Odds of Various Results With Six Sided Dice
These tables are generated by a program I wrote that uses statistics theory
to calculate results. Unfortunately, because of limitations of the size
of integers on my computer and the lack of time to work out additional math
to overcome this limitation, I have limited calculating the odds only up
to 8 dice.
"outcomes" is the total number of different possible outcomes. Note
that for 8 dice the total number of different outcomes is 6^8 or over 1.6
million cases!
The "occurrences for" is the number of outcomes that will generate that
specific number.
"percent" is the simply the total different outcomes divided by number of
occurrences for that specific number.
The "total" is the sum total occurrences for that and all lower numbers.
The last "percent" is the sum total percent for that number and all lower
numbers.
number of dice 1
outcomes: 6, highest sum: 6, lowest sum: 1, different sums: 6
occurrences for 1: 1 percent: 16 total: 1 percent: 16
occurrences for 2: 1 percent: 16 total: 2 percent: 33
occurrences for 3: 1 percent: 16 total: 3 percent: 50
occurrences for 4: 1 percent: 16 total: 4 percent: 66
occurrences for 5: 1 percent: 16 total: 5 percent: 83
occurrences for 6: 1 percent: 16 total: 6 percent:100
number of dice 2
outcomes: 36, highest sum:12, lowest sum: 2, different sums:11
occurrences for 2: 1 percent: 2 total: 1 percent: 2
occurrences for 3: 2 percent: 5 total: 3 percent: 8
occurrences for 4: 3 percent: 8 total: 6 percent: 16
occurrences for 5: 4 percent: 11 total: 10 percent: 27
occurrences for 6: 5 percent: 13 total: 15 percent: 41
occurrences for 7: 6 percent: 16 total: 21 percent: 58
occurrences for 8: 5 percent: 13 total: 26 percent: 72
occurrences for 9: 4 percent: 11 total: 30 percent: 83
occurrences for 10: 3 percent: 8 total: 33 percent: 91
occurrences for 11: 2 percent: 5 total: 35 percent: 97
occurrences for 12: 1 percent: 2 total: 36 percent:100
number of dice 3
outcomes: 216, highest sum:18, lowest sum: 3, different sums:16
occurrences for 3: 1 percent: 0 total: 1 percent: 0
occurrences for 4: 3 percent: 1 total: 4 percent: 1
occurrences for 5: 6 percent: 2 total: 10 percent: 4
occurrences for 6: 10 percent: 4 total: 20 percent: 9
occurrences for 7: 15 percent: 6 total: 35 percent: 16
occurrences for 8: 21 percent: 9 total: 56 percent: 25
occurrences for 9: 25 percent: 11 total: 81 percent: 37
occurrences for 10: 27 percent: 12 total: 108 percent: 50
occurrences for 11: 27 percent: 12 total: 135 percent: 62
occurrences for 12: 25 percent: 11 total: 160 percent: 74
occurrences for 13: 21 percent: 9 total: 181 percent: 83
occurrences for 14: 15 percent: 6 total: 196 percent: 90
occurrences for 15: 10 percent: 4 total: 206 percent: 95
occurrences for 16: 6 percent: 2 total: 212 percent: 98
occurrences for 17: 3 percent: 1 total: 215 percent: 99
occurrences for 18: 1 percent: 0 total: 216 percent:100
number of dice 4
outcomes: 1296, highest sum:24, lowest sum: 4, different sums:21
occurrences for 4: 1 percent: 0 total: 1 percent: 0
occurrences for 5: 4 percent: 0 total: 5 percent: 0
occurrences for 6: 10 percent: 0 total: 15 percent: 1
occurrences for 7: 20 percent: 1 total: 35 percent: 2
occurrences for 8: 35 percent: 2 total: 70 percent: 5
occurrences for 9: 56 percent: 4 total: 126 percent: 9
occurrences for 10: 80 percent: 6 total: 206 percent: 15
occurrences for 11: 104 percent: 8 total: 310 percent: 23
occurrences for 12: 125 percent: 9 total: 435 percent: 33
occurrences for 13: 140 percent: 10 total: 575 percent: 44
occurrences for 14: 146 percent: 11 total: 721 percent: 55
occurrences for 15: 140 percent: 10 total: 861 percent: 66
occurrences for 16: 125 percent: 9 total: 986 percent: 76
occurrences for 17: 104 percent: 8 total: 1090 percent: 84
occurrences for 18: 80 percent: 6 total: 1170 percent: 90
occurrences for 19: 56 percent: 4 total: 1226 percent: 94
occurrences for 20: 35 percent: 2 total: 1261 percent: 97
occurrences for 21: 20 percent: 1 total: 1281 percent: 98
occurrences for 22: 10 percent: 0 total: 1291 percent: 99
occurrences for 23: 4 percent: 0 total: 1295 percent: 99
occurrences for 24: 1 percent: 0 total: 1296 percent:100
number of dice 5
outcomes: 7776, highest sum:30, lowest sum: 5, different sums:26
occurrences for 5: 1 percent: 0 total: 1 percent: 0
occurrences for 6: 5 percent: 0 total: 6 percent: 0
occurrences for 7: 15 percent: 0 total: 21 percent: 0
occurrences for 8: 35 percent: 0 total: 56 percent: 0
occurrences for 9: 70 percent: 0 total: 126 percent: 1
occurrences for 10: 126 percent: 1 total: 252 percent: 3
occurrences for 11: 205 percent: 2 total: 457 percent: 5
occurrences for 12: 305 percent: 3 total: 762 percent: 9
occurrences for 13: 420 percent: 5 total: 1182 percent: 15
occurrences for 14: 540 percent: 6 total: 1722 percent: 22
occurrences for 15: 651 percent: 8 total: 2373 percent: 30
occurrences for 16: 735 percent: 9 total: 3108 percent: 39
occurrences for 17: 780 percent: 10 total: 3888 percent: 50
occurrences for 18: 780 percent: 10 total: 4668 percent: 60
occurrences for 19: 735 percent: 9 total: 5403 percent: 69
occurrences for 20: 651 percent: 8 total: 6054 percent: 77
occurrences for 21: 540 percent: 6 total: 6594 percent: 84
occurrences for 22: 420 percent: 5 total: 7014 percent: 90
occurrences for 23: 305 percent: 3 total: 7319 percent: 94
occurrences for 24: 205 percent: 2 total: 7524 percent: 96
occurrences for 25: 126 percent: 1 total: 7650 percent: 98
occurrences for 26: 70 percent: 0 total: 7720 percent: 99
occurrences for 27: 35 percent: 0 total: 7755 percent: 99
occurrences for 28: 15 percent: 0 total: 7770 percent: 99
occurrences for 29: 5 percent: 0 total: 7775 percent: 99
occurrences for 30: 1 percent: 0 total: 7776 percent:100
number of dice 6
outcomes: 46656, highest sum:36, lowest sum: 6, different sums:31
occurrences for 6: 1 percent: 0 total: 1 percent: 0
occurrences for 7: 6 percent: 0 total: 7 percent: 0
occurrences for 8: 21 percent: 0 total: 28 percent: 0
occurrences for 9: 56 percent: 0 total: 84 percent: 0
occurrences for 10: 126 percent: 0 total: 210 percent: 0
occurrences for 11: 252 percent: 0 total: 462 percent: 0
occurrences for 12: 456 percent: 0 total: 918 percent: 1
occurrences for 13: 756 percent: 1 total: 1674 percent: 3
occurrences for 14: 1161 percent: 2 total: 2835 percent: 6
occurrences for 15: 1666 percent: 3 total: 4501 percent: 9
occurrences for 16: 2247 percent: 4 total: 6748 percent: 14
occurrences for 17: 2856 percent: 6 total: 9604 percent: 20
occurrences for 18: 3431 percent: 7 total: 13035 percent: 27
occurrences for 19: 3906 percent: 8 total: 16941 percent: 36
occurrences for 20: 4221 percent: 9 total: 21162 percent: 45
occurrences for 21: 4332 percent: 9 total: 25494 percent: 54
occurrences for 22: 4221 percent: 9 total: 29715 percent: 63
occurrences for 23: 3906 percent: 8 total: 33621 percent: 72
occurrences for 24: 3431 percent: 7 total: 37052 percent: 79
occurrences for 25: 2856 percent: 6 total: 39908 percent: 85
occurrences for 26: 2247 percent: 4 total: 42155 percent: 90
occurrences for 27: 1666 percent: 3 total: 43821 percent: 93
occurrences for 28: 1161 percent: 2 total: 44982 percent: 96
occurrences for 29: 756 percent: 1 total: 45738 percent: 98
occurrences for 30: 456 percent: 0 total: 46194 percent: 99
occurrences for 31: 252 percent: 0 total: 46446 percent: 99
occurrences for 32: 126 percent: 0 total: 46572 percent: 99
occurrences for 33: 56 percent: 0 total: 46628 percent: 99
occurrences for 34: 21 percent: 0 total: 46649 percent: 99
occurrences for 35: 6 percent: 0 total: 46655 percent: 99
occurrences for 36: 1 percent: 0 total: 46656 percent:100
number of dice 7
outcomes: 279936, highest sum:42, lowest sum: 7, different sums:36
occurrences for 7: 1 percent: 0 total: 1 percent: 0
occurrences for 8: 7 percent: 0 total: 8 percent: 0
occurrences for 9: 28 percent: 0 total: 36 percent: 0
occurrences for 10: 84 percent: 0 total: 120 percent: 0
occurrences for 11: 210 percent: 0 total: 330 percent: 0
occurrences for 12: 462 percent: 0 total: 792 percent: 0
occurrences for 13: 917 percent: 0 total: 1709 percent: 0
occurrences for 14: 1667 percent: 0 total: 3376 percent: 1
occurrences for 15: 2807 percent: 1 total: 6183 percent: 2
occurrences for 16: 4417 percent: 1 total: 10600 percent: 3
occurrences for 17: 6538 percent: 2 total: 17138 percent: 6
occurrences for 18: 9142 percent: 3 total: 26280 percent: 9
occurrences for 19: 12117 percent: 4 total: 38397 percent: 13
occurrences for 20: 15267 percent: 5 total: 53664 percent: 19
occurrences for 21: 18327 percent: 6 total: 71991 percent: 25
occurrences for 22: 20993 percent: 7 total: 92984 percent: 33
occurrences for 23: 22967 percent: 8 total: 115951 percent: 41
occurrences for 24: 24017 percent: 8 total: 139968 percent: 50
occurrences for 25: 24017 percent: 8 total: 163985 percent: 58
occurrences for 26: 22967 percent: 8 total: 186952 percent: 66
occurrences for 27: 20993 percent: 7 total: 207945 percent: 74
occurrences for 28: 18327 percent: 6 total: 226272 percent: 80
occurrences for 29: 15267 percent: 5 total: 241539 percent: 86
occurrences for 30: 12117 percent: 4 total: 253656 percent: 90
occurrences for 31: 9142 percent: 3 total: 262798 percent: 93
occurrences for 32: 6538 percent: 2 total: 269336 percent: 96
occurrences for 33: 4417 percent: 1 total: 273753 percent: 97
occurrences for 34: 2807 percent: 1 total: 276560 percent: 98
occurrences for 35: 1667 percent: 0 total: 278227 percent: 99
occurrences for 36: 917 percent: 0 total: 279144 percent: 99
occurrences for 37: 462 percent: 0 total: 279606 percent: 99
occurrences for 38: 210 percent: 0 total: 279816 percent: 99
occurrences for 39: 84 percent: 0 total: 279900 percent: 99
occurrences for 40: 28 percent: 0 total: 279928 percent: 99
occurrences for 41: 7 percent: 0 total: 279935 percent: 99
occurrences for 42: 1 percent: 0 total: 279936 percent:100
number of dice 8
outcomes: 1679616, highest sum:48, lowest sum: 8, different sums:41
occurrences for 8: 1 percent: 0 total: 1 percent: 0
occurrences for 9: 8 percent: 0 total: 9 percent: 0
occurrences for 10: 36 percent: 0 total: 45 percent: 0
occurrences for 11: 120 percent: 0 total: 165 percent: 0
occurrences for 12: 330 percent: 0 total: 495 percent: 0
occurrences for 13: 792 percent: 0 total: 1287 percent: 0
occurrences for 14: 1708 percent: 0 total: 2995 percent: 0
occurrences for 15: 3368 percent: 0 total: 6363 percent: 0
occurrences for 16: 6147 percent: 0 total: 12510 percent: 0
occurrences for 17: 10480 percent: 0 total: 22990 percent: 1
occurrences for 18: 16808 percent: 1 total: 39798 percent: 2
occurrences for 19: 25488 percent: 1 total: 65286 percent: 3
occurrences for 20: 36688 percent: 2 total: 101974 percent: 6
occurrences for 21: 50288 percent: 2 total: 152262 percent: 9
occurrences for 22: 65808 percent: 3 total: 218070 percent: 12
occurrences for 23: 82384 percent: 4 total: 300454 percent: 17
occurrences for 24: 98813 percent: 5 total: 399267 percent: 23
occurrences for 25:113688 percent: 6 total: 512955 percent: 30
occurrences for 26:125588 percent: 7 total: 638543 percent: 38
occurrences for 27:133288 percent: 7 total: 771831 percent: 45
occurrences for 28:135954 percent: 8 total: 907785 percent: 54
occurrences for 29:133288 percent: 7 total:1041073 percent: 61
occurrences for 30:125588 percent: 7 total:1166661 percent: 69
occurrences for 31:113688 percent: 6 total:1280349 percent: 76
occurrences for 32: 98813 percent: 5 total:1379162 percent: 82
occurrences for 33: 82384 percent: 4 total:1461546 percent: 87
occurrences for 34: 65808 percent: 3 total:1527354 percent: 90
occurrences for 35: 50288 percent: 2 total:1577642 percent: 93
occurrences for 36: 36688 percent: 2 total:1614330 percent: 96
occurrences for 37: 25488 percent: 1 total:1639818 percent: 97
occurrences for 38: 16808 percent: 1 total:1656626 percent: 98
occurrences for 39: 10480 percent: 0 total:1667106 percent: 99
occurrences for 40: 6147 percent: 0 total:1673253 percent: 99
occurrences for 41: 3368 percent: 0 total:1676621 percent: 99
occurrences for 42: 1708 percent: 0 total:1678329 percent: 99
occurrences for 43: 792 percent: 0 total:1679121 percent: 99
occurrences for 44: 330 percent: 0 total:1679451 percent: 99
occurrences for 45: 120 percent: 0 total:1679571 percent: 99
occurrences for 46: 36 percent: 0 total:1679607 percent: 99
occurrences for 47: 8 percent: 0 total:1679615 percent: 99
occurrences for 48: 1 percent: 0 total:1679616 percent:100
total 1679616
calculations successfully complete
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