Math Hammer

Its a very long time since I did Statistics, choosing decision maths and mechanics as my modules at college.

Now, I'm fine with simple things, working out hits, wounds, saves ect, using the simple process of dividing by 6 and multiplying by 7-the dice roll needed.

So if you have one shot, and you need a 4 to hit, 1/6*(7-4) = 0.5
And if you have rerolls, original shots, - predicted hits, gives you predicted rerolls.

For Melta, I simply created a matrix and used a variety of ifs and lookups.

And now I have got to fleet.
Now, my matrix works for normal charges, one out of 36 results gets you a 12" charge, 3 in 36 get you an 11" charge, 6 in 36 give you a ten" charge and so on.
Now, with a flat reroll, thats workable.

But its not a flat reroll.
If you need an 8" charge, and roll a 6 and a 1, you would just reroll the one
Thats fairly simple, but I've seen people argue if you rolled a 5 and 2, if you rerolled the 2 for another 2, you could reroll the 5 hoping for a 6.
And that raises a lot more issues
Now, without mapping every possible combination, of which there are at least 1296, possibly a LOT more, I cant think of a way to make the numbers dance.

So, does anyone have any thoughts?
Has anyone brute forced the results?

The link bellow should be helpful.

Fleet and Charging in 6th Edition

However it doesn't take into account the situation you mentioned. I never actually though of re-rolling one dice, seeing the result and then potentially re-rolling the second dice. I'm not even sure you are allowed to do it.

If it's allowed. I'll knock out a quick brute force program to see what it would yield.

Very interesting, but, I'm not sure its quite, correct.

Rerolling 3 or less is a way to look at it, but from my understanding, your graph calculates rolling a four and a three, rerolling the three and gettng a one.
Correct in its way, but only applicable for trying to charge 8" or more.

Because we can now measure, we selectivly reroll a lot more than we would at first glance.

Brute forced this today, results to come

Ok, here goes.
I've worked these out using 72000 randomly generated numbers.
If the first two results didnt get a high enough charge result, I rerolled the lowest, and if that wasnt high enough, rerolled the second.
Anyway

A 12" charge without reroll has a 2.78% chance of success
With, 9.44%
11" without 8.33%
24.24% with
10" without 16.67%
41.83%
9", 27.78% / 59.74%

Yes, thats right, a 60% charge of a 9" charge!!!!!

8", 41.66 / 75.37
7", 72.22 / 87.37

We shouldnt rely on extreme range charges, but we have a credible chance of hitting 11", and a near evens of hitting 10"

Thanks for this, its nice to know the chances of success are that good even at such distances.