Rocket, berserk damage

[vdgg]

Source of inspiration: http://www.doom2.net/single/weaponfaq.html

vdgg said: (that's me, in the shotgun thread)
I love this page (DOOM Weapon Damage Information). A pity there are no more probabilities there which are relevant in casual play:
- odds of killing a cacodemon with 2 rockets
- odds of killing a baron with 5 rockets
- odds of killing an arch-vile with 3 rockets, 4 rockets

Too lazy to calculate it ATM, but I find killing a caco with 2 rockets less likely than a baron with 5 rockets, which is kinda strange.

myk said: (in the shotgun thread)
More hits means the results tend to get closer to average, thus barons usually get around 218 points of damage per rocket in total. With only two hits, the damage to cacos varies more, which means below-average damage is more common while above-average damage just causes the same effect as median damage. Likewise, it's easier to kill a hell knight with two rockets than a baron with four.

OK, here we go, rockets first, berserk will come later.

ODDS OF KILLING CERTAIN MONSTERS

DIRECT ROCKET HITS

DEMON / SPECTRE (150 HP)
1 rocket = 7/8 = 0.875  // I always thought the probability was much higher

REVENANT (300 HP)
2 rockets = 63/64 = 0.984375

CACODEMON / PAIN ELEMENTAL (400 HP)
2 rockets = 43/64 = 0.671875

ARACHNOTRON / HELL KNIGHT (500 HP)
2 rockets = 10/64 = 0.15625
3 rockets or fewer = 502/512 = 0.98 aprox.

MANCUBUS (600 HP)
3 rockets = 392/512 = 0.765626

ARCH-VILE (700 HP)
3 rockets = 162/512 = 0.32 aprox. (incredible!!)
4 rockets or fewer = 3970/4096 = 0.97 aprox. (also much higher than expected)

BARON (1000 HP)
4 rockets = 330/4096 = 0.08 aprox.
5 rockets or fewer = 27210/32768 = 0.83 aprox.

BERSERK

SERGEANT (30 HP)
1 punch = 9/10 = 0.9

IMP (60 HP)
1 punch = 8/10 = 0.8
2 punches or fewer = 99/100 = 0.99

CHAINGUNNER (70 HP)
1 punch = 7/10 = 0.7
2 punches or fewer = 97/100 = 0.97
3 punches or fewer = 999/1000 = 0.999

LOST SOUL (100 HP)
1 punch = 6/10 = 0.6
2 punches or fewer = 94/100 = 0.94
3 punches or fewer = 996/1000 = 0.996

DEMON / SPECTRE (150 HP)
1 punch = 3/10 = 0.3
2 punches or fewer = 79/100 = 0.79
3 punches or fewer = 965/1000 = 0.965
4 punches or fewer = 9965/10000 = 0.9965
5 punches or fewer = 99979/100000 = 0.99979

REVENANT (300 HP)
2 punches = 0.21
3 punches or fewer = 0.648
4 punches or fewer = 0.9003
5 punches or fewer = 0.97998
6 punches or fewer = 0.996997
7 punches or fewer = 0.99966 aprox.

CACODEMON / PAIN ELEMENTAL (400 HP)
2 punches = 0.01
3 punches or fewer = 0.283
4 punches or fewer = 0.6628
5 punches or fewer = 0.89002
6 punches or fewer = 0.973372
7 punches or fewer = 0.99499 aprox.
8 punches or fewer = 0.99924 aprox.

ARACHNOTRON / HELL KNIGHT (500 HP)
3 punches = 0.056
4 punches or fewer = 0.3372
5 punches or fewer = 0.67506
6 punches or fewer = 0.883422
7 punches or fewer = 0.96779 aprox.
8 punches or fewer = 0.99289 aprox.

MANCUBUS (600 HP)
3 punches = 0.001
4 punches or fewer = 0.0997
5 punches or fewer = 0.38125
6 punches or fewer = 0.686512
7 punches or fewer = 0.87912 aprox.
8 punches or fewer = 0.96312 aprox.

ARCH-VILE (700 HP)
4 punches = 0.0126
5 punches or fewer = 0.14244
6 punches or fewer = 0.417627
7 punches or fewer = 0.6971 aprox.
8 punches or fewer = 0.87643 aprox.

I assumed all the damage values are really random, i.e. they have the same probability.

[EvilNed]

Wow! Can't remember ever killing a Baron OR Arachnotron with two rockets! That's pretty amazing.

[vdgg]

EvilNed said:

Wow! Can't remember ever killing a Baron OR Arachnotron with two rockets! That's pretty amazing.

You mean, hell knight :-) In demos, the one I remember best, in MAP14 of Memento Mori there is one case (arachnotron): http://doomedsda.us/674col126.html

[EvilNed]

Yeah, Hell Knight sorry.

What's wildly ironic is that after I made my post, and ran through Aztec in Plutonia and managed to kill an arachnotron with two rockets...

[printz]

Did you calculate those odds assuming the pseudorandom numbering in Doom? Or just math? Because the randomness in Doom is actually a static cyclical sequence of 256 numbers from 0 to 255, in no particular order. Not any combination is liable to happen on multiple hits.

[Gez]

printz said:

Did you calculate those odds assuming the pseudorandom numbering in Doom? Or just math?

vdgg said:

I assumed all the damage values are really random, i.e. they have the same probability.

[Graf Zahl]

printz said:

Did you calculate those odds assuming the pseudorandom numbering in Doom? Or just math? Because the randomness in Doom is actually a static cyclical sequence of 256 numbers from 0 to 255, in no particular order. Not any combination is liable to happen on multiple hits.

Depends on the source port you use. Boom and all descendants use a real random number generator instead of Doom's table.

[Creaphis]

Do larger monsters suffer less splash damage from rockets that directly collide with them? I ask this because the larger radii of cacodemons than of barons could explain why it seems that rockets do less damage to cacos on average (ie. the center of the cacodemon is farther from the rocket when it explodes).

I'm going to guess that this isn't a factor, though, because I can't remember ever killing a hell knight with two rockets, though I've killed arachnotrons with two rockets a number of times. (Furthermore, this last apparent difference could be explained by the fact that I'm more likely to kill individual arachnotrons with rockets than I am to kill individual hell knights with rockets, which makes it unlikely that I'll ever clearly observe a hell knight dying in two hits.)

[Maes]

printz said:

the randomness in Doom is actually a static cyclical sequence of 256 numbers from 0 to 255, in no particular order

Actually, there is a particular order each time you use an attack, which makes certain outcomes more probable than others, especially in weapons that cause multiple uninterrupted calls to p_Random().

In the SSG thread, me and GreyGhost did a pretty detailed dissection of the shotgun firing code. The bottom line is that when you fire the shotgun, the very least 21 random values will be used in sequence (if you don't hit anything), up to a maximum of 80 in certain cases.

The super shotgun will probably use the entire table more than once, and only certain values can add to damage. And it gets even more of a nightmare if you consider conditional cases and mixed occurences e.g. one pellet hits nothing, others hit some monster, some hit the wall etc.

In general, the overall damage distributions are not affected no matter which method you choose, but some extreme cases like max or min damage probability may change dramatically with different analysis methods.

[TimeOfDeath]

Apparently killing an archvile with 3 ssg shots is impossible, but I could've sworn I've seen it happen a few times. But I guess the only times it happened were when you were right next to the archvile when he fired you and he got some splash damage from his attack??

[vdgg]

I added some berserk odds. You may think putting values such as 0.996997 is a sort of perversion, but no :-) I'll explain it below.

@Creaphis: I think the monster radius has nothing to do with the odds. In theory, not. In practice, I would have to make a test map and run it a few times. As for 2 rockets vs. hell knight I find it quite common; so common I can't recall an example in a demo, because I didn't find it noteworthy. A 4 rockets vs. baron you may find in z0diac's demo (http://www.doomworld.com/vb/doom-speed-demos/49909-deus-vult-demos/) which I haven't watched, to be honest.

Now, let's take a look at the extreme odds. Looks like the Doom engine is playing a game with us and with the statistics :-)

5 berserk punches against a demon: I know berserking demons is very common, but it occured to me quite a few times. According to pure probability, it is next to impossible.

7 berserk punches against a revenant: here's a demo: http://doomedsda.us/1231col258.html
City of Doom, MAP04 UV Max. Thing number: 121. Time: about 2:40. The RNG chose the following damage values: 20,20,20,40,120,40,200 (ha ha, too late). BTW, Doom Wiki says (http://doom.wikia.com/wiki/Fist), the max value is 6, what does it mean?

3 SSG shots vs. arch-vile. You'd have to deal at least 234 HP on average on each shot. This does not sound impossible to me. I haven't experienced it, but I have a strong preference to using rockets and plasma against the arch-viles...

[ArmouredBlood]

TimeOfDeath said:

Apparently killing an archvile with 3 ssg shots is impossible, but I could've sworn I've seen it happen a few times. But I guess the only times it happened were when you were right next to the archvile when he fired you and he got some splash damage from his attack??

I'm pretty sure I've had this at least once when playing through SoD for fdas - I'll see if I can find exactly where. I definitely noticed it was a lot more common to 3-rocket them (=maybe 1/10 ... there are a lot of arch-viles in SoD ;).

[TimeOfDeath]

I was going by what the doom wiki said was the minimum number of ssg shots to kill an archvile - 4. Before that, I always assumed it was 3 (but maybe I misunderstood the info on the wiki).