You're right of course, I shouldn't have used 50/50 that's very misleading especially on a thread where we're actually quoting real probabilities! What I was trying to say is the chance is not "1" (1+ to hit is not possible in Epic), and different rolls have different chances of achieving required hits even with the same average (as you have just demonstrated in a slightly different way). Perhaps we can now expand this to say: having more rolls increases the chances of hitting average, but lower rolls increases it by more? My brain is not capable right now of telling me whether that is true or not! Is it?

In any case, is this yet another reason why only considering averages is not so great?

Oh and I agree variability is a better word, unless you actually feel the need to calculate the variance of the distribution of course!

Ulrik/madd0ct0r: don't feel too bad, you're still right about multiple dice producing tighter bell curves, especially if you imagine them visually. The extents of the curve are wider, but the chances of reaching those extents is very small. Actually what got me started thinking about this was when "reducing the dice to reduce the variability" was first mentioned in the GS thread, and I thought: "Hang on, surely more dice smooths out the probabilities?" If you flip a coin 100 times, you are going to get pretty close to 50 heads if you think about it in terms of proportion. The chance of you getting all heads is nigh zero, whereas of course if you flip 1 coin the chance of you getting all heads is 50%.

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you could have corrected that statement to say 'the chance of scoring average hits (when there is a chance of variability) is 50/50'

in adam77's example, a 4+ chance of scoring average hits is 0.5

2x4+ the chance of scoring average hits (1 hit) is also 0.5

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True, but not much use for anything except 4+ rolls. 3x5+ for example: average is 1 hit but chance of getting 1 hit is only 96/216. No, I just said something stupid is all

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Normal distributions have this property (because unlike binomials they're continuous valued and always symmetrical). However, binomials will tend toward normal as the number of trials increases, so i think you would have close to 50/50 if you were rolling a huge bucket of dice.

I think this is an error. True, relatively speaking it trends toward 50/50. But the absolute difference matters. If you're throwing a hundred dice on 4+, you'd get somewhere between 45 and 55 hits, a very narrow distribution. But that's still a range of 10 hits, absolutely huge in game terms.

If you roll 2 dice at 4+, you have a 100% chance of getting average +/-1. If you're rolling 12, you have only a 60% chance of getting average +/-1. And for combat resolution, +/-1 is mostly the same value no matter if it's 2 +/-1 or 8 +/-1.

When comparing 2 different stats...
I guess it's always worth considering the distribution as a whole, however, i think it only really comes into play when the means are the same. [I'm not sure there are many situations where a stat with a worse mean is significantly better due to a lesser (or greater) spread. (the GS debate for example, a .17 difference in mean was enough to make the difference in variability irrelavant; comparing 2x4+ vs 2+).]

When evaluating chance of winning an assault...
As others have said, I agree variability is a key factor here. Not sure I agree completely with your conclusions, will have to think on it some more...

100 dice at 4+:
mean = 50
p(mean or better) = .54

1000 dice at 4+:
mean = 500
p(mean or better) = .51

I'm not sure where the error is?

100 dice, p = .54 means +/- 4

1000 dice p = .51 means +/-10

When you're adding up all the results and not just calculating the average, this matters.

.51 is chance of getting 500 or more hits (c.f. Kyrt's original statement that you have .50 chance of getting average or more hits)

.51 is not the expected % of hits, so what is +/-10 signifying?

still not sure what you mean

Yeah, I knew I was using the stats wrong. Although now that you explain it, I can't quite see your point either...?

My point is that as you increase the number of dice the bell curve sharpens, but the range of numbers for a given probability widens, which is important because we count margin of victory in absolute numbers and not odds. That is, a 20-18 victory is exactly the same as a 4-2 victory.

Hmm, I think I'm meandering a bit. This is important, but I can't quite explain why at this time of day.

Cool, my point was that Kyrt's statement is (almost) true for large number of dice (which is academic because we never get to 100's of dice in a single to hit roll). That's all

It seems you are getting at the trickier of issue of how numbers of dice affect assault outcomes.

Math has never been one of my strengths ... Of course I could read a map and call-in artillery, airstikes or even naval gunfire with the best of them ...

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Well, I played Future War Commander last evening so I've indeed rolled 100s of dice in a single go... what an annoying ruleset that is.

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I wonder if an electronic gizmo of some sort would remove the annoyance, or just remove the fun?

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I've tried using a computer to replace dice rolling to speed things up.

it really sucked the fun out.