Quick question about calculations

[Hama2]

I’m trying to make an army list and to balance things out I’m trying to theory hammer them against other units in the game. However I’m not entirely sure if my calculation is correct (I never had chance calculation and is has been ages since I did any math whatsoever) so what I do is the following.

Say I got 21(3x7) ws 5 s 3 I5 elves with light armour, shield and hand weapon fighting against exactly the same unit. That’s 22 attacks(22:2) resulting in 11 hits resulting in 5.5(11/2) wounds resulting in 3.67(5.5/3x2) wounds after saves.
Or the same but with one unit having first strike.
22 attacks(22:2 + 11:2(re-roll)) resulting in 16.5 hits, 8.25 wounds and 5.5 wounds after saves

Is this calculation correct or am I doing it wrong ?

[John Rainbow]

So you have 22 attacks. Against a mirror unit you will hit on 4s and wound on 4s. Assuming you are strength 3 this will not modify armour so they have both a 5+ AS and a 6++ parry.

22*0.5 = 11 hits first of all
11*0.5 = 5.5 wounds
5.5*(2/3) = 3.67 that get through the armour save
3.67*(5/6) = 3.06 wounds that get through the parry save also.

With rerolls to hit you do 4.58 wounds after all the rest (16.5 hits is correct).

Your method was correct but you forgot about parry saves I think.

[Prince of Spires]

As far as I can tell, John Rainbow's answer is correct (though I didn't do the maths).

In general, when I have some sort of calculator nearby at least, I find it easiest to calculate this sort of thing on a 6 base (since a dice always has 6 options).

For to hit and to wound rolls, count the possible outcomes that give succes. 3+ has 3,4,5,6, so 4. 5+ has 5,6, so 2. If you want a formula, it's 6 - (to hit value) + 1. Now, if you have the number of possible succesfull rolls, divide this number by 6 and you have your chance of hitting / wounding, which you can then multiply by the number of attacks etc.

For armour / ward saves, you count the other way round, since succes here means no wound is done. So a 5+ armour save means 5,6 are failures (from a wounding perspective), and 1,2,3,4 means a kill. Formula wise it would be (armour save value) -1. Again, add up the number of possible kill rolls and divide by 6 for the chance of failing the armour save. Which you can then multiply be the number of wounds dealt.

The reason to always work with dividing by 6 is that you don't get confused over when to use 2/3's or 1/2 etc. Same way every time.

Your example: 4+ to hit, 4+ to wound, 5+ armour and 6+ ward
4+ to hit: succes is 4,5,6 => 3 options
4+ to wound: same as to hit
5+ armour: 1,2,3,4 give a wound => 4 options
6+ ward: 1,2,3,4,5 give a wound => 5 options

This gives:
21 X (3/6) X (3/6) X (4/6) X (5/6), which should give Johns answer.

If you have a reroll, you take the to hit value and the number of attacks missed and multiply them for the attacks that will hit on the reroll.

For something like 3+ to hit, 2+ to wound, no armour and 5+ ward it would end up like:
#of attacks X (4/6) X (5/6) X (4/6) (with no armour save factor in there...)

Rod

[Bashtrigger]

If the question is about the difference between a reroll to hit and a normal hit, how I calculate it is by taking the dice you would normally miss (11 dice) and just calculate how much hits you would gain on your normal hits by rolling those dice to hit again (+5.5)

Total hits will therefore be 11+5.5=16.5

Same trick can be done with rerolls to wound, as long as you just keep thinking in dice, the calculations become a lot easier

So imagine I would now have to roll to wound, I just assume it as a single roll again, starting with 16.5 dice, wounding on a 4+, so half the dice, meaning 16.5/2 = 8.25. Now your opponent gets a 5+ armour save, so just take it like it is a single roll again, starting with 8.25 dice, one third will miss, which comes down to 8.25/3 = 2.75. So the number of unsaved wounds will be 8.25-2.75 = 5.5
Then your opponents gets a parry save, meaning one in 6 of those wounds will be saved: 5.5/6= .916666666... so the number of total wounds will be 4.48 something

To avoid difficult calculations, what I normally do in case of half numbers is consider a dice to be either win or fail (I calculate 2 results, one being where every half gets rounded down after every single diceroll, en one where every half dice gets rounded up after every single diceroll and rougly take the average between the two results to be what I expect to throw)

Most of the time during a game your only interested in rough estimates anyway, if a combat simulation is not decisively in your favor, you shouldn't commit to that combat unless you can't avoid it. Sometimes if I want to make sure, I estimate combat by rounding down my results, then if I still come out ahead I know that IRL I'll probably win decisively