Dice Odds for Settlers of Catan

This is a quick discussion of the distribution of rolls you get over time with a pair of 6 sided dice -- something you happen to care about quite a lot in the game Settlers of Catan. (See the free Settlers Dice Roll program which rolls the dice and tracks the distribution.) The probability of rolling a particular number with two dice is the number of ways the dice can fall that add up to that number divided by the total number of ways the dice can fall. So for example, the odds of a 4 roll are 3/36 since out of the total of 36 ways the two dice can fall, 3 of those ways add to 4: 1+3, 2+2, 3+1. Note that 1+3 and 3+1 count as 2 different ways along with 2+2, yielding 3 ways total.

odds for 7 6/36 =0.167 odds for 6 and 8

5/36 =0.139 odds for 5 and 9

4/36 =0.111 odds for 4 and 10 3/36 =0.083 odds for 3 and 11

2/36 =0.056 odds for 2 and 12

1/36 =0.028



at all

both

Nick Parlante, nick.parlante@cs.stanford.edu, March 2003



