Update tradeship spawn & gold meta (#3232)

## Description:

Now that pathfinding is much more efficient with hpa*, we can add more
trade ships.

This PR does the following:

1. No gold bonus for additional ports, keeps the meta simple
2. cut the gold per trade ship roughly in half.
3. Use a "pity bonus", the more times a port has failed to spawn a
tradeship, the higher the likelyhood it will spawn one
4. Increase the sigmoid so the mid-point is 200, with a half life of 50.
In tests about ~400 trade ships max.

It's pretty difficult to balance on singleplayer so I'm sure the values
will be adjusted after playtests.

## 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:

evan

src/core/configuration/DefaultConfig.ts

@@ -297,52 +297,29 @@ export class DefaultConfig implements Config {
     return 120;
   }
 
-  tradeShipGold(dist: number, numPorts: number): Gold {
+  tradeShipGold(dist: number): Gold {
     // Sigmoid: concave start, sharp S-curve middle, linear end - heavily punishes trades under range debuff.
     const debuff = this.tradeShipShortRangeDebuff();
     const baseGold =
-      100_000 / (1 + Math.exp(-0.03 * (dist - debuff))) + 100 * dist;
-    const numPortBonus = numPorts - 1;
-    // Hyperbolic decay, midpoint at 5 ports, 3x bonus max.
-    const bonus = 1 + 2 * (numPortBonus / (numPortBonus + 5));
+      50_000 / (1 + Math.exp(-0.03 * (dist - debuff))) + 50 * dist;
     const multiplier = this.goldMultiplier();
-    return BigInt(Math.floor(baseGold * bonus * multiplier));
+    return BigInt(Math.floor(baseGold * multiplier));
   }
 
   // Probability of trade ship spawn = 1 / tradeShipSpawnRate
   tradeShipSpawnRate(
+    tradeShipSpawnRejections: number,
     numTradeShips: number,
-    numPlayerPorts: number,
-    numPlayerTradeShips: number,
   ): number {
-    // Geometric mean of base spawn rate and port multiplier
-    const combined = Math.sqrt(
-      this.tradeShipBaseSpawn(numTradeShips, numPlayerTradeShips) *
-        this.tradeShipPortMultiplier(numPlayerPorts),
-    );
+    const decayRate = Math.LN2 / 50;
 
-    return Math.floor(25 / combined);
-  }
+    // Approaches 0 as numTradeShips increase
+    const baseSpawnRate = 1 - sigmoid(numTradeShips, decayRate, 200);
 
-  private tradeShipBaseSpawn(
-    numTradeShips: number,
-    numPlayerTradeShips: number,
-  ): number {
-    if (numPlayerTradeShips < 3) {
-      // If other players have many ports, then they can starve out smaller players.
-      // So this prevents smaller players from being completely starved out.
-      return 1;
-    }
-    const decayRate = Math.LN2 / 10;
-    return 1 - sigmoid(numTradeShips, decayRate, 55);
-  }
+    // Pity timer: increases spawn chance after consecutive rejections
+    const rejectionModifier = 1 / (tradeShipSpawnRejections + 1);
 
-  private tradeShipPortMultiplier(numPlayerPorts: number): number {
-    // Hyperbolic decay function with midpoint at 10 ports
-    // Expected trade ship spawn rate is proportional to numPlayerPorts * multiplier
-    // Gradual decay prevents scenario where more ports => fewer ships
-    const decayRate = 1 / 10;
-    return 1 / (1 + decayRate * numPlayerPorts);
+    return Math.floor((100 * rejectionModifier) / baseSpawnRate);
   }
 
   unitInfo(type: UnitType): UnitInfo {