Especially because probabilities are non-linear.

The great thing about 'doing the math' is that it can completely change one's viewpoint (our intutition is often way off when it comes to stats). The trouble is that it totally disrupts threads (which understandably annoys those who believe math to be meddlesome trickery that sucks all joy out of the game).

I suggest that from now on, we have a "let's take this one outside" convention. If anyone wishes to challenge a statistical assertion, then they state that they wish to "take this one outside". The belligerants may then switch to this thread and attempt to math-hammer the other into submission; meanwhile the original thread can move on. The mathletes can subsequently return to the original thread with their conclusions (if anyone beyond them still cares by that point).

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It's a good suggestion. However, maths should have a place in any game with probabilities, so any conclusions from the maths thread should be respected, even if you're a mathophobe yourself.

Good luck with that

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It´s quite simple really:

3+ is great if you need a certain number of sure hits.

5+ has the same probability, but you can get two hits (you will never do that with 3+, so this option is stronger).

They are not the same, that is clear, but what about simplicity?. Why even think about 2x5+ having the choice of 3+??, Why not keeping 1 die per unit and therefore avoiding having to roll dozens of dice, making everything simpler and faster (I mean simplicity, not lack of tactics)??

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4+
avg hits = 1/2
chance of getting average hits or better = .5

2x4+
avg hits = 1
chance of getting average hits or better = .75

1+
avg hits = 1
chance of getting average hits or better = 1.

typically, chance of getting average hits or better > .5

?

Knowing and considering the variance of the probability of rolls can and does give a player an advantage as a table top general, I can vouch for that personally .

Having worked on quite a few lists in the last couple of years I'd say it is taken into account very early on in the process of list design, especially when concerning formation sizing, extra attacks, ranged attacks etc. .

In all honesty, I want to understand all this but my brain does not let me - It must be why I'm a crap-ish general

Before attemptimg more in-depth anaylsis, we should stop abusing the term 'variance'. Variance is a well defined parameter you can calculate for a distribution, it gives some useful information but it doesn't tell you things like range of possible values, skew, inter-quartiles, etc. E.g. you can have two distributions with equal variance and mean, but very different ranges.

When talking more generally about the spread of values I suggest using the term 'variability'*, which itself can be described using, for example, variance, range, inter-quartiles, etc...

*'swingy-ness' is also popular

@Dobbsy, never underestimate the General's gut instinct! Fire beats Ice (sort of) etc...

I do all the maths in my head when I play, but the sample sizes are so small in this game that anything can happen. It is particularly laughable when a list is mentioned as being fully playtested and it's had all of 12 or 20 games - and those games are random ones, not specific setups to test each situation a 100 or a 1000 times. Then again, that's the industry (ie GW) standard anyway.

Nothing in this topic is really detailed thinking and the patronising tone is very off-putting.

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Not quite, if you are on +4 for combat resolution then the only way to lose the assault is to roll double 1 whilst your opponent rolls a 6 on either of their two dice.
If you do roll a double 1 (which has a 2.777....% chance of occuring) only then does your opponent have a 30.555....% chance of winning by rolling one 6 on either of their two dice.
I believe this works out roughly at around 0.909 % chance of actually losing the assault from being on +4, although it does feel like it happens more than that .

A fair point... though I'm not sure that Ulrik would disagree with you -- the way I read him, he was trying to set up assaults that would probably result in a +4 differential (a sure thing, as you point out)... as insurance against bad hit rolls and good saving throws. The interesting thing about assaults is that the variation within the combat resolution can lead to fairly sharp swings in the final differential -- vis. a 10-4 assault can work out to 7-4, losing one of the presumed modifiers, you can lose your inspiring character, and you can fail to inflict any casualties -- and suddenly you're rolling at -1.

It was more in response to your statement that we were over thinking it or wasting our time.

Stuff like the difference in performance between 2x5+ and 3+ is important.

I don't like sending my troops into something unless I know how much they are likely to kill, and how badly they might fail.
With a formation of 10 units say, I'd actually expect the 2x5+ to be closer to the average then the 3+ (the opposite conclusion of Kyrt). Now I'm going to have to go away and check the probability distribution for them both. Binomials ahoy!

EDIT: and done.
bugger. kyrt was right.

It is interesting to note that the curves aren't symmetrical, but they are probably close enough for head maths during a game.

Yup. I was thinking situations where you "on average" should come out with +4 (ie your estimate before rolling attacks). If you need to be sure I think you need something more like an expected +8.

Like madd0ctor I had always assumed that more dice gave a more reliable result (because xd6 produces a tighter bell curve with higher x), so I was surprised to discover that it isn't so. For list the design I think that's a good thing actually, because a single 3+ "feels" like an elite, precision unit while 2x5+ "feels" like something more wild and chaotic - and it matches up with the maths.

Now we need to campaign for Khorne Berzerkers to be changed CC2+to CC6+, EA+4

That's true, but the point was about the chance of achieving your average number of hits in the first place not being particularly high.

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