Path of Chaos analysis

Amount	  ----d4----	  ----d6----	  ----d8----	 ----d10----
Needed	Normal	Chaos	Normal	Chaos	Normal	Chaos	Normal	Chaos
-----------------------------------------------------------------------------
1	100%	66.41%	100%	59.95%	100%	57.13%	100%	55.55%
2	75%	66.41%	83.33%	59.95%	87.5%	57.13%	90%	55.55%
3	50%	41.41%	66.67%	43.29%	75%	44.63%	80%	45.55%
4	25%	41.41%	50%	43.29%	62.5%	44.63%	70%	45.55%
5	25%	41.41%	33.33%	43.29%	50%	44.63%	60%	45.55%
6	18.75%	41.41%	16.67%	43.29%	37.5%	44.63%	50%	45.55%
7	12.5%	16.41%	16.67%	26.62%	25%	32.13%	40%	35.55%
8	6.25%	16.41%	13.89%	26.62%	12.5%	32.13%	30%	35.55%
9	6.25%	16.41%	11.11%	26.62%	12.5%	32.13%	20%	35.55%
10	4.69%	16.41%	8.33%	26.62%	10.94%	32.13%	10%	35.55%
11	3.13%	10.16%	5.56%	9.95%	9.38%	19.63%	10%	25.55%
12	1.56%	10.16%	2.78%	9.95%	7.81%	19.63%	9%	25.55%
13	1.56%	10.16%	2.78%	9.95%	6.25%	19.63%	8%	25.55%
14	1.17%	10.16%	2.31%	9.95%	4.69%	19.63%	7%	25.55%
15	0.78%	3.91%	1.85%	7.18%	3.13%	7.13%	6%	15.55%
16	0.39%	3.91%	1.39%	7.18%	1.56%	7.13%	5%	15.55%
17	0%	3.91%	0.93%	7.18%	1.56%	7.13%	4%	15.55%
18	0%	3.91%	0.46%	7.18%	1.37%	7.13%	3%	15.55%
19	0%	2.34%	0.46%	4.40%	1.17%	5.57%	2%	5.55%
20	0%	2.34%	0.39%	4.40%	0.98%	5.57%	1%	5.55%


Treating negative values as 0 (since we assume you're using these only when you're pretty sure you'd fail without it anyway):
>A d4 has an expected average value of 4.34 (3.32 normally)
>A d6 has an expected average value of 5.01 (4.20 normally)
>A d8 has an expected average value of 5.87 (5.14 normally)
>A d10 has an expected average value of 6.79 (6.11 normally)

http://anydice.com/program/3f05