LW - DandD.Sci Long War: Defender of Data-mocracy Evaluation and Ruleset by aphyer

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Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: D&D.Sci Long War: Defender of Data-mocracy Evaluation & Ruleset, published by aphyer on May 14, 2024 on LessWrong.
This is a follow-up to last week's D&D.Sci scenario: if you intend to play that, and haven't done so yet, you should do so now before spoiling yourself.
There is a web interactive here you can use to test your answer, and generation code available here if you're interested, or you can read on for the ruleset and scores.
RULESET
Each alien has a different amount of HP:
Alien
HP
Threat*
Swarming Scarab
1
1
Chitinous Crawler
3
2
Voracious Venompede
5
3
Arachnoid Abomination
9
4
Towering Tyrant
15
5
*Threat has no effect on combat directly - it's a measure of how threatening Earth considers each alien to be, which scales how many soldiers they send. (The war has been getting worse - early on, Earth sent on average ~1 soldier/4 Threat of aliens, but today it's more like 1 soldier/6 Threat. The wave you're facing has 41 Threat, Earth would send on average ~7 soldiers to it.
Earth doesn't exercise much selection with weapons, but sends soldiers in pairs such that each pair has two different weapons - this is a slight bias towards diversity.)
Each weapon has a damage it deals per shot, and a rate of fire that determines how many shots it can get off before the wielder is perforated by venomous spines/dissolved into a puddle of goo/voraciously devoured by a ravenous toothed maw:
Weapon
Damage
Min Shots
Max Shots
Macross Minigun
1
5
8
Fusion Flamethrower
1
3
12
Pulse Phaser
2
4
6
Rail Rifle
3
3
5
Laser Lance
5
2
5
Gluon Grenades
7
2
3
Thermo-Torpedos
13
1
3
Antimatter Artillery
20
1
2
Each soldier will be able to fire a number of shots chosen randomly between Min Shots and Max Shots - for example, a soldier with a Laser Lance will have time to fire 1d4+1 shots, each doing 5 damage.
During a battle, humans roll for how many shots each weapon gets, and then attempt to allocate damage from their shots to bring down all aliens. If they succeed, the humans win - if not, the humans lose. While doing this optimally is theoretically very difficult, your soldiers are well-trained and the battles are not all that large, so your soldiers will reliably find a solution if one exists.
For example, if you are fighting two Towering Tyrants and two Swarming Scarabs using two soldiers:
If you bring one soldier with Antimatter Artillery and one with a Macross Minigun, the Minigun soldier will reliably kill the Scarabs and have 3-6 shots left over (not enough to kill a Tyrant). The Artillery soldier will get either 1 or 2 shots: half the time they will roll a 2, kill both Tyrants and you will win, while the other half they will roll a 1, a Tyrant will survive and you will lose.
You can do a little better by bringing one soldier with Antimatter Artillery and one with a Laser Lance. The Laser Lance rolls 2-5 shots - it will always kill both Scarabs, and 1/4 of the time it will roll 5 shots and also be able to kill a Tyrant (at which point you'll win even if the Antimatter Artillery rolls a 1), giving you a 5/8 winrate overall.
You can do better still by bringing one soldier with Thermo-Torpedos and one with a Pulse Phaser. The Phaser soldier gets at least 4 shots, with which they kill both Scarabs and do 2 damage to each Tyrant (dropping the Tyrants both to 13 HP). And the Torpedo soldier gets 1-3 shots, with a 2/3 chance of being able to kill both Tyrants now that they've been softened up. I believe this is the best winrate you can get in this example.
STRATEGY
The most important element of strategy was sending the right kind of weapons for each alien: high-health aliens like Tyrants are extremely inefficient to kill with light weapons like Miniguns, while small, numerous aliens like Scarabs are extremely inefficient to kill with heavy weapons like artillery.
There were a few subtler ...