Ultimate Doom E3M9 No Damage Completion, with Live Commentary
90:00 Intro
0:30 Attempt #1
1:35 Attempt #2
4:40 The big reveal
8:45 Bolt For Gun
10:30 Taking down the mighty and the many
13:45 Outro, with alternative strategy
#Warrens#Reality#UltimateDoom
This video comprises two attempts, including one successful, at the challenge of scoring all monsters, items and secrets on Ultimate Doom's E3M9 'Warrens' without taking any damage, from a pistol start. There is also commentary, recorded live as I played. The outro includes investigation of an alternative strategy for the challenge.
This secret map's gimmick is that until you enter the fake exit, it almost exactly resembles the episode opener 'Hell Keep'. Ammo is tight, but infighting can help avoid tedious use of the pistol. As far as no damage play is concerned, things get interesting when the cyberdemon is revealed.
For my main strategy in the video, I pick up the invulnerability near the boss with that monster heavily damaged, so I can finish it off and remain protected by the powerup to pick up the radiation suit being guarded nearby by lost souls and poisonous blood.
The awkward position of the BFG in poison, in an area well hidden but not an official secret, makes that radiation suit crucial. Then the second invulnerability can be used on the many shotgun guys at the exit.
The alternative I demonstrate in the outro involves using tic counting to reach the lost souls and radiation suit, allowing us to totally rely on invulnerability to kill the cyberdemon safely.
Tic counting is the technique of using a consistent starting position and direction for a journey across poison, and making our timing reliably avoid the weapon-bobbing cycle, the multiples of 32/35ths of a second when poison would get us injured at the following tic.
There is yet ANOTHER strategy possible, which I don't recommend, of running away from the shotgun guys at the end and sniping them from the starting area when they follow you. This could free up another invulnerability.
When executing the main strategy, the cyberdemon did not die even after being hit by 51 rockets, so I used probability theory to calculate just how unlucky I was --- the results are shown on screen with the game footage. I promised more detail in the video description, so here it is:
The Central Limit Theorem states that summing the values of R identically distributed independent random variables X_i (from i = 1 to i = R) will converge to a Normal distribution as R becomes large.
See https://en.wikipedia.org/wiki/Central_limit_theorem
The key simplifying assumption to make this work, where R is the number of rockets and X_i is the damage done by one rocket (the i'th rocket), is that the damage values for the rockets are independent --- this is not quite true because of how the RNG works in Doom. However, making this assumption allows use of the Central Limit Theorem.
I will show an example of one of the values calculated for the video of the cyberdemon's 'Survival Probability', i.e. the likelihood that a fully fit cyberdemon hit by R rockets will have taken less than 4000 h.p. damage, it's total health.
For example if R = 40, the distribution for damage by one rocket is that it is equally likely to take the values 20,40,60,80,100,120,140, or 160, since cyberdemons are immune to splash damage. Therefore each X_i has mean = 90 and variance = 2100.
Using our independence assumption, the variance for the total damage of 40 rockets is 40 * 2100 = 84000
The mean total damage by 40 rockets is 40 * 90 = 3600.
Assuming that the total damage is Normally distributed (Central Limit Theorem) means we can work out how many standard deviations 4000 is above the mean value of 3600 and use a look-up table to get the final probability. Since standard deviation = square root of variance, the Z value we
require (for using a look-up table) is (4000 - 3600)/sqrt(84000) = 1.38
Using a look-up table, for example at:
https://en.wikipedia.org/wiki/Standard_normal_table
We see that Prob(Z less than 1.38) = 0.916, so the cyberdemon has a 91.6 per cent chance of surviving 40 rocket strikes.
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