Rebalance Doomsday Clock: late-game stalemate-breaker (10min grace + wave squeeze), slower troop drain, gentler-but-steeper warship attrition (#4518)

Resolves #<add your approved & assigned issue number>

## Description:

Rebalances the Doomsday Clock so it acts as a **late-game
stalemate-breaker** rather than an early-game culler, softens how fast
it removes troops and warships, and makes the HUD countdown clearer.

**Clock schedule (all presets):**
- A flat **10-minute grace** at 0% required share — the early game is
decided by combat, not the clock.
- Then a 6-wave squeeze at accelerating levels (4 / 9 / 16 / 26 / 40 /
55%) with short pauses, reaching the final 55% at each preset's cap:
**45 / 35 / 25 / 15 min** for slow / normal / fast / veryfast.
- `WaveSchedule` `rampSeconds`/`pauseSeconds` are now **per-wave
arrays**, so the curve can be shaped (gentle early, steeper late)
instead of one uniform ramp. `requiredBasisPoints` and the HUD companion
`doomsdayClockWaveState` walk the per-wave segments in lockstep.

**Troop drain:** warn window `10s → 30s`, drain eased (`2%→5%` over
`90s`), so a caught side takes ~2 minutes to wipe instead of ~1.

**Warship attrition:** warships get their own gentler start plus a
**convex** decay curve — a ship caught when its side is first doomed
lasts about as long as troops, but the rate ramps up steeply so a side
at full attrition still loses its fleet in ~2s. Adds a `curveExponent`
argument to `doomsdayClockDrain` (1 = linear, used for troops; higher =
convex, used for ships).

**Determinism:** the drain curve is **integer-only** (fixed-point power,
no floats), so the floored per-tick loss is bit-identical on every
client in the lockstep sim. The linear troop path keeps its exact
existing integer form; only the convex warship path is reshaped.

**HUD countdown clarity:** the clock readout now shows a live countdown
in both states — `Will reach 16% in M:SS` while the bar is actively
climbing, and `Starts rising to 26% in M:SS` during a pause (previously
`Next 26% in …`, which read as if it jumped there instantly). Backed by
a new `secondsToTarget` field on the shared wave state so the sim and
HUD stay in agreement. All display text goes through `translateText()` /
`en.json`.
<img width="278" height="116" alt="image"
src="https://github.com/user-attachments/assets/e0be3d2c-bb88-46be-b344-34d63e4859bd"
/>
<img width="304" height="171" alt="image"
src="https://github.com/user-attachments/assets/da74bd05-0b9a-4aec-bbf5-e7380fbda88e"
/>

**Danger skull:** while a side is below the bar in the warn window, its
on-map skull now blinks progressively faster as the countdown runs out
(accelerating to the moment the drain begins), then holds steady once it
is actually draining — a clearer "you are about to be hit" cue.

Rationale: the previous schedule removed players heavily in the first
half of a match and could leave a drawn-out endgame. Holding the clock
at 0% early keeps the opening about fighting, and concentrating its
pressure in the back half reserves it for actually breaking stalemates.
Values are tuning starting points and easy to adjust in
`DoomsdayClock.ts` / the config defaults.

## 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

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

<add your Discord username>

src/client/components/DoomsdayClockPanel.ts

@@ -124,6 +124,7 @@ export class DoomsdayClockPanel extends LitElement {
       : wave.growing
         ? translateText("doomsday_clock.growing", {
             pct: scalePct(wave.targetPercent),
+            time: this.secondsToHms(wave.secondsToTarget),
           })
         : translateText("doomsday_clock.next_wave", {
             pct: scalePct(wave.targetPercent),

src/client/render/frame/derive/PlayerStatus.ts

@@ -107,10 +107,20 @@ export function computePlayerStatus(
     const inDoomsdayClock = ps.inDoomsdayClock;
     // Past the warn grace the side is actively bleeding troops; the skull holds
     // steady then (vs blinking while merely in danger).
+    const doomsdayClockUnderTicks =
+      (opts.tick ?? 0) - ps.markedDoomsdayClockTick;
+    const doomsdayClockWarnTicks = opts.doomsdayClockWarnTicks ?? 0;
     const doomsdayClockDraining =
-      inDoomsdayClock &&
-      (opts.tick ?? 0) - ps.markedDoomsdayClockTick >=
-        (opts.doomsdayClockWarnTicks ?? 0);
+      inDoomsdayClock && doomsdayClockUnderTicks >= doomsdayClockWarnTicks;
+    // How far through the warn countdown (0->1); the danger skull blinks faster
+    // as this nears 1, i.e. as the side approaches draining.
+    const doomsdayClockWarnProgress =
+      inDoomsdayClock && doomsdayClockWarnTicks > 0
+        ? Math.max(
+            0,
+            Math.min(1, doomsdayClockUnderTicks / doomsdayClockWarnTicks),
+          )
+        : 0;
     const traitorRemainingTicks = ps.traitorRemainingTicks;
 
     // Relative flags
@@ -179,6 +189,7 @@ export function computePlayerStatus(
         disconnected,
         inDoomsdayClock,
         doomsdayClockDraining,
+        doomsdayClockWarnProgress,
         alliance,
         allianceReq,
         target,

src/client/render/gl/passes/name-pass/Types.ts

@@ -77,6 +77,7 @@ export interface PlayerSlot {
   nukeTargetsMe: boolean;
   inDoomsdayClock: boolean;
   doomsdayClockDraining: boolean;
+  doomsdayClockWarnProgress: number;
   traitorRemainingTicks: number;
   allianceFraction: number;
   allianceRemainingTicks: number;

src/client/render/gl/passes/name-pass/index.ts

@@ -327,6 +327,7 @@ export class NamePass {
             nukeTargetsMe: false,
             inDoomsdayClock: false,
             doomsdayClockDraining: false,
+            doomsdayClockWarnProgress: 0,
             traitorRemainingTicks: 0,
             allianceFraction: 0,
             allianceRemainingTicks: 0,
@@ -459,6 +460,7 @@ export class NamePass {
       const disconnected = sd?.disconnected ?? false;
       const inDoomsdayClock = sd?.inDoomsdayClock ?? false;
       const doomsdayClockDraining = sd?.doomsdayClockDraining ?? false;
+      const doomsdayClockWarnProgress = sd?.doomsdayClockWarnProgress ?? 0;
       const alliance = sd?.alliance ?? false;
       const allianceReq = sd?.allianceReq ?? false;
       const target = sd?.target ?? false;
@@ -475,6 +477,7 @@ export class NamePass {
         disconnected !== slot.disconnected ||
         inDoomsdayClock !== slot.inDoomsdayClock ||
         doomsdayClockDraining !== slot.doomsdayClockDraining ||
+        doomsdayClockWarnProgress !== slot.doomsdayClockWarnProgress ||
         alliance !== slot.alliance ||
         allianceReq !== slot.allianceReq ||
         target !== slot.target ||
@@ -490,6 +493,7 @@ export class NamePass {
         slot.disconnected = disconnected;
         slot.inDoomsdayClock = inDoomsdayClock;
         slot.doomsdayClockDraining = doomsdayClockDraining;
+        slot.doomsdayClockWarnProgress = doomsdayClockWarnProgress;
         slot.alliance = alliance;
         slot.allianceReq = allianceReq;
         slot.target = target;
@@ -576,14 +580,17 @@ export class NamePass {
     d[off + 15] = slot.nameHalfWidth;
 
     // Column 4: flagLayerIdx, emojiAtlasIdx, smallID, doomsdayClock state
-    // (0 none, 1 danger -> blinking skull, 2 draining -> steady skull).
+    // (0 none, 1.0-1.49 danger -> blinking skull, 2 draining -> steady skull).
+    // The warn-countdown progress (0->1) is packed into the danger value's
+    // fraction so the shader can blink faster as drain nears; it stays < 1.5 so
+    // the draining threshold is untouched.
     d[off + 16] = slot.flagLayerIdx;
     d[off + 17] = slot.emojiAtlasIdx;
     d[off + 18] = slot.static.smallID;
     d[off + 19] = slot.doomsdayClockDraining
       ? 2.0
       : slot.inDoomsdayClock
-        ? 1.0
+        ? 1.0 + slot.doomsdayClockWarnProgress * 0.49
         : 0.0;
 
     // Column 5: crown, traitor, disconnected, alliance

src/client/render/gl/shaders/name/status-icon.vert.glsl

@@ -268,12 +268,19 @@ void main() {
     }
   }
 
-  // Doomsday Clock skull: slot 8. Blinks ~2 Hz while in danger (flag 1.0); holds
-  // steady once the side is draining (flag 2.0).
+  // Doomsday Clock skull: slot 8. While in danger (flag 1.0-1.49) the skull
+  // blinks and speeds up as the warn countdown runs out — the progress 0->1 is
+  // packed into the flag's fraction. Base ~2 Hz plus a p^2 phase term so it
+  // accelerates toward the drain (same trick as the alliance-renewal flash
+  // above, which keeps the phase continuous). Holds steady once draining (>=1.5).
   if (iconSlot == 8) {
-    vFlashAlpha = (statusFlag[8] < 1.5)
-      ? 0.35 + 0.65 * (0.5 + 0.5 * cos(uTime * 2.0 * 6.2832))
-      : 1.0;
+    if (statusFlag[8] < 1.5) {
+      float p = clamp((statusFlag[8] - 1.0) / 0.49, 0.0, 1.0);
+      float phase = uTime * 2.0 + p * p * 40.0;
+      vFlashAlpha = 0.35 + 0.65 * (0.5 + 0.5 * cos(phase * 6.2832));
+    } else {
+      vFlashAlpha = 1.0;
+    }
   }
 
   vDiscard = 0;

src/client/render/types/Renderer.ts

@@ -193,6 +193,7 @@ export interface PlayerStatusData {
   nukeTargetsMe: boolean;
   inDoomsdayClock: boolean;
   doomsdayClockDraining: boolean;
+  doomsdayClockWarnProgress: number;
   traitorRemainingTicks: number;
   allianceFraction: number;
   allianceRemainingTicks: number;

src/core/configuration/Config.ts

@@ -85,19 +85,23 @@ export const SAM_CONSTRUCTION_TICKS = 30 * 10;
 // Times in seconds. The required map share rises in waves (levels + times in
 // DoomsdayClock.ts, chosen by `speed`). A side caught below the bar gets a
 // warnSeconds cooldown ("Danger, decay in Xs"), then troops bleed to zero: the
-// warn (10s) + the linear drain (~55s from full troops, sooner with fewer troops
-// or a shrinking territory) make ~1 minute from caught to wiped out.
+// warn (30s) + the linear drain (~90s from full troops, sooner with fewer troops
+// or a shrinking territory) make ~2 minutes from caught to wiped out.
 const DOOMSDAY_CLOCK_DEFAULTS = {
   enabled: false,
   speed: "normal" as DoomsdayClockSpeed,
-  warnSeconds: 10, // cooldown before decay after the bar catches you
+  warnSeconds: 30, // cooldown (the flashing danger cue) before decay begins
   drainStartPercent: 2, // starts bleeding at once (already beats troop income)
-  drainMaxPercent: 6,
-  drainRampSeconds: 50, // ramps LINEARLY to the max over this long
-  // Warships bleed on the same start + ramp but to a much higher ceiling than
-  // troops, so a fleet at full attrition sinks in ~2s (50% of a ship's max
-  // health per second) instead of riding out the gentle troop rate. Ships only.
+  drainMaxPercent: 5,
+  drainRampSeconds: 90, // ramps LINEARLY to the max over this long (~1:30 to zero)
+  // Warships bleed on their OWN gentler start + a STEEP (convex) ramp to a much
+  // higher ceiling. A ship caught when its side is first doomed lasts about as
+  // long as troops (the low start + no income ≈ the troop net rate), but the rate
+  // curves up sharply (warshipDrainCurveExponent), so once a side has been under
+  // the clock the full ramp, ships sink in ~2s (50%/s). Ships only.
+  warshipDrainStartPercent: 1,
   warshipDrainMaxPercent: 50,
+  warshipDrainCurveExponent: 8, // >1 = convex: stays gentle early, then spikes
 };
 
 export class Config {
@@ -134,7 +138,9 @@ export class Config {
       drainStartPercent: d.drainStartPercent,
       drainMaxPercent: d.drainMaxPercent,
       drainRampSeconds: d.drainRampSeconds,
+      warshipDrainStartPercent: d.warshipDrainStartPercent,
       warshipDrainMaxPercent: d.warshipDrainMaxPercent,
+      warshipDrainCurveExponent: d.warshipDrainCurveExponent,
     };
   }
   spawnImmunityDuration(): Tick {

src/core/execution/DoomsdayClockExecution.ts

@@ -44,11 +44,13 @@ export class DoomsdayClockExecution implements Execution {
     const mg = this.mg;
     const cfg = mg.config().doomsdayClockConfig();
     if (!cfg.enabled) return;
-    // Warships bleed on the same start + ramp as troops but toward a much higher
-    // ceiling (warshipDrainMaxPercent), so a fleet at full attrition sinks in
-    // ~2s. Only the max differs from the troop drain.
+    // Warships bleed on their OWN gentler start + higher ceiling, and (via the
+    // curve exponent passed to the drain below) a STEEP convex ramp: a ship
+    // caught when its side is first doomed lasts ~as long as troops, but a side
+    // that has been under the clock the full ramp loses ships in ~2s.
     const warshipDrainCfg = {
       ...cfg,
+      drainStartPercent: cfg.warshipDrainStartPercent,
       drainMaxPercent: cfg.warshipDrainMaxPercent,
     };
 
@@ -122,6 +124,7 @@ export class DoomsdayClockExecution implements Execution {
                   ws.maxHealth(),
                   secondsPastWarn,
                   warshipDrainCfg,
+                  cfg.warshipDrainCurveExponent,
                 ),
               );
             }

src/core/game/DoomsdayClock.ts

@@ -22,53 +22,57 @@ export const DOOMSDAY_CLOCK_SPEEDS: DoomsdayClockSpeed[] = [
 ];
 
 interface WaveSchedule {
-  /** Flat 0% for this long at the very start (the one grace period). */
+  /** Flat 0% for this long at the very start: a COMBAT-ONLY window — the clock
+   *  does not touch real players early; eliminations there come from fighting. */
   graceSeconds: number;
-  /** Each wave grows its share up linearly over this long. */
-  rampSeconds: number;
-  /** Flat hold after each ramp before the next one starts. */
-  pauseSeconds: number;
+  /** Per-wave: wave i grows its share up linearly over rampSeconds[i]. */
+  rampSeconds: number[];
+  /** Per-wave: flat hold after wave i's ramp before the next one starts. */
+  pauseSeconds: number[];
   /** Share (basis points, 100 = 1%) reached at the end of each ramp, ascending. */
   levels: number[];
 }
 
-// Grace once, then a repeating cycle of [ramp up over rampSeconds] + [hold for
-// pauseSeconds]. The share rises linearly during each ramp and is flat during
-// the grace and every pause. Easy to tune: change grace, ramp, pause, or levels.
-// Same levels everywhere (the ofstats FFA territory median, then a final 55%
-// squeeze); the presets only change the pace. The median run is 3/5/10/20/30%;
-// normal hits it dead on at 10/15/20/25/30 min. The 6th wave (55%) only one side
-// can hold, so, together with the crown exemption, it forces out everyone but
-// the leader for a single winner. slow is ~20% slower, fast ~30% faster, very
-// fast 50% faster.
-const LEVELS = [300, 500, 1000, 2000, 3000, 5500]; // 3, 5, 10, 20, 30, 55%
+// Grace once (a long COMBAT-ONLY window — 0% bar, the clock ignores everyone),
+// then per wave a [ramp up over rampSeconds[i]] + [hold for pauseSeconds[i]]. The
+// share rises linearly during each ramp and is flat during the grace and pauses.
+//
+// Design: the clock is a STALEMATE-BREAKER, not an early-game culler. It stays at
+// 0% for the first 10 minutes (combat decides the early game), then a 6-wave
+// squeeze climbs to 55% by the preset's cap. Levels accelerate (4/9/16/26/40/55%)
+// so the endgame tightens; the 6th wave (55%) only one side can hold, so — with
+// the crown exemption — it forces out everyone but the leader for a single winner.
+// Grace is a flat 10:00 on every preset; presets differ only in how long the
+// squeeze takes: 55% at 45/35/25/15 min for slow/normal/fast/veryfast.
+const LEVELS = [400, 900, 1600, 2600, 4000, 5500]; // 4, 9, 16, 26, 40, 55%
 const SCHEDULES: Record<DoomsdayClockSpeed, WaveSchedule> = {
-  // grace 5:30, 4:30 ramps + 30s pauses -> 3/5/10/20/30/55% at 10/15/20/25/30/35 min.
+  // grace 10:00, then six ~208s ramps + 50s pauses -> 55% at 35:00.
   normal: {
-    graceSeconds: 330,
-    rampSeconds: 270,
-    pauseSeconds: 30,
+    graceSeconds: 600,
+    rampSeconds: [208, 208, 208, 208, 208, 210],
+    pauseSeconds: [50, 50, 50, 50, 50, 0],
     levels: LEVELS,
   },
-  // grace 6:30, 5:30 ramps -> reaches at 12/18/24/30/36/42 min.
+  // grace 10:00, then six ~292s ramps + 70s pauses -> 55% at 45:00.
   slow: {
-    graceSeconds: 390,
-    rampSeconds: 330,
-    pauseSeconds: 30,
+    graceSeconds: 600,
+    rampSeconds: [292, 292, 292, 292, 292, 290],
+    pauseSeconds: [70, 70, 70, 70, 70, 0],
     levels: LEVELS,
   },
-  // grace 4:30, 2:50 ramps -> reaches at 7:20/10:40/14/17:20/20:40/24 min.
+  // grace 10:00, then six 125s ramps + 30s pauses -> 4/9/16/26/40/55% at
+  // 12:05/14:40/17:15/19:50/22:25/25:00.
   fast: {
-    graceSeconds: 270,
-    rampSeconds: 170,
-    pauseSeconds: 30,
+    graceSeconds: 600,
+    rampSeconds: [125, 125, 125, 125, 125, 125],
+    pauseSeconds: [30, 30, 30, 30, 30, 0],
     levels: LEVELS,
   },
-  // grace 3:00, 2:00 ramps -> reaches at 5/7:30/10/12:30/15/17:30 min.
+  // grace 10:00, then six 40s ramps + 12s pauses -> 55% at 15:00 (tight squeeze).
   veryfast: {
-    graceSeconds: 180,
-    rampSeconds: 120,
-    pauseSeconds: 30,
+    graceSeconds: 600,
+    rampSeconds: [40, 40, 40, 40, 40, 40],
+    pauseSeconds: [12, 12, 12, 12, 12, 0],
     levels: LEVELS,
   },
 };
@@ -88,15 +92,18 @@ function requiredBasisPoints(
 ): number {
   const s = schedule(speed);
   if (elapsed <= s.graceSeconds) return 0;
-  const cycle = s.rampSeconds + s.pauseSeconds;
-  const t = elapsed - s.graceSeconds;
-  const i = Math.floor(t / cycle);
-  if (i >= s.levels.length) return s.levels[s.levels.length - 1];
-  const into = t - i * cycle;
-  const prev = i === 0 ? 0 : s.levels[i - 1];
-  const target = s.levels[i];
-  if (into >= s.rampSeconds) return target; // in the pause: hold
-  return prev + Math.floor(((target - prev) * into) / s.rampSeconds);
+  let t = elapsed - s.graceSeconds;
+  let prev = 0;
+  for (let i = 0; i < s.levels.length; i++) {
+    const ramp = s.rampSeconds[i];
+    const target = s.levels[i];
+    if (t < ramp) return prev + Math.floor(((target - prev) * t) / ramp); // ramping
+    t -= ramp;
+    if (t < s.pauseSeconds[i]) return target; // in the pause: hold
+    t -= s.pauseSeconds[i];
+    prev = target;
+  }
+  return s.levels[s.levels.length - 1];
 }
 
 /**
@@ -137,6 +144,8 @@ export interface DoomsdayClockWaveState {
   growing: boolean;
   /** Seconds until the next ramp begins (0 while growing or once done). */
   secondsToNextGrowth: number;
+  /** Seconds until the current rise reaches its target level (0 unless growing). */
+  secondsToTarget: number;
   /** Within 5s before or after a ramp starting (the orange cue window). */
   waveFlash: boolean;
   /** True once the final level has been reached. */
@@ -153,7 +162,6 @@ export function doomsdayClockWaveState(
 ): DoomsdayClockWaveState {
   const s = schedule(speed);
   const currentPercent = requiredBasisPoints(speed, elapsed) / 100;
-  const cycle = s.rampSeconds + s.pauseSeconds;
   const n = s.levels.length;
   const last = s.levels[n - 1] / 100;
 
@@ -164,36 +172,51 @@ export function doomsdayClockWaveState(
       targetPercent: s.levels[0] / 100,
       growing: false,
       secondsToNextGrowth: s.graceSeconds - elapsed,
+      secondsToTarget: 0,
       waveFlash: s.graceSeconds - elapsed <= 5,
       done: false,
     };
   }
 
-  const t = elapsed - s.graceSeconds;
-  const i = Math.floor(t / cycle);
-  if (i >= n) {
-    return {
-      currentPercent,
-      targetPercent: last,
-      growing: false,
-      secondsToNextGrowth: 0,
-      waveFlash: false,
-      done: true,
-    };
+  // Walk the per-wave ramp/pause segments to locate the current wave.
+  let t = elapsed - s.graceSeconds;
+  for (let i = 0; i < n; i++) {
+    const ramp = s.rampSeconds[i];
+    const pause = s.pauseSeconds[i];
+    const isLast = i === n - 1;
+    if (t < ramp) {
+      return {
+        currentPercent,
+        targetPercent: s.levels[i] / 100,
+        growing: true,
+        secondsToNextGrowth: 0,
+        secondsToTarget: ramp - t, // reaches this wave's level when the ramp ends
+        waveFlash: t <= 5, // just started ramping
+        done: false,
+      };
+    }
+    t -= ramp;
+    if (t < pause) {
+      return {
+        currentPercent,
+        targetPercent: (isLast ? s.levels[i] : s.levels[i + 1]) / 100,
+        growing: false,
+        secondsToNextGrowth: isLast ? 0 : pause - t,
+        secondsToTarget: 0,
+        waveFlash: !isLast && pause - t <= 5, // next ramp imminent
+        done: isLast,
+      };
+    }
+    t -= pause;
   }
-
-  const into = t - i * cycle;
-  const growing = into < s.rampSeconds;
-  const isLast = i === n - 1;
-  const nextRampStart = s.graceSeconds + (i + 1) * cycle;
   return {
     currentPercent,
-    targetPercent: (growing || isLast ? s.levels[i] : s.levels[i + 1]) / 100,
-    growing,
-    secondsToNextGrowth: growing || isLast ? 0 : nextRampStart - elapsed,
-    // 5s into a ramp (just started) or 5s before the next ramp begins.
-    waveFlash: into <= 5 || (!isLast && nextRampStart - elapsed <= 5),
-    done: isLast && !growing,
+    targetPercent: last,
+    growing: false,
+    secondsToNextGrowth: 0,
+    secondsToTarget: 0,
+    waveFlash: false,
+    done: true,
   };
 }
 
@@ -203,26 +226,57 @@ export interface DoomsdayClockDrainConfig {
   drainRampSeconds: number;
 }
 
+// Fixed-point scale for the convex drain curve. (t/r)^exponent is evaluated as a
+// fraction of this via repeated integer multiply, so the ramp never touches a
+// float and lands bit-identically on every client in the lockstep sim.
+const DRAIN_CURVE_SCALE = 1_000_000;
+
 /**
- * Troops a skulled side loses this second: a LINEAR ramp from drainStartPercent
- * up to drainMaxPercent over drainRampSeconds. It is a percentage of the side's
- * MAX troop capacity (not current), so it outpaces troop income from the first
- * second and accelerates as it grows, driving the side to zero in ~55s from full
- * troops (sooner with fewer troops or a shrinking territory). The caller caps it
- * at the side's current troops (removeTroops does, and the HUD shows
- * min(current, this)). Shared by the sim and the HUD.
+ * (t/r)^exponent as a fraction of DRAIN_CURVE_SCALE, integer-only. Squares down
+ * from 1.0 with a floored multiply per step; t <= r and exponent >= 2, so the
+ * intermediates stay well inside Number.MAX_SAFE_INTEGER.
+ */
+function drainCurveFraction(t: number, r: number, exponent: number): number {
+  const ratio = Math.floor((t * DRAIN_CURVE_SCALE) / r); // in [0, SCALE]
+  let acc = DRAIN_CURVE_SCALE; // represents 1.0
+  for (let i = 0; i < exponent; i++) {
+    acc = Math.floor((acc * ratio) / DRAIN_CURVE_SCALE);
+  }
+  return acc;
+}
+
+/**
+ * Troops (or warship health) a skulled side loses this second: a ramp from
+ * drainStartPercent up to drainMaxPercent over drainRampSeconds, as a percentage
+ * of MAX capacity/health (not current), so it outpaces income from the first
+ * second. `curveExponent` shapes the ramp: 1 = LINEAR (troops → ~1:30 to zero
+ * from full); >1 = CONVEX (warships → stays near the gentle start for most of the
+ * ramp, then spikes hard, so a ship caught early lasts ~as long as troops but a
+ * side at full attrition loses ships in ~2s). The caller caps it at the side's
+ * current value. Integer-only and floored throughout — no floats — so the drain
+ * is deterministic across clients (required by the lockstep sim).
  */
 export function doomsdayClockDrain(
   maxTroops: number,
   secondsPastWarn: number,
   cfg: DoomsdayClockDrainConfig,
+  curveExponent = 1,
 ): number {
   const t = Math.max(0, secondsPastWarn);
   const r = cfg.drainRampSeconds;
   const span = cfg.drainMaxPercent - cfg.drainStartPercent;
-  const pct =
-    r <= 0 || t >= r
-      ? cfg.drainMaxPercent
-      : cfg.drainStartPercent + Math.floor((span * t) / r);
+  let pct = cfg.drainMaxPercent;
+  if (r > 0 && t < r) {
+    // Linear is the exact integer form the sim has always used; the convex case
+    // reshapes it through the fixed-point curve above (still integer-only).
+    const grown =
+      curveExponent <= 1
+        ? Math.floor((span * t) / r)
+        : Math.floor(
+            (span * drainCurveFraction(t, r, curveExponent)) /
+              DRAIN_CURVE_SCALE,
+          );
+    pct = cfg.drainStartPercent + grown;
+  }
   return Math.max(1, Math.floor((maxTroops * pct) / 100));
 }