Have MIRV damage asymptote to 5% of total population (#1570)

## Description:

Decreasing MIRV warhead blast radius nerfed them too much, so have them
destroy 95% of population.

## Please complete the following:

- [x] I have added screenshots for all UI updates
- [x] I process any text displayed to the user through translateText()
and I've added it to the en.json file
- [x] I have added relevant tests to the test directory
- [x] I confirm I have thoroughly tested these changes and take full
responsibility for any bugs introduced
- [x] I have read and accepted the CLA aggreement (only required once).

## Please put your Discord username so you can be contacted if a bug or
regression is found:

evan

src/core/configuration/Config.ts

@@ -1,6 +1,5 @@
 import { Colord } from "colord";
 import { JWK } from "jose";
-import { GameConfig, GameID, TeamCountConfig } from "../Schemas";
 import {
   Difficulty,
   Game,
@@ -18,6 +17,8 @@ import {
 import { GameMap, TileRef } from "../game/GameMap";
 import { PlayerView } from "../game/GameView";
 import { UserSettings } from "../game/UserSettings";
+import { GameConfig, GameID, TeamCountConfig } from "../Schemas";
+import { NukeType } from "../StatsSchemas";
 
 export enum GameEnv {
   Dev,
@@ -157,7 +158,12 @@ export interface Config {
   defaultNukeSpeed(): number;
   defaultNukeTargetableRange(): number;
   defaultSamRange(): number;
-  nukeDeathFactor(humans: number, tilesOwned: number): number;
+  nukeDeathFactor(
+    nukeType: NukeType,
+    humans: number,
+    tilesOwned: number,
+    maxPop: number,
+  ): number;
   structureMinDist(): number;
   isReplay(): boolean;
   allianceExtensionPromptOffset(): number;

src/core/configuration/DefaultConfig.ts

@@ -23,6 +23,7 @@ import { TileRef } from "../game/GameMap";
 import { PlayerView } from "../game/GameView";
 import { UserSettings } from "../game/UserSettings";
 import { GameConfig, GameID, TeamCountConfig } from "../Schemas";
+import { NukeType } from "../StatsSchemas";
 import { assertNever, simpleHash, within } from "../Util";
 import { Config, GameEnv, NukeMagnitude, ServerConfig, Theme } from "./Config";
 import { PastelTheme } from "./PastelTheme";
@@ -822,8 +823,21 @@ export class DefaultConfig implements Config {
   }
 
   // Humans can be population, soldiers attacking, soldiers in boat etc.
-  nukeDeathFactor(humans: number, tilesOwned: number): number {
-    return (5 * humans) / Math.max(1, tilesOwned);
+  nukeDeathFactor(
+    nukeType: NukeType,
+    humans: number,
+    tilesOwned: number,
+    maxPop: number,
+  ): number {
+    if (nukeType !== UnitType.MIRVWarhead) {
+      return (5 * humans) / Math.max(1, tilesOwned);
+    }
+
+    const targetPop = 0.05 * maxPop;
+    const excessPop = Math.max(0, humans - targetPop);
+    const scalingFactor = 20000;
+
+    return (scalingFactor * excessPop * excessPop) / (maxPop * maxPop);
   }
 
   structureMinDist(): number {

src/core/execution/NukeExecution.ts

@@ -203,6 +203,10 @@ export class NukeExecution implements Execution {
     const toDestroy = this.tilesToDestroy();
     this.maybeBreakAlliances(toDestroy);
 
+    const maxPop = this.target().isPlayer()
+      ? this.mg.config().maxPopulation(this.target() as Player)
+      : 1;
+
     for (const tile of toDestroy) {
       const owner = this.mg.owner(tile);
       if (owner.isPlayer()) {
@@ -210,25 +214,45 @@ export class NukeExecution implements Execution {
         owner.removeTroops(
           this.mg
             .config()
-            .nukeDeathFactor(owner.troops(), owner.numTilesOwned()),
+            .nukeDeathFactor(
+              this.nukeType,
+              owner.troops(),
+              owner.numTilesOwned(),
+              maxPop,
+            ),
         );
         owner.removeWorkers(
           this.mg
             .config()
-            .nukeDeathFactor(owner.workers(), owner.numTilesOwned()),
+            .nukeDeathFactor(
+              this.nukeType,
+              owner.workers(),
+              owner.numTilesOwned(),
+              maxPop,
+            ),
         );
         owner.outgoingAttacks().forEach((attack) => {
           const deaths =
             this.mg
               ?.config()
-              .nukeDeathFactor(attack.troops(), owner.numTilesOwned()) ?? 0;
+              .nukeDeathFactor(
+                this.nukeType,
+                attack.troops(),
+                owner.numTilesOwned(),
+                maxPop,
+              ) ?? 0;
           attack.setTroops(attack.troops() - deaths);
         });
         owner.units(UnitType.TransportShip).forEach((attack) => {
           const deaths =
             this.mg
               ?.config()
-              .nukeDeathFactor(attack.troops(), owner.numTilesOwned()) ?? 0;
+              .nukeDeathFactor(
+                this.nukeType,
+                attack.troops(),
+                owner.numTilesOwned(),
+                maxPop,
+              ) ?? 0;
           attack.setTroops(attack.troops() - deaths);
         });
       }