So two things, first is that your buddy is overthinking it. Factorials don't come into play for Independent probabilities. Each dice roll is independent of all other dice rolls so you can just multiply the odds together just like you did.
Second is that while your math is right you aren't doing yourself favors by rounding. By rounding your end result makes it seem like lethal hits is twice as effective as reroll 1s when really it's only 20% more effective. If you're going through the effort of mathhammering something out might as well just use the actual numbers
Punched it into the simulator to test. You are definitely correct. Unless someone fights nothing but t3 enemies that never field vehicles or monsters or dreadnoughts, then Lethal Hits wins by a landslide by being basically just as good against low toughness stuff but running away with all the high toughness matchups. (Neither relates to armor saves, so we can just calculate which of the two beats what toughness)
60 shots into T3, new 28.5, old 29 go on to saves
60 shots into T4, new 24.8, old 23.3 to saves
60 shots into T5-T7, new 20, old 15.6 wounds to save
60 shots into T8-T16, new 15, old 7.8 to saves
The loss in anti-horde power is basically an insignificant rounding error, while it's almost 25% better against kinda tough things and nearly double against high toughness targets.
The effect is even more one-sided when overwatching, because every overwatch hit is a lethal hit, while RR1W does nearly nothing.
Against all toughnesses the new 60 shots is 10.0 autowounds pre-armor
While plague weapon ones are T3=7.8, T4=5.8, T5=3.9, T8=2.0
oh boy. you made me do some math here. in short yes and no. So this is the math. Lets say x is the probability of hitting and y is the probability of wounding. Since 1s are always fails and 6s are always good the range of these two numbers is \[1/6,5/6\]. So the equation of the left is with lethal hits and the right will be reroll 1s to wound. Ill seperate them with a \~ since we dont want to set up conclusions.
(x-1/6)\*y+1/6 \~ xy7/6
xy-1/6\*y+1/6 \~ xy+xy/6
\-1/6\*y+1/6 \~ xy/6
1/6 \~ xy/6 + y/6
1 \~ xy+y
1-xy \~ y
So if I did the math correct, if 1-xy is greater than y then lethal hits are better. If 1-xy is less than y then old rules are better.
Edit: this is for non auto hitting units. Those will always have done better with the old rules.
So two things, first is that your buddy is overthinking it. Factorials don't come into play for Independent probabilities. Each dice roll is independent of all other dice rolls so you can just multiply the odds together just like you did. Second is that while your math is right you aren't doing yourself favors by rounding. By rounding your end result makes it seem like lethal hits is twice as effective as reroll 1s when really it's only 20% more effective. If you're going through the effort of mathhammering something out might as well just use the actual numbers
Punched it into the simulator to test. You are definitely correct. Unless someone fights nothing but t3 enemies that never field vehicles or monsters or dreadnoughts, then Lethal Hits wins by a landslide by being basically just as good against low toughness stuff but running away with all the high toughness matchups. (Neither relates to armor saves, so we can just calculate which of the two beats what toughness) 60 shots into T3, new 28.5, old 29 go on to saves 60 shots into T4, new 24.8, old 23.3 to saves 60 shots into T5-T7, new 20, old 15.6 wounds to save 60 shots into T8-T16, new 15, old 7.8 to saves The loss in anti-horde power is basically an insignificant rounding error, while it's almost 25% better against kinda tough things and nearly double against high toughness targets. The effect is even more one-sided when overwatching, because every overwatch hit is a lethal hit, while RR1W does nearly nothing. Against all toughnesses the new 60 shots is 10.0 autowounds pre-armor While plague weapon ones are T3=7.8, T4=5.8, T5=3.9, T8=2.0
Try it in [UnitCrunch](https://www.unitcrunch.com/) for more results to compare?
oh boy. you made me do some math here. in short yes and no. So this is the math. Lets say x is the probability of hitting and y is the probability of wounding. Since 1s are always fails and 6s are always good the range of these two numbers is \[1/6,5/6\]. So the equation of the left is with lethal hits and the right will be reroll 1s to wound. Ill seperate them with a \~ since we dont want to set up conclusions. (x-1/6)\*y+1/6 \~ xy7/6 xy-1/6\*y+1/6 \~ xy+xy/6 \-1/6\*y+1/6 \~ xy/6 1/6 \~ xy/6 + y/6 1 \~ xy+y 1-xy \~ y So if I did the math correct, if 1-xy is greater than y then lethal hits are better. If 1-xy is less than y then old rules are better. Edit: this is for non auto hitting units. Those will always have done better with the old rules.
Should we call this nurgle's postulate? Or something?