fix!: reject malformed games at the Game boundary too

I fixed this at `History`'s ingestion chokepoint and said the boundary
was complete. It was not. `Game` is a separate public entry point that
does not pass through that chokepoint, and every one of the same four
defects was still live there:

  Game::ranked(&[&[a]], ..)  -> PANIC at src/game.rs:317
  Game::scored(&[&[a]], ..)  -> PANIC at src/game.rs:317
  Game::ranked(&[&[], &[a]]) -> Ok, finite posterior for the opponent
  Game::scored(.., [NaN, 1]) -> Ok

The same panic, from safe API, in release. Fixing one path and
generalising from it is exactly the mistake that produced the
latest-slice joint bug: validating on the shape that cannot expose the
problem, then reporting the property as held.

`Game::validate_teams` is shared by `ranked` and `scored`, with the
non-finite score check in `scored` alongside it. Ranks need no equivalent
— they are `u32`.

`one_v_one` and `free_for_all` build their teams internally and are
unaffected; a test asserts all three well-formed constructors still
succeed, so the check cannot quietly widen.

BREAKING CHANGE: `Game::ranked` and `Game::scored` return
`NotEnoughTeams`, `EmptyTeam` or `InvalidParameter` for inputs they
previously panicked on or silently accepted.

Refs #18, #26

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ

src/game.rs

@@ -431,6 +431,29 @@ impl<'a, T: Time, D: Drift<T>> Game<'a, T, D> {
 }
 
 impl<T: Time, D: Drift<T>> Game<'_, T, D> {
+    /// Reject the team shapes inference cannot represent.
+    ///
+    /// `run_chain` builds one diff link per adjacent pair of teams, so fewer
+    /// than two teams leaves it indexing `links[1..]` on an empty vector — a
+    /// panic, in release, from safe API. An empty team is the quiet half: it
+    /// contributes no performance, so a malformed game returns a finite,
+    /// plausible-looking posterior for whoever it was matched against.
+    ///
+    /// `History` validates the same two things at its own ingestion
+    /// chokepoint. `Game` is a separate public entry point that does not pass
+    /// through it, so it needs its own check rather than inheriting one.
+    fn validate_teams(teams: &[&[Rating<T, D>]]) -> Result<(), crate::InferenceError> {
+        if teams.len() < 2 {
+            return Err(crate::InferenceError::NotEnoughTeams { got: teams.len() });
+        }
+        for (team, members) in teams.iter().enumerate() {
+            if members.is_empty() {
+                return Err(crate::InferenceError::EmptyTeam { team });
+            }
+        }
+        Ok(())
+    }
+
     /// # Errors
     ///
     /// - `InvalidParameter` if `options.convergence` is out of range — an
@@ -442,12 +465,15 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
     /// - `TieWithoutDrawProbability` if the outcome ties two teams while
     ///   `p_draw` is zero: the truncation margin is then zero and the two-sided
     ///   tie update evaluates `0/0`.
+    /// - `NotEnoughTeams` for fewer than two teams, and `EmptyTeam` for a team
+    ///   with no members.
     pub fn ranked(
         teams: &[&[Rating<T, D>]],
         outcome: crate::Outcome,
         options: &GameOptions,
     ) -> Result<OwnedGame<T, D>, crate::InferenceError> {
         options.convergence.validate()?;
+        Self::validate_teams(teams)?;
         if !(0.0..1.0).contains(&options.p_draw) {
             return Err(crate::InferenceError::InvalidProbability {
                 value: options.p_draw,
@@ -499,12 +525,15 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
     ///   or is NaN, or if `options.convergence` is out of range.
     /// - `MismatchedShape` if the outcome's score count differs from `teams.len()`.
     /// - `WrongOutcomeKind` if `outcome` is not `Outcome::Scored`.
+    /// - `NotEnoughTeams` for fewer than two teams, `EmptyTeam` for a team with
+    ///   no members, and `InvalidParameter` for a non-finite score.
     pub fn scored(
         teams: &[&[Rating<T, D>]],
         outcome: crate::Outcome,
         options: &GameOptions,
     ) -> Result<OwnedGame<T, D>, crate::InferenceError> {
         options.convergence.validate()?;
+        Self::validate_teams(teams)?;
         if options.score_sigma <= 0.0 || options.score_sigma.is_nan() {
             return Err(crate::InferenceError::InvalidParameter {
                 name: "score_sigma",
@@ -526,6 +555,16 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
                 got: "Outcome::Ranked",
             })?
             .to_vec();
+        // A non-finite score poisons the chain rather than failing it. Ranks
+        // need no equivalent: they are `u32`.
+        for value in &scores {
+            if !value.is_finite() {
+                return Err(crate::InferenceError::InvalidParameter {
+                    name: "score",
+                    value: *value,
+                });
+            }
+        }
         let teams_owned: Vec<Vec<Rating<T, D>>> = teams.iter().map(|t| t.to_vec()).collect();
         let weights: Vec<Vec<f64>> = teams.iter().map(|t| vec![1.0; t.len()]).collect();
         Ok(OwnedGame::new_scored(