I was musing around with an alternative that could get the desired result with a smaller number of cards. I noticed that you get pretty good results - not perfect -- with just 12 cards numbered 0-1-2-2-3-3-4-4-5-5-6-7. Take three cards at random and add them together.
Here's how that compares to 3d6:
Code:
Freq Pct 3d6%
3 12 0.9% 0.5%
4 18 1.4% 1.4%
5 42 3.2% 2.8%
6 66 5.0% 4.6%
7 96 7.3% 6.9%
8 120 9.1% 9.7%
9 150 11.4% 11.6%
10 156 11.8% 12.5%
11 156 11.8% 12.5%
12 150 11.4% 11.6%
13 120 9.1% 9.7%
14 96 7.3% 6.9%
15 66 5.0% 4.6%
16 42 3.2% 2.8%
17 18 1.4% 1.4%
18 12 0.9% 0.5%