Ah good, I
did enable tables in posts. That'll make this easier.
Now then: consider the question of 1d8+1 versus 2*(1d4)+1. The former has eight equally likely outcomes (2 to 9), each with 1/8 probability. The latter has four possible outcomes (3, 5, 7, 9), each with 1/4 probability. Let's make a chart....
1d8+1
2*(1d4)+1  2 3
3  4 5
5  6 7
7  8 9
9 
Each "box" here has a 1/4 probability. Now, if one die is in a higher box than the other, it wins, guaranteed. There's a 3/4 chance of that. But if both dice land in the same box, the d4 will win half the time and tie the other half. Thus it has a clear advantage. (Specifically, its probability of winning is 1/2, compared to 3/8 that the d8 will win and 1/8 that they'll tie.)
Now, Sa'ar's method  using expected values  is very straightforward and it'll always tell you which die has the better chance of winning. For instance, by comparing expected values, we can instantly find that 5d6+3 (expected value 20.5) will beat 2d201 (expected value 20) in the long run. The drawback is that expected values don't tell you exactly what those odds of winning
are. That's generally a tougher problem.
More on random fivers later.
Quote:
Wow, it really is that serious. :P

Assuming you mean serious
pain, yes, yes it is.
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FiveMinute.net: because stuff is long and life is short
[03:17]
FiveMinZeke: Galactica clearly needs the advanced technology of
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[03:17]
IJD: cylons can hack any blades working in conjunction