Strange dice game
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The document describes a strange dice game where each die has the same number on the opposite sides. It analyzes the probabilities of winning for each die if chosen first against the other dice. It determines that no matter which die is chosen first, the second player has a 5/9 probability of choosing a die that wins due to the symmetrical nature of the dice. Therefore, the first player is always at a disadvantage in this game.
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- 1. Sanjana Urmy 13CSE030 University of Barisal
- 2. A Strange Dice Game
- 3. The number on each concealed face is the same as the number on the opposite, exposed face . The rules are simple. You pick one of the three dice, and then I pick one of the two remainders. We both roll and the player with the higher number wins.
- 4. • Which of the dice should you choose to maximize your chances of winning? # Die B is appealling , because it has a 9, the highest number overall. # Then again, die A has two relatively large numbers, 6 and 7. # But die C has an 8 and no very small numbers at all.
- 5. Die A versus Die B
- 6. • Pr (A > B) = Pr (2, 1) + Pr (6, 1) + Pr (6, 5) + Pr (7, 1) + Pr (7, 5) =1/9+1/9+1/9+1/9+1/9 =5/9
- 7. Die B versus Die C
- 8. Die C versus Die A
- 9. This means that no matter what die the first player chooses, the second player can choose a die that beats it with probability 5/9. The player who picks first is always at a disadvantage!
- 10. Thank You