially eliminate each other first, increasing your chances of being the last non - eliminated player.