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Dice Rolling Odds

The type and number of dice rolled has a major impact on game play. Here are the odds for different combinations of dice.

Shortcuts:   2d4   2d6   2d8   2d10   2d12   2d20   3d6   3d8   3d10   4d6   Xd10   Xd10*

Two Dice

2d4
Roll Odds Chance % Chance # or less Roll Odds Chance % Chance # or less
215:11/16 6.3%6.3% 64.3:13/16 18.8%81.3%
37:12/16 12.5%18.8% 77:12/16 12.5%93.8%
44.3:13/16 18.8%37.5% 815:11/16 6.3%100%
53:14/16 25%62.5%

2d6
Roll Odds Chance % Chance # or less Roll Odds Chance % Chance # or less
235:11/36 2.8%2.8% 86.2:15/36 13.9%72.2%
317:12/36 5.6%8.4% 98:14/36 11.1%83.3%
411:13/36 8.3%16.7% 1011:13/36 8.3%91.6%
58:14/36 11.1%27.8% 1117:12/36 5.6%97.2%
66.2:15/36 13.9%41.7% 1235:11/36 2.8%100%
75:16/36 16.7%58.4%

2d8
Roll Odds Chance % Chance # or less Roll Odds Chance % Chance # or less
263:11/64 1.6%1.6% 108.1:17/64 10.9%67.1%
331:12/64 3.1%4.7% 119.7:16/64 9.4%76.6%
420.3:13/64 4.7%9.4% 1211.8:15/64 7.8%84.4%
515:14/64 6.7%15.6% 1315:14/64 6.7%90.6%
611.8:15/64 7.8%23.4% 1420.3:13/64 4.7%95.3%
79.7:16/64 9.4%32.8% 1531:12/64 3.1%98.4%
88.1:17/64 10.9%43.8% 1663:11/64 1.6%100%
97:18/64 12.5%56.2%

2d10
Roll Odds Chance % Chance # or less Roll Odds Chance % Chance # or less
299:11/100 1%1% 1210.1:19/100 9%64%
349:12/100 2%3% 1311.5:18/100 8%72%
432.3:13/100 3%6% 1413.3:17/100 7%79%
524:14/100 4%10% 1515.7:16/100 6%85%
619:15/100 5%15% 1619:15/100 5%90%
715.7:16/100 6%21% 1724:14/100 4%94%
813.3:17/100 7%28% 1832.3:13/100 3%97%
911.5:18/100 8%36% 1949:12/100 2%99%
1010.1:19/100 9%45% 2099:11/100 1%100%
119:110/100 10%55%

2d12
Roll Odds Chance % Chance # or less Roll Odds Chance % Chance # or less
2143:11/144 0.7%0.7% 1412.1:111/144 7.6%61.8%
371:12/144 1.4%2.1% 1513.4:110/144 6.9%68.8%
447:13/144 2.1%4.2% 1615:19/144 6.3%75%
535:14/144 2.8%6.9% 1717:18/144 5.6%80.6%
627.8:15/144 3.5%10.4% 1819.6:17/144 4.9%85.4%
723:16/144 4.2%14.6% 1923:16/144 4.2%89.6%
819.6:17/144 4.9%19.4% 2027.8:15/144 3.5%93.1%
917:18/144 5.6%25% 2135:14/144 2.8%95.8%
1015:19/144 6.3%31.2% 2247:13/144 2.1%97.9%
1113.4:110/144 6.9%38.2% 2371:12/144 1.4%99.3%
1212.1:111/144 7.6%45.8% 24143:11/144 0.7%100%
1311:112/144 8.3%54.2%

2d20
Roll Odds Chance % Chance # or less Roll Odds Chance % Chance # or less
2399:11/400 0.3%0.3% 2220.1:119/400 4.8%57.3%
3199:12/400 0.5%0.8% 2321.2:118/400 4.5%61.8%
4132.3:13/400 0.8%1.5% 2422.5:117/400 4.3%66%
599:14/400 1%2.5% 2524:116/400 4%70%
679:15/400 1.3%3.8% 2625.7:115/400 3.8%73.4%
765.7:16/400 1.5%5.3% 2727.6:114/400 3.5%77.3%
856.1:17/400 1.8%7% 2829.8:113/400 3.3%80.5%
949:18/400 2%9% 2932.3:112/400 3%83.5%
1043.4:19/400 2.3%11.3% 3035.4:111/400 2.8%86.3%
1139:110/400 2.5%13.8% 3139:110/400 2.5%88.8%
1235.4:111/400 2.8%16.5% 3243.4:19/400 2.3%91%
1332.3:112/400 3%19.5% 3349:18/400 2%93%
1429.8:113/400 3.3%22.8% 3456.1:17/400 1.8%94.8%
1527.6:114/400 3.5%26.3% 3565.7:16/400 1.5%96.3%
1625.7:115/400 3.8%30% 3679:15/400 1.3%97.5%
1724:116/400 4%34% 3799:14/400 1%98.5%
1822.5:117/400 4.3%38.3% 38132.3:13/400 0.8%99.3%
1921.2:118/400 4.5%42.8% 39199:12/400 0.5%99.8%
2020.1:119/400 4.8%47.5% 40399:11/400 0.3%100%
2119:120/400 5%52.5%


Three Dice

3d6
Roll Odds Chance % Chance # or less Roll Odds Chance % Chance # or less
3215:11/216 0.5%0.5% 117:127/216 12.5%62.5%
471:13/216 1.4%1.9% 127.6:125/216 11.6%74.1%
535:16/216 2.8%4.6% 139.3:121/216 9.7%83.8%
623:110/216 4.2%9.3% 1413.4:115/216 6.9%90.7%
711:115/216 8.3%16.2% 1520.6:110/216 4.6%95.4%
89.3:121/216 9.7%25.9% 1635:16/216 2.8%98.1%
98:125/216 11.1%37.5% 1771:13/216 1.4%99.5%
107:127/216 12.5%50% 18215:11/216 0.5%100%

3d8
Roll Odds Chance % Chance # or less Roll Odds Chance % Chance # or less
3511:11/512 0.2%0.2% 149.7:148/512 9.4%59.4%
4169.7:13/512 0.6%0.8% 1510.1:146/512 9%68.4%
584.3:16/512 1.2%1.6% 1611.2:142/512 8.2%76.6%
628.4:110/512 2.5%3.9% 1713.2:136/512 7%83.6%
733.1:115/512 3%6.8% 1817.3:128/512 5.5%89.1%
827.4:121/512 3.5%10.9% 1923.4:121/512 4.1%93.1%
917.3:128/512 5.5%16.4% 2027.4:115/512 3.5%96.1%
1013.2:136/512 7%23.4% 2150.2:110/512 2%98.1%
1110.4:142/512 8.8%31.6% 2284.3:16/512 1.2%99.2%
1210.1:146/512 9%40.6% 23169.7:13/512 0.6%99.8%
139.7:148/512 9.4%50% 24511:11/512 0.2%100%

3d10
Roll Odds Chance % Chance # or less Roll Odds Chance % Chance # or less
3999:11/1000 0.1%0.1% 1712.3:175/1000 7.5%57.5%
4332.3:13/1000 0.3%0.4% 1812.7:173/1000 7.3%64.8%
5165.7:16/1000 0.6%1% 1912.9:169/1000 7.2%71.7%
682.3:110/1000 1.2%2% 2014.9:163/1000 6.3%78%
754.6:115/1000 1.8%3.5% 2117.2:155/1000 5.5%83.5%
846.6:121/1000 2.1%5.6% 2221.2:145/1000 4.5%88%
934.7:128/1000 2.8%8.4% 2326.8:136/1000 3.6%91.6%
1026.8:136/1000 3.6%12% 2434.7:128/1000 2.8%94.4%
1122.8:145/1000 4.2%16.5% 2546.6:121/1000 2.1%96.5%
1217.2:155/1000 4.5%22% 2665.7:115/1000 1.5%98%
1314.9:163/1000 6.3%28.3% 2799:110/1000 1%99%
1413.5:169/1000 6.9%35.2% 28165.7:16/1000 0.6%99.6%
1512.2:173/1000 7.6%42.5% 29332.3:13/1000 0.3%99.9%
1612.3:175/1000 7.5%50% 30999:11/1000 0.1%100%


Four Dice

4d6
Roll Odds Chance % Chance # or less Roll Odds Chance % Chance # or less
41295:11/1296 0.1%0.1% 158.3:1140/1296 10.8%66.4%
5323:14/1296 0.3%0.4% 169.4:1125/1296 9.7%76.1%
6128.6:110/1296 0.8%1.2% 1711.5:1104/1296 8%84.1%
763.8:120/1296 1.5%2.7% 1815.2:180/1296 6.2%90.3%
836:135/1296 2.7%5.4% 1922.1:156/1296 4.3%94.6%
922.1:156/1296 4.3%9.7% 2036:135/1296 2.7%97.3%
1015.2:180/1296 6.2%15.9% 2163.8:120/1296 1.5%98.8%
1111.5:1104/1296 8%23.9% 22128.6:110/1296 0.8%99.6%
129.4:1125/1296 9.7%33.6% 23323:14/1296 0.3%99.9%
138.3:1140/1296 10.8%44.4% 241295:11/1296 0.1%100%
147.9:1146/1296 11.3%55.6%


Cumulative Dice

Xd10
# of Dice Chance of 1+ Successes at Difficulty
234 567 8910
1d 90%80%70% 60%50%40% 30%20%10%
2d 99%96%91% 84%75%64% 51%36%19%
3d 100%99%97% 94%87%78% 65%48%27%
4d 100%100%100% 98%94%87% 76%59%35%
5d 100%100%100% 99%97%92% 83%67%40%
6d 100%100%100% 100%98%95% 87%73%46%
7d 100%100%100% 100%99%97% 92%78%52%
8d 100%100%100% 100%100%99% 94%82%57%
9d 100%100%100% 100%100%100% 96%86%61%
10d 100%100%100% 100%100%100% 97%88%65%

Xd10*
# of Dice Chance of 1+ Successes at Difficulty
Where 1's Are "Botches" That Cancel Successes
234 567 8910
1d 90%80%70% 60%50%40% 30%20%10%
2d 81%80%77% 72%65%56% 45%32%17%
3d 97%92%87% 81%74%65% 54%40%22%
4d 95%94%91% 86%80%71% 60%45%26%
5d 99%97%94% 90%84%76% 65%49%28%
6d 98%98%96% 93%88%80% 69%53%30%
7d 100%99%97% 95%90%83% 72%55%32%
8d 99%99%98% 96%92%85% 75%58%33%
9d 100%99%99% 97%94%87% 77%60%35%