Stage 17 round 5 (L2): robot play-to-win intent + next-move ETA in the admin game card

The admin game detail now shows, per robot seat, the game's deterministic play-to-win
decision (from the bag seed) and — while it is that robot's turn — its scheduled next-move
ETA (sampled think-time delay, deferred past the sleep window), plus a caption with the
~40% global target. Wiring: robot.PlayToWin/NextMoveAt/PlayToWinTargetPercent exports,
account.IsRobot, game RobotSchedule (seed + turn-start). Tests: NextMoveAt invariants
(never early, never in the sleep window), PlayToWin export, and an admin render integration
test asserting the intent + ETA + target appear.

backend/internal/adminconsole/templates/pages/game_detail.gohtml

@@ -17,13 +17,14 @@
 </section>
 <section class="panel"><h2>Seats</h2>
 <table class="list">
-<thead><tr><th>Seat</th><th>Player</th><th>Score</th><th>Hints used</th><th>Winner</th></tr></thead>
+<thead><tr><th>Seat</th><th>Player</th><th>Score</th><th>Hints used</th><th>Winner</th><th>Robot</th></tr></thead>
 <tbody>
 {{range .Seats}}
-<tr><td>{{.Seat}}</td><td><a href="/_gm/users/{{.AccountID}}">{{.DisplayName}}</a></td><td>{{.Score}}</td><td>{{.HintsUsed}}</td><td>{{if .Winner}}<span class="ok">winner</span>{{end}}</td></tr>
+<tr><td>{{.Seat}}</td><td><a href="/_gm/users/{{.AccountID}}">{{.DisplayName}}</a></td><td>{{.Score}}</td><td>{{.HintsUsed}}</td><td>{{if .Winner}}<span class="ok">winner</span>{{end}}</td><td>{{if .IsRobot}}🤖 {{.RobotIntent}}{{if .NextMove}}<br><small>next move {{.NextMove}}</small>{{end}}{{end}}</td></tr>
 {{end}}
 </tbody>
 </table>
+{{if .HasRobot}}<p><small>Play-to-win is decided once per game from the bag seed; robots play to win in ~{{.RobotTargetPct}}% of games.</small></p>{{end}}
 </section>
 {{end}}
 {{- end}}

backend/internal/adminconsole/views.go

@@ -145,9 +145,15 @@ type GameDetailView struct {
 	UpdatedAt   string
 	FinishedAt  string
 	Seats       []SeatRow
+	// HasRobot is true when any seat is a robot, gating the robot-target caption;
+	// RobotTargetPct is the configured global play-to-win rate, in percent.
+	HasRobot       bool
+	RobotTargetPct int
 }
 
-// SeatRow is one seat of a game.
+// SeatRow is one seat of a game. For a robot seat (IsRobot) RobotIntent is the game's
+// deterministic play-to-win decision ("play to win"/"play to lose"), and NextMove is the
+// scheduled next-move ETA shown only while it is that robot's turn in an active game.
 type SeatRow struct {
 	Seat        int
 	DisplayName string
@@ -155,6 +161,9 @@ type SeatRow struct {
 	Score       int
 	HintsUsed   int
 	Winner      bool
+	IsRobot     bool
+	RobotIntent string
+	NextMove    string
 }
 
 // ComplaintsView is the paginated complaint review queue.