The 9 Most Likely Numbers to Roll with 3 Dice
The 9 most likely numbers to roll with 3 dice
To calculate the 9 most likely numbers to roll with all three dice, you need to work out the possible die combinations for each roll (from 3 to 18).
They are the following:
3 - (1+1+1) Possible Combinations: 1
4 - (1+2+1) Possible Combinations:1
5 - (1+3+1) (1,2,2) Possible Combinations:2
6 - (1,4,1) (1,3,2) (2,2,2) Possible Combinations:3
7 - (1,4,2) (1,3,3) (5,1,1) (3,2,2) Possible Combinations:4
8 - (1,4,3) (1,2,5) (1,1,6) (4,2,2) (3,3,2) Possible Combinations: 5
9 - (6,2,1) (5,3,1) (5,2,2) (4,4,1) (4,3,2) (3,3,3) Possible Combinations:6
10 - (6,3,1) (6,2,2) (5,3,2) (5,4,1) (4,4,2) (4,3,3) Possible Combinations:6
11 - (6,4,1) (6,3,2) (5,5,1) (5,4,2) (5,3,3) (4,4,3) Possible Combinations:6
12 - (6,5,1) (6,4,2) (6,3,3) (5,5,2) (5,4,3) (4,4,4) Possible Combinations:6
13 - (6,6,1) (6,5,2) (6,4,3) (5,5,3) (5,4,4) Possible Combinations:5
14 - (6,4,4) (6,5,3) (5,5,4) (6,6,2) Possible Combinations:4
15- (6,6,3) (6,4,5) (5,5,5) Possible Combinations:3
16- (6,6,4) (6,5,5) Possible Combinations:2
17- (6,6,5) Possible Combinations:1
18- (6,6,6) Possible Combinations:1
This means that there are a total of 56 possible combinations in total. So, to put it in fractions:
3- 1/56
4- 1/56
5- 2/56
6- 3/56
7- 4/56
8- 5/56
9- 6/56
10- 6/56
11- 6/56
12- 6/56
13- 5/56
14- 4/56
15- 3/56
16- 2/56
17- 1/56
18- 1/56
This shows that the numbers 9, 10, 11 and 12 all have a probability of 6/56 (the highest) and 18, 17, 1 and 2 all have a probability of 1/56 (the lowest). So four of the numbers are chosen (9, 10, 11, 12). The numbers with the second highest probability (5/56) are 8 and 13. Those are added to the list. Then, both with 4/56, 7 and 14. And, finally, either 15 or 6, both with 3/56. So, our table should look like this:
9 10 11
12 13 8
14 7
To calculate the 9 most likely numbers to roll with all three dice, you need to work out the possible die combinations for each roll (from 3 to 18).
They are the following:
3 - (1+1+1) Possible Combinations: 1
4 - (1+2+1) Possible Combinations:1
5 - (1+3+1) (1,2,2) Possible Combinations:2
6 - (1,4,1) (1,3,2) (2,2,2) Possible Combinations:3
7 - (1,4,2) (1,3,3) (5,1,1) (3,2,2) Possible Combinations:4
8 - (1,4,3) (1,2,5) (1,1,6) (4,2,2) (3,3,2) Possible Combinations: 5
9 - (6,2,1) (5,3,1) (5,2,2) (4,4,1) (4,3,2) (3,3,3) Possible Combinations:6
10 - (6,3,1) (6,2,2) (5,3,2) (5,4,1) (4,4,2) (4,3,3) Possible Combinations:6
11 - (6,4,1) (6,3,2) (5,5,1) (5,4,2) (5,3,3) (4,4,3) Possible Combinations:6
12 - (6,5,1) (6,4,2) (6,3,3) (5,5,2) (5,4,3) (4,4,4) Possible Combinations:6
13 - (6,6,1) (6,5,2) (6,4,3) (5,5,3) (5,4,4) Possible Combinations:5
14 - (6,4,4) (6,5,3) (5,5,4) (6,6,2) Possible Combinations:4
15- (6,6,3) (6,4,5) (5,5,5) Possible Combinations:3
16- (6,6,4) (6,5,5) Possible Combinations:2
17- (6,6,5) Possible Combinations:1
18- (6,6,6) Possible Combinations:1
This means that there are a total of 56 possible combinations in total. So, to put it in fractions:
3- 1/56
4- 1/56
5- 2/56
6- 3/56
7- 4/56
8- 5/56
9- 6/56
10- 6/56
11- 6/56
12- 6/56
13- 5/56
14- 4/56
15- 3/56
16- 2/56
17- 1/56
18- 1/56
This shows that the numbers 9, 10, 11 and 12 all have a probability of 6/56 (the highest) and 18, 17, 1 and 2 all have a probability of 1/56 (the lowest). So four of the numbers are chosen (9, 10, 11, 12). The numbers with the second highest probability (5/56) are 8 and 13. Those are added to the list. Then, both with 4/56, 7 and 14. And, finally, either 15 or 6, both with 3/56. So, our table should look like this:
9 10 11
12 13 8
14 7