Lobby Gold Options (Starting Gold, Gold Multiplier) 💰 (#2915)

## Description:

We might want to add this to v29 to have a third possible public game
modifier from the beginning on 😄 Would be fun

- Add starting gold option (0 to 1_000_000_000 allowed, also applies to
nations)
- Add gold multiplier option (0.1 to 1000 allowed, also applies to
nations and bots)
- Add third public game modifier (3% chance of starting with 5M gold)
- Why 5M? It's enough gold to massively change the game start but not
enough to insta-hydro someone (launcher + hydro is 6M)

<img width="357" height="140" alt="image"
src="https://github.com/user-attachments/assets/72acc15c-e788-4e04-8590-ac72dd9657c7"
/>


## 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

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

FloPinguin

src/core/Schemas.ts

@@ -190,6 +190,7 @@ export const GameConfigSchema = z.object({
     .object({
       isCompact: z.boolean(),
       isRandomSpawn: z.boolean(),
+      startingGold: z.number().int().min(0).optional(),
     })
     .optional(),
   disableNations: z.boolean(),
@@ -204,6 +205,8 @@ export const GameConfigSchema = z.object({
   spawnImmunityDuration: z.number().int().min(0).optional(), // In ticks
   disabledUnits: z.enum(UnitType).array().optional(),
   playerTeams: TeamCountConfigSchema.optional(),
+  goldMultiplier: z.number().min(0.1).max(1000).optional(),
+  startingGold: z.number().int().min(0).max(1000000000).optional(),
 });
 
 export const TeamSchema = z.string();

src/core/configuration/Config.ts

@@ -76,6 +76,8 @@ export interface Config {
   numSpawnPhaseTurns(): number;
   userSettings(): UserSettings;
   playerTeams(): TeamCountConfig;
+  goldMultiplier(): number;
+  startingGold(playerInfo: PlayerInfo): Gold;
 
   startManpower(playerInfo: PlayerInfo): number;
   troopIncreaseRate(player: Player | PlayerView): number;

src/core/configuration/DefaultConfig.ts

@@ -245,6 +245,15 @@ export class DefaultConfig implements Config {
   donateTroops(): boolean {
     return this._gameConfig.donateTroops;
   }
+  goldMultiplier(): number {
+    return this._gameConfig.goldMultiplier ?? 1;
+  }
+  startingGold(playerInfo: PlayerInfo): Gold {
+    if (playerInfo.playerType === PlayerType.Bot) {
+      return 0n;
+    }
+    return BigInt(this._gameConfig.startingGold ?? 0);
+  }
 
   trainSpawnRate(numPlayerFactories: number): number {
     // hyperbolic decay, midpoint at 10 factories
@@ -252,15 +261,21 @@ export class DefaultConfig implements Config {
     return (numPlayerFactories + 10) * 18;
   }
   trainGold(rel: "self" | "team" | "ally" | "other"): Gold {
+    const multiplier = this.goldMultiplier();
+    let baseGold: bigint;
     switch (rel) {
       case "ally":
-        return 35_000n;
+        baseGold = 35_000n;
+        break;
       case "team":
       case "other":
-        return 25_000n;
+        baseGold = 25_000n;
+        break;
       case "self":
-        return 10_000n;
+        baseGold = 10_000n;
+        break;
     }
+    return BigInt(Math.floor(Number(baseGold) * multiplier));
   }
 
   trainStationMinRange(): number {
@@ -281,7 +296,8 @@ export class DefaultConfig implements Config {
     const numPortBonus = numPorts - 1;
     // Hyperbolic decay, midpoint at 5 ports, 3x bonus max.
     const bonus = 1 + 2 * (numPortBonus / (numPortBonus + 5));
-    return BigInt(Math.floor(baseGold * bonus));
+    const multiplier = this.goldMultiplier();
+    return BigInt(Math.floor(baseGold * bonus * multiplier));
   }
 
   // Probability of trade ship spawn = 1 / tradeShipSpawnRate
@@ -791,10 +807,14 @@ export class DefaultConfig implements Config {
   }
 
   goldAdditionRate(player: Player): Gold {
+    const multiplier = this.goldMultiplier();
+    let baseRate: bigint;
     if (player.type() === PlayerType.Bot) {
-      return 50n;
+      baseRate = 50n;
+    } else {
+      baseRate = 100n;
     }
-    return 100n;
+    return BigInt(Math.floor(Number(baseRate) * multiplier));
   }
 
   nukeMagnitudes(unitType: UnitType): NukeMagnitude {

src/core/game/Game.ts

@@ -211,6 +211,7 @@ export enum GameMapSize {
 export interface PublicGameModifiers {
   isCompact: boolean;
   isRandomSpawn: boolean;
+  startingGold?: number;
 }
 
 export interface UnitInfo {

src/core/game/PlayerImpl.ts

@@ -112,7 +112,7 @@ export class PlayerImpl implements Player {
   ) {
     this._name = playerInfo.name;
     this._troops = toInt(startTroops);
-    this._gold = 0n;
+    this._gold = mg.config().startingGold(playerInfo);
     this._displayName = this._name;
     this._pseudo_random = new PseudoRandom(simpleHash(this.playerInfo.id));
   }