Fuse Durations

When you light a fuse and toss an explosive in combat in Spirit of the Century, about how long do you have?

The official rules. To summarize, you roll 2dF (Fudge dice, capable of generating -1, 0, or +1) each action, sum them, then consult the following table. Two "Fizzle" results indicate a dud.

Dice result	Short Fuse	Medium Fuse	Long Fuse
+2	Explode	Explode	Explode
+1	Explode	Explode	No explosion
+0	Explode	No Explosion	No Explosion
-1	No Explosion	No Explosion	No Explosion
-2	Fizzle	Fizzle	Fizzle

(The above table is released under the Open Game License 1.0a.)

So here are your chances of an explosion or dud each round:

Short Fuses

Action	Approx. Chance of Explosion	Approx. Chance of Dud	Exact Chance of Explosion		Exact Chance of Dud
1	0.666667	0.000000	2/	3	0
2	0.222222	0.012346	2/	9	1/	81
3	0.065844	0.005487	16/	243	4/	729
4	0.018290	0.001829	40/	2,187	4/	2,187
5	0.004877	0.000542	32/	6,561	32/	59,049
6	0.001264	0.000151	224/	177,147	80/	531,441

Chance of the bomb being unresolved:

1 Fizzle:	0.000361	64/	177,147
No explosion:	0.000120	64/	531,441

Medium Fuses

Action	Approx. Chance of Explosion	Approx. Chance of Dud	Exact Chance of Explosion		Exact Chance of Dud
1	0.333333	0.000000	1/	3	0
2	0.222222	0.012346	2/	9	1/	81
3	0.144033	0.013717	35/	243	10/	729
4	0.091449	0.011431	200/	2,187	25/	2,187
5	0.057156	0.008468	125/	2,187	500/	59,049
6	0.035281	0.005880	6,250/	177,147	3,125/	531,441
7	0.021561	0.003920	34,375/	1,594,323	6,250/	1,594,323
8	0.013067	0.002541	62,500/	4,782,969	109,375/	43,046,721
9	0.007865	0.001613	1,015,625/	129,140,163	625,000/	387,420,489
10	0.004705	0.001008	5,468,750/	1,162,261,467	390,625/	387,420,489
11	0.002801	0.000622	9,765,625/	3,486,784,401	19,531,250/	31,381,059,609
12	0.001660	0.000380	156,250,000/	94,143,178,827	107,421,875/	282,429,536,481
13	0.000980	0.000231	830,078,125/	847,288,609,443	195,312,500/	847,288,609,443
14	0.000576	0.000139	488,281,250/	847,288,609,443	3,173,828,125/	22,876,792,454,961
15	0.000338	0.000083	23,193,359,375/	68,630,377,364,883	17,089,843,750/	205,891,132,094,649

Chance of the bomb being unresolved:

1 Fizzle:	0.000445	30,517,578,125/	68,630,377,364,883
No explosion:	0.000148	30,517,578,125/	205,891,132,094,649

Long Fuses

Action	Approx. Chance of Explosion	Approx. Chance of Dud	Exact Chance of Explosion		Exact Chance of Dud
1	0.111111	0.000000	1/	9	0
2	0.098765	0.012346	8/	81	1/	81
3	0.086420	0.019204	7/	81	14/	729
4	0.074684	0.022405	490/	6,561	49/	2,187
5	0.063896	0.023235	3,773/	59,049	1,372/	59,049
6	0.054215	0.022590	9,604/	177,147	12,005/	531,441
7	0.045681	0.021084	218,491/	4,782,969	33,614/	1,594,323
8	0.038263	0.019131	1,647,086/	43,046,721	823,543/	43,046,721
9	0.031886	0.017006	4,117,715/	129,140,163	6,588,344/	387,420,489
10	0.026453	0.014880	92,236,816/	3,486,784,401	5,764,801/	387,420,489
11	0.021861	0.012859	686,011,319/	31,381,059,609	403,536,070/	31,381,059,609
12	0.018003	0.011002	564,950,498/	31,381,059,609	3,107,227,739/	282,429,536,481
13	0.014780	0.009335	37,569,208,117/	2,541,865,828,329	7,909,306,972/	847,288,609,443
14	0.012101	0.007865	276,825,744,020/	22,876,792,454,961	179,936,733,613/	22,876,792,454,961
15	0.009882	0.006588	678,223,072,849/	68,630,377,364,883	1,356,446,145,698/	205,891,132,094,649
16	0.008052	0.005490	14,920,907,602,678/	1,853,020,188,851,841	3,391,115,364,245/	617,673,396,283,947
17	0.006548	0.004555	109,193,914,728,689/	16,677,181,699,666,569	75,960,984,159,088/	16,677,181,699,666,569
18	0.005314	0.003764	265,863,444,556,808/	50,031,545,098,999,707	564,959,819,683,217/	150,094,635,296,999,121
19	0.004305	0.003100	5,815,762,849,680,175/	1,350,851,717,672,992,089	465,261,027,974,414/	150,094,635,296,999,121
20	0.003482	0.002545	42,338,753,545,671,674/	12,157,665,459,056,928,801	30,939,858,360,298,531/	12,157,665,459,056,928,801
21	0.002813	0.002084	11,398,895,185,373,143/	4,052,555,153,018,976,267	227,977,903,707,462,860/	109,418,989,131,512,359,209
22	0.002269	0.001702	2,234,183,456,333,136,028/	984,770,902,183,611,232,881	558,545,864,083,284,007/	328,256,967,394,537,077,627
23	0.001828	0.001386	16,197,830,058,415,236,203/	8,862,938,119,652,501,095,929	12,288,009,009,832,248,154/	8,862,938,119,652,501,095,929
24	0.001470	0.001127	39,098,210,485,829,880,490/	26,588,814,358,957,503,287,787	89,925,884,117,408,725,127/	79,766,443,076,872,509,863,361
25	0.001182	0.000915	848,431,167,542,508,406,633/	717,897,987,691,852,588,770,249	218,949,978,720,647,330,744/	239,299,329,230,617,529,590,083
26	0.000949	0.000741	6,130,599,404,178,125,260,832/	6,461,081,889,226,673,298,932,241	4,789,530,784,514,160,360,025/	6,461,081,889,226,673,298,932,241
27	0.000761	0.000600	14,751,754,816,303,613,908,877/	19,383,245,667,680,019,896,796,723	34,867,784,111,263,087,420,982/	58,149,737,003,040,059,690,390,169
28	0.000610	0.000484	319,174,331,480,023,646,392,066/	523,347,633,027,360,537,213,511,521	9,387,480,337,647,754,305,649/	19,383,245,667,680,019,896,796,723
29	0.000488	0.000391	2,299,932,682,723,699,804,884,005/	4,710,128,697,246,244,834,921,603,689	1,839,946,146,178,959,843,907,204/	4,710,128,697,246,244,834,921,603,689
30	0.000391	0.000315	1,839,946,146,178,959,843,907,204/	4,710,128,697,246,244,834,921,603,689	13,339,609,559,797,458,868,327,229/	42,391,158,275,216,203,514,294,433,201

Chance of the bomb being unresolved:

1 Fizzle:	0.002279	32,199,057,558,131,797,268,376,070/	14,130,386,091,738,734,504,764,811,067
No explosion:	0.000532	22,539,340,290,692,258,087,863,249/	42,391,158,275,216,203,514,294,433,201