Mathhammer: Gets Hot! Part 1

So as the resident math nerd, I figure I'd do a semi-regular article on the probability behind some of the things we see in 40k and WHFB.

This time I'm going to look at weapons that "Gets Hot!" So what I looked at was the chance of surviving firing one of these weapons. So for a "Gets Hot!" if you roll a 1 on the to hit roll, the weapon has overloaded and the firing model suffers a wound.

So in essence, we're looking at what is the probability of rolling a 1 on a d6, which is 1 out of 6, and then finding out the probability of passing the armor save.

What I've done is figured this out for the number of shots fired, and then the different armor saves possible. What I came up with is this:

		Armor Save
		2+	3+	4+	5+	6+
Shots Fired	1	97.2%	94.4%	91.7%	88.9%	86.1%
	2	94.5%	89.2%	84.0%	79.0%	74.2%
	3	91.9%	84.2%	77.0%	70.2%	63.9%
	4	89.3%	79.6%	70.6%	62.4%	55.0%
	5	86.9%	75.1%	64.7%	55.5%	47.3%
	6	84.4%	71.0%	59.3%	49.3%	40.8%
	7	82.1%	67.0%	54.4%	43.8%	35.1%
	8	79.8%	63.3%	49.9%	39.0%	30.2%
	9	77.6%	59.8%	45.7%	34.6%	26.0%
	10	75.4%	56.5%	41.9%	30.8%	22.4%
	11	73.4%	53.3%	38.4%	27.4%	19.3%
	12	71.3%	50.4%	35.2%	24.3%	16.6%
	13	69.3%	47.6%	32.3%	21.6%	14.3%
	14	67.4%	44.9%	29.6%	19.2%	12.3%

So there you go, a model with a 2+ armor save has about a 67% chance of shooting 14 shots without suffering a wound, and a model with a 6+ armor save has about an 86.1% of surviving shooting once.

Now this of course really only applies to models with one wound. If you have multiple wounds you obviously have a higher probability of surviving. I'll be looking at that in Part 2.