Hey guys, it looks like he is asking for the math to find various probabilities he isn’t asking about averaged dice or low luck dice. He just wants to be able to find the various probabilities of x number of hits with a mixed force.
Now i am no math wiz so all i can do is show some brute force calculations. But in the end i don’t know of a formula that you can plug in numbers and get the results i think the o.p. is looking for.
But here is some brute force calculations:
Take a 3 infantry attack as an example:
1st infantry rolls 1/6 hit and 5/6 miss
2nd infantry rolls and 1/6 hit and 5/6 miss, but your totals now are more complicated. 1/6 of the time your first roll will have hit and 1/6 of the time your second will have hit, 5/6 of the time your second will have missed. 5/6 of the time your first will have missed and 1/6 of the time your second will hit. So you get 2 hits 1/6 * 1/6 or 1/36 times, you get 1 hit 1/6 * 5/6 + 5/6 * 1/6 or 5/36 + 5/36 = 10/36 giving you totals of 2 hits 1/36 and 1 hit 10/36 and no hits 25/36 times.
3rd infantry rolls 1/6 hit and 5/6 miss now 1/36 times you will already have 2 hits so you get 3 hits now 1/36 * 1/6 = 1/216 you keep your 2 hits 1/36 * 5/6 or 5/216 times. 10/36 times you have 1 hit and 1/6 * 10/36 you get another for 2 hits 10/216 times, 5/6 * 10/36 is 50/216 times you stay at 1 hit. You have no hits 25/36 times so you get 1 hit 1/6 * 25/36 or 25/216 times and 5/6 * 25/216 is 125/216 for still no hits.
You end up
3 hits 1/216, 2 hits 15/216, 1 hit 75/216, and no hits 125/216
Now add a tank into the mix and we start having some real fun.
A tank being simply 1 out of 2 hits gives us 432 new possibilities:
3 hits 2/432 (same as 1/216), 2 hits 30/432 , 1 hit 150/432, No hits 250/432
On half of these the tank hits and half the tank misses
1/432 get 4 hits 1/432 stay at 3
15/432 get a 3rd hit 15/432 stay at 2
75/432 get a second hit and 75/432 stay at 1 hit
Lastly 125/432 get 1 hit and 125/432 still have not hit anything
Giving you 4 hits 1/432 3 hits 16/432 2 hits 90/432, 1 hit 200/432 and no hits 125/432
Now as I said earlier I do not know of any formula to replicate this type of math, but if one exists I am sure someone here will let you know.