Who said there is no such thing as luck?
Yesterday, I had my friend Claude over and told him about this discussion. I then asked if he would like to join me in a test, he said sure, it'd be fun.
This is the test we preformed. We each rolled 5 dice 20 times, we took note of how many 6's turned up. We then repeated this test 10 times to see what kind of averages we came up with.
code:
David / Claude
14 / 34
12 / 32
17 / 35
20 / 37
17 / 28
16 / 31
21 / 36
32 / 27 (wow I beat him! 
)
18 / 33
15 / 33
---------------
18.2 / 32.6
Now if those numbers don't show some degree of luck I don't know how else to explain the results.
Would someone here like to roll this test and see how their results compare? (It would be nice to see how an outside 'neutral' person did with this simple test.)
Oh, now you can understand why I hate playing RISK against him, he always wins. (his best battle win against me in RISK was when I attacked him with 37 armies and he only had 5. He won. (and still had 3 of his 5 armies left after the battle.)
Cheers! 