Stage 17: backend defect fixes (nudge code, TG name, robot names/timing, multi-device push, move-duration metric + admin analytics)

- #3 nudge-on-own-turn: distinct result code nudge_own_turn + i18n (was reused 'not_your_turn')
- #2 sanitize connector registration name to the editable format; Player/Игрок-XXXXX fallback
- #5 variant-aware robot name pools (composed full/colloquial first + surname forms; ru gets <=20% latin)
- #4 move-number-aware robot move timing (early 1-5min -> late 10-90min, skew k=4)
- #7 emit move event to the actor too (multi-device sync); opponent_moved stays in-app only
- #1 live game_move_duration{variant,phase} histogram + admin console per-user min/avg/max columns and an inline-SVG move-time-by-move-number chart (offline from the journal)
- ProvisionRobot bypasses editor name validation (system names like 'Peter J.')

backend/internal/robot/strategy.go

@@ -23,17 +23,27 @@ const (
 	// human wins about 60% of games (docs/ARCHITECTURE.md §7).
 	playToWinPercent = 40
 
-	// delayMinMinutes and delayMaxMinutes bound a move delay; delaySkew shapes the
-	// right-skewed distribution (short delays frequent). With skew 3.5 the median
-	// is about 10 minutes and the mean about 20, with a tail out to the maximum.
-	delayMinMinutes = 2.0
-	delayMaxMinutes = 90.0
-	delaySkew       = 3.5
+	// The robot's think time depends on how far the game has progressed: early moves
+	// are quick and late moves can be long (endgame deliberation). The delay is drawn
+	// from a band that interpolates with the move count from [delayEarlyLoMinutes,
+	// delayEarlyHiMinutes] at the first move to [delayLateLoMinutes, delayLateHiMinutes]
+	// by avgGameMoves, then right-skewed by delaySkew (a larger exponent concentrates
+	// delays near the band's floor — an active player). The result is clamped to
+	// [delayHardMinMinutes, delayHardMaxMinutes]. The numbers are deliberate estimates,
+	// to be retuned once real play statistics arrive (docs/ARCHITECTURE.md §7).
+	delayEarlyLoMinutes = 1.0
+	delayEarlyHiMinutes = 5.0
+	delayLateLoMinutes  = 10.0
+	delayLateHiMinutes  = 90.0
+	delaySkew           = 4.0
+	avgGameMoves        = 28.0
+	delayHardMinMinutes = 1.0
+	delayHardMaxMinutes = 90.0
 
-	// nudgeReplyMinMinutes and nudgeReplyMaxMinutes bound how soon the robot
-	// answers a daytime nudge on its turn.
-	nudgeReplyMinMinutes = 2.0
-	nudgeReplyMaxMinutes = 10.0
+	// nudgeReplySpreadMinutes is the width of the quick window, anchored at the move's
+	// lower band (delayBand's lo), within which the robot answers a daytime nudge on
+	// its turn — so a nudged robot replies near the floor of its think time.
+	nudgeReplySpreadMinutes = 5.0
 
 	// sleepStartHour and sleepEndHour bound the robot's nightly sleep in its
 	// (opponent-anchored, drifted) local time: it makes no move and sends no nudge
@@ -104,19 +114,48 @@ func playToWin(seed int64) bool {
 	return mix(seed, "win")%100 < playToWinPercent
 }
 
-// moveDelay is the robot's think time for the move at moveCount, sampled from the
-// right-skewed distribution and bounded to [delayMinMinutes, delayMaxMinutes).
+// delayBand returns the lower and upper bounds, in minutes, of the move-delay band
+// for the move at moveCount. It interpolates linearly with game progress (the move
+// count over avgGameMoves, capped at 1): early moves sit in a short band and late
+// moves in a long one.
+func delayBand(moveCount int) (lo, hi float64) {
+	p := float64(moveCount) / avgGameMoves
+	if p > 1 {
+		p = 1
+	}
+	lo = delayEarlyLoMinutes + (delayLateLoMinutes-delayEarlyLoMinutes)*p
+	hi = delayEarlyHiMinutes + (delayLateHiMinutes-delayEarlyHiMinutes)*p
+	return lo, hi
+}
+
+// moveDelay is the robot's think time for the move at moveCount: a right-skewed
+// sample from the move's delayBand, clamped to the hard bounds. The skew (delaySkew
+// > 1) makes short delays frequent and long ones rare, with a tail to the band's top.
 func moveDelay(seed int64, moveCount int) time.Duration {
+	lo, hi := delayBand(moveCount)
 	u := unitFloat(mix(seed, "delay", moveCount))
-	mins := delayMinMinutes + (delayMaxMinutes-delayMinMinutes)*math.Pow(u, delaySkew)
-	return time.Duration(mins * float64(time.Minute))
+	return clampMinutes(lo + (hi-lo)*math.Pow(u, delaySkew))
 }
 
 // nudgeReplyDelay is how soon after a daytime nudge the robot answers the move at
-// moveCount, sampled uniformly from [nudgeReplyMinMinutes, nudgeReplyMaxMinutes).
+// moveCount: a uniform sample from the quick window [lo, lo+nudgeReplySpreadMinutes],
+// where lo is the move's lower band — so a nudge pulls the move in near the floor of
+// the robot's think time.
 func nudgeReplyDelay(seed int64, moveCount int) time.Duration {
+	lo, _ := delayBand(moveCount)
 	u := unitFloat(mix(seed, "nudge", moveCount))
-	mins := nudgeReplyMinMinutes + (nudgeReplyMaxMinutes-nudgeReplyMinMinutes)*u
+	return clampMinutes(lo + nudgeReplySpreadMinutes*u)
+}
+
+// clampMinutes converts a minute count to a duration, clamping it to the hard delay
+// bounds so an out-of-range band can never produce an absurd think time.
+func clampMinutes(mins float64) time.Duration {
+	if mins < delayHardMinMinutes {
+		mins = delayHardMinMinutes
+	}
+	if mins > delayHardMaxMinutes {
+		mins = delayHardMaxMinutes
+	}
 	return time.Duration(mins * float64(time.Minute))
 }