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## A Thrilling Game of Swaff

 Category: Probability Submitted By: bigSWAFF_69_ Fun: (2.48) Difficulty: (2.2)

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?

16/81

There 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.