Probabilities of 6-Sided Dice

It's sometimes handy to know the probabilities of an action succeeding in TFT. Since TFT uses 6-sided dice exclusively (as does GURPS), these tables do not include any other possibilities. The first table gives the probability of rolling a specific number; the second table gives the probability of rolling less than or equal to a specific number.

This table gives the probability of rolling a particular number on a set of so many 6-sided dice.

Roll 1 die 2 dice 3 dice 4 dice 5 dice
1 1/6 (16.667%) 0 0 0 0
2 1/6 (16.667%) 1/36 (2.778%) 0 0 0
3 1/6 (16.667%) 2/36 (5.556%) 1/216 (0.463%) 0 0
4 1/6 (16.667%) 3/36 (8.333%) 3/216 (1.389%) 1/1296 (0.077%) 0
5 1/6 (16.667%) 4/36 (11.111%) 6/216 (2.778%) 4/1296 (0.309%) 1/7776 (0.013%)
6 1/6 (16.667%) 5/36 (13.889%) 10/216 (4.630%) 10/1296 (0.772%) 5/7776 (0.064%)
7 0 6/36 (16.667%) 15/216 (6.944%) 20/1296 (1.543%) 15/7776 (0.193%)
8 0 5/36 (13.889%) 21/216 (9.722%) 35/1296 (2.701%) 35/7776 (0.450%)
9 0 4/36 (11.111%) 25/216 (11.574%) 56/1296 (4.321%) 70/7776 (0.900%)
10 0 3/36 (8.333%) 27/216 (12.500%) 80/1296 (6.173%) 126/7776 (1.620%)
11 0 2/36 (5.556%) 27/216 (12.500%) 104/1296 (8.025%) 205/7776 (2.636%)
12 0 1/36 (2.778%) 25/216 (11.574%) 125/1296 (9.645%) 305/7776 (3.922%)
13 0 0 21/216 (9.722%) 140/1296 (10.802%) 420/7776 (5.401%)
14 0 0 15/216 (6.944%) 146/1296 (11.265%) 540/7776 (6.944%)
15 0 0 10/216 (4.630%) 140/1296 (10.802%) 651/7776 (8.372%)
16 0 0 6/216 (2.778%) 125/1296 (9.645%) 735/7776 (9.452%)
17 0 0 3/216 (1.389%) 104/1296 (8.025%) 780/7776 (10.031%)
18 0 0 1/216 (0.463%) 80/1296 (6.173%) 780/7776 (10.031%)
19 0 0 0 56/1296 (4.321%) 735/7776 (9.452%)
20 0 0 0 35/1296 (2.701%) 651/7776 (8.372%)
21 0 0 0 20/1296 (1.543%) 540/7776 (6.944%)
22 0 0 0 10/1296 (0.772%) 420/7776 (5.401%)
23 0 0 0 4/1296 (0.309%) 305/7776 (3.922%)
24 0 0 0 1/1296 (0.077%) 205/7776 (2.636%)
25 0 0 0 0 126/7776 (1.620%)
26 0 0 0 0 70/7776 (0.900%)
27 0 0 0 0 35/7776 (0.450%)
28 0 0 0 0 15/7776 (0.193%)
29 0 0 0 0 5/7776 (0.064%)
30 0 0 0 0 1/7776 (0.013%)

This table gives the probability of rolling a particular number or less on a set of so many 6-sided dice. It can also be used to find the probability of rolling a particular number or more. Since the probability of rolling N or more is the same as the probability of not rolling N-1 or less, simply look up the N-1 value on this table, and subtract it from 1 or 100%. For example, to find the probability of rolling 8 or more on 3 dice, look up the probability of rolling 7 or less, which is 35/216 or 16.204%. Subtract that from 1, giving 181/216 (216 - 35 = 181) or 83.796%.

Roll 1 die 2 dice 3 dice 4 dice 5 dice
1 1/6 (16.667%) 0 0 0 0
2 2/6 (33.333%) 1/36 (2.778%) 0 0 0
3 3/6 (50.000%) 3/36 (8.333%) 1/216 (0.463%) 0 0
4 4/6 (66.667%) 6/36 (16.667%) 4/216 (1.852%) 1/1296 (0.077%) 0
5 5/6 (83.333%) 10/36 (27.778%) 10/216 (4.630%) 5/1296 (0.386%) 1/7776 (0.013%)
6 6/6 (100%) 15/36 (41.667%) 20/216 (9.259%) 15/1296 (1.157%) 6/7776 (0.077%)
7 100% 21/36 (58.333%) 35/216 (16.204%) 35/1296 (2.701%) 21/7776 (0.270%)
8 100% 26/36 (72.222%) 56/216 (25.926%) 70/1296 (5.401%) 56/7776 (0.720%)
9 100% 30/36 (83.333%) 81/216 (37.500%) 126/1296 (9.722%) 126/7776 (1.620%)
10 100% 33/36 (91.667%) 108/216 (50.000%) 206/1296 (15.895%) 252/7776 (3.241%)
11 100% 35/36 (97.222%) 135/216 (62.500%) 310/1296 (23.920%) 457/7776 (5.877%)
12 100% 36/36 (100%) 160/216 (74.074%) 435/1296 (33.565%) 762/7776 (9.799%)
13 100% 100% 181/216 (83.796%) 575/1296 (44.367%) 1182/7776 (15.201%)
14 100% 100% 196/216 (90.741%) 721/1296 (55.633%) 1722/7776 (22.145%)
15 100% 100% 206/216 (95.370%) 861/1296 (66.435%) 2373/7776 (30.517%)
16 100% 100% 212/216 (98.148%) 986/1296 (76.080%) 3108/7776 (39.969%)
17 100% 100% 215/216 (99.537%) 1090/1296 (84.105%) 3888/7776 (50.000%)
18 100% 100% 216/216 (100%) 1170/1296 (90.278%) 4668/7776 (60.031%)
19 100% 100% 100% 1226/1296 (94.599%) 5403/7776 (69.483%)
20 100% 100% 100% 1261/1296 (97.299%) 6054/7776 (77.855%)
21 100% 100% 100% 1281/1296 (98.843%) 6594/7776 (84.799%)
22 100% 100% 100% 1291/1296 (99.614%) 7014/7776 (90.201%)
23 100% 100% 100% 1295/1296 (99.923%) 7319/7776 (94.123%)
24 100% 100% 100% 1296/1296 (100%) 7524/7776 (96.759%)
25 100% 100% 100% 100% 7650/7776 (98.380%)
26 100% 100% 100% 100% 7720/7776 (99.280%)
27 100% 100% 100% 100% 7755/7776 (99.730%)
28 100% 100% 100% 100% 7770/7776 (99.923%)
29 100% 100% 100% 100% 7775/7776 (99.987%)
30 100% 100% 100% 100% 7776/7776 (100%)