Brain Teasers
A Thrilling Game of Swaff
Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.Probability
In a game of Swaff, players have 1 turn to roll 2 dice, to achieve a total number that is a multiple of 3. If the combined number is NOT a multiple of three, the player is out. If it is, he/she goes on to the next round. If no players get a multiple of 3, in any round, the game is over in a tie.
Example: John rolls a 2 and a 4. Total score is 6 - a multiple of 3. John would then move on to the next round.
Lets say that John, Sally, Suzan, and Jimmy were playing a game of Swaff. What is the probability that the game ends the first round as a tie?
Example: John rolls a 2 and a 4. Total score is 6 - a multiple of 3. John would then move on to the next round.
Lets say that John, Sally, Suzan, and Jimmy were playing a game of Swaff. What is the probability that the game ends the first round as a tie?
Answer
16/81There are 36 roll combinations:
1-6, 1-5, 1-4, 1-3, 1-2, 1-1,
2-6, 2-5, 2-4, 2-3, 2-2, 2-1,
3-6, 3-5, 3-4, 3-3, 3-2, 3-1,
4-6, 4-5, 4-4, 4-3, 4-2, 4-1,
5-6, 5-5, 5-4, 5-3, 5-2, 5-1,
6-6, 6-5, 6-4, 6-3, 6-2, 6-1,
24 of which are NOT multiples of 3:
1-6, 1-4, 1-3, 1-1,
2-6, 2-5, 2-3, 2-2,
3-5, 3-4, 3-2, 3-1,
4-6, 4-4, 4-3, 4-1,
5-6, 5-5, 5-3, 5-2,
6-5, 6-4, 6-2, 6-1
There is a 2/3 chance for one person to lose (not get a multiple of 3).
2/3 to the power of 4 (for the four players) is 16/81.
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