fix: reject ties without draw probability; never report NaN as converged

A tie with `p_draw == 0.0` produced NaN posteriors in release builds and
`converge()` reported `converged: true`, because every comparison against
NaN is false and `tuple_gt` therefore read NaN as "below epsilon".

Two independent defects, fixed together:

- Ingestion now rejects tied outcomes when the draw probability is zero,
  promoting the existing `debug_assert!` in `Game::ranked_with_arena` to a
  real `InferenceError::TieWithoutDrawProbability`. Validation sits in
  `add_events_with_prior`, the chokepoint every route reaches — including
  `record_draw`, which bypasses `Outcome` entirely.
- `converge()` treats a non-finite step as failure and returns
  `InferenceError::NonFiniteResult` rather than claiming convergence.

Also in this change:

- `History::converge()` on an empty history returned a `usize` underflow
  panic from `0..len()-1`; it now short-circuits to a zero-iteration report.
- `Outcome::scores_with_sigma` no longer panics on a non-positive sigma;
  the value is validated at ingestion so callers get an error instead.
- `InferenceError` gains `WrongOutcomeKind`, replacing the misuse of
  `MismatchedShape` for variant mismatches (which rendered as the nonsense
  "expected length 0, got 0"), and is now `#[non_exhaustive]`.

Note `Outcome::winner(w, n)` for n >= 3 ties every loser, so those events
now require a positive `p_draw`. They previously returned NaN.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01DnsaJg74eNSva3PJjK2eej

src/error.rs

@@ -1,6 +1,7 @@
 use std::fmt;
 
 #[derive(Debug, Clone, PartialEq)]
+#[non_exhaustive]
 pub enum InferenceError {
     /// Expected and actual lengths of some array-shaped input differ.
     MismatchedShape {
@@ -8,15 +9,35 @@ pub enum InferenceError {
         expected: usize,
         got: usize,
     },
+    /// An `Outcome` of the wrong variant was supplied for the requested inference.
+    WrongOutcomeKind {
+        context: &'static str,
+        expected: &'static str,
+        got: &'static str,
+    },
     /// A probability value is outside `[0, 1]`.
     InvalidProbability { value: f64 },
     /// A scalar parameter is outside its valid range.
     InvalidParameter { name: &'static str, value: f64 },
+    /// An event contains tied teams, but the draw probability is zero.
+    ///
+    /// A zero draw probability asserts that draws cannot occur, so a tied
+    /// result has no representable likelihood. Configure a positive `p_draw`
+    /// (via `HistoryBuilder::p_draw` or `GameOptions::p_draw`) to admit ties.
+    TieWithoutDrawProbability { teams: (usize, usize) },
     /// Convergence exceeded `max_iter` without falling below `epsilon`.
     ConvergenceFailed {
         last_step: (f64, f64),
         iterations: usize,
     },
+    /// Inference produced a non-finite value (NaN or infinity).
+    ///
+    /// Indicates numerical breakdown; the resulting skills are meaningless
+    /// and must not be treated as a converged estimate.
+    NonFiniteResult {
+        context: &'static str,
+        step: (f64, f64),
+    },
     /// Negative precision: a Gaussian with `pi < 0` slipped into an API call.
     NegativePrecision { pi: f64 },
 }
@@ -31,9 +52,29 @@ impl fmt::Display for InferenceError {
             } => {
                 write!(f, "{kind}: expected length {expected}, got {got}")
             }
+            Self::WrongOutcomeKind {
+                context,
+                expected,
+                got,
+            } => {
+                write!(f, "{context}: expected {expected}, got {got}")
+            }
             Self::InvalidProbability { value } => {
                 write!(f, "probability must be in [0, 1]; got {value}")
             }
+            Self::TieWithoutDrawProbability { teams } => {
+                write!(
+                    f,
+                    "teams {} and {} are tied, but p_draw is 0.0; set a positive draw probability to admit ties",
+                    teams.0, teams.1
+                )
+            }
+            Self::NonFiniteResult { context, step } => {
+                write!(
+                    f,
+                    "{context}: inference produced a non-finite result (step = {step:?})"
+                )
+            }
             Self::InvalidParameter { name, value } => {
                 write!(f, "{name} is invalid: {value}")
             }

src/game.rs

@@ -458,11 +458,18 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
 
         let ranks = outcome
             .as_ranks()
-            .ok_or(crate::InferenceError::MismatchedShape {
+            .ok_or(crate::InferenceError::WrongOutcomeKind {
-                kind: "Game::ranked requires Outcome::Ranked",
+                context: "Game::ranked",
-                expected: 0,
+                expected: "Outcome::Ranked",
-                got: 0,
+                got: "Outcome::Scored",
             })?;
+
+        if options.p_draw == 0.0
+            && let Some(tied) = crate::first_tied_pair(ranks)
+        {
+            return Err(crate::InferenceError::TieWithoutDrawProbability { teams: tied });
+        }
+
         let max_rank = ranks.iter().copied().max().unwrap_or(0) as f64;
         let result: Vec<f64> = ranks.iter().map(|&r| max_rank - r as f64).collect();
         let teams_owned: Vec<Vec<Rating<T, D>>> = teams.iter().map(|t| t.to_vec()).collect();
@@ -497,10 +504,10 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         }
         let scores = outcome
             .as_scores()
-            .ok_or(crate::InferenceError::MismatchedShape {
+            .ok_or(crate::InferenceError::WrongOutcomeKind {
-                kind: "Game::scored requires Outcome::Scored",
+                context: "Game::scored",
-                expected: 0,
+                expected: "Outcome::Scored",
-                got: 0,
+                got: "Outcome::Ranked",
             })?
             .to_vec();
         let teams_owned: Vec<Vec<Rating<T, D>>> = teams.iter().map(|t| t.to_vec()).collect();
@@ -1124,7 +1131,10 @@ mod tests {
             &GameOptions::default(),
         )
         .unwrap_err();
-        assert!(matches!(err, crate::InferenceError::MismatchedShape { .. }));
+        assert!(matches!(
+            err,
+            crate::InferenceError::WrongOutcomeKind { .. }
+        ));
     }
 
     #[test]

src/history.rs

@@ -220,6 +220,10 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     fn iteration(&mut self) -> (f64, f64) {
         let mut step = (0.0, 0.0);
 
+        if self.time_slices.is_empty() {
+            return step;
+        }
+
         competitor::clean(self.agents.values_mut(), false);
 
         for j in (0..self.time_slices.len() - 1).rev() {
@@ -435,6 +439,18 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
         use smallvec::SmallVec;
 
         let opts = self.convergence;
+
+        if self.time_slices.is_empty() {
+            return Ok(ConvergenceReport {
+                iterations: 0,
+                final_step: (0.0, 0.0),
+                log_evidence: 0.0,
+                converged: true,
+                per_iteration_time: SmallVec::new(),
+                slices_skipped: 0,
+            });
+        }
+
         let mut step = (f64::INFINITY, f64::INFINITY);
         let mut i = 0;
         let mut per_iter: SmallVec<[std::time::Duration; 32]> = SmallVec::new();
@@ -444,8 +460,24 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
             per_iter.push(t0.elapsed());
             i += 1;
             self.observer.on_iteration_end(i, step);
+
+            // A non-finite step means EP has broken down; further iterations
+            // cannot recover, and `tuple_gt` would read NaN as converged.
+            if !crate::step_is_finite(step) {
+                break;
             }
-        let converged = !tuple_gt(step, opts.epsilon);
+        }
+
+        if !crate::step_is_finite(step) {
+            self.observer.on_converged(i, step, false);
+
+            return Err(InferenceError::NonFiniteResult {
+                context: "History::converge",
+                step,
+            });
+        }
+
+        let converged = crate::step_converged(step, opts.epsilon);
         let log_evidence = self.log_evidence_internal(false, &[]);
         self.observer.on_converged(i, step, converged);
         Ok(ConvergenceReport {
@@ -498,6 +530,19 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
             });
         }
 
+        // Chokepoint for tie validation: every ingestion route lands here,
+        // including `record_draw`, which builds its results directly rather
+        // than going through `Outcome`.
+        if self.p_draw == 0.0 {
+            for (event_results, kind) in results.iter().zip(kinds.iter()) {
+                if matches!(kind, EventKind::Ranked)
+                    && let Some(tied) = crate::first_tied_output(event_results)
+                {
+                    return Err(InferenceError::TieWithoutDrawProbability { teams: tied });
+                }
+            }
+        }
+
         competitor::clean(self.agents.values_mut(), true);
 
         let mut this_agent = Vec::with_capacity(1024);
@@ -734,10 +779,13 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
                 }
                 crate::Outcome::Scored { scores, sigma } => {
                     let resolved = sigma.unwrap_or(self.score_sigma);
-                    debug_assert!(
+                    if !(resolved > 0.0) {
-                        resolved > 0.0,
+                        return Err(InferenceError::InvalidParameter {
-                        "resolved score_sigma must be > 0.0 (got {resolved})"
+                            name: "score_sigma",
-                    );
+                            value: resolved,
+                        });
+                    }
+
                     kinds.push(EventKind::Scored {
                         score_sigma: resolved,
                     });

src/lib.rs

@@ -184,6 +184,56 @@ pub(crate) fn tuple_gt(t: (f64, f64), e: f64) -> bool {
     t.0 > e || t.1 > e
 }
 
+/// Whether a convergence step is finite in both components.
+///
+/// A NaN step means EP broke down numerically. Because every comparison
+/// against NaN is false, `tuple_gt` reads NaN as "below epsilon" — so
+/// convergence checks must test finiteness explicitly rather than inferring
+/// success from `!tuple_gt(..)`.
+pub(crate) fn step_is_finite(t: (f64, f64)) -> bool {
+    t.0.is_finite() && t.1.is_finite()
+}
+
+/// Whether a step counts as converged: finite *and* within `epsilon`.
+pub(crate) fn step_converged(t: (f64, f64), epsilon: f64) -> bool {
+    step_is_finite(t) && !tuple_gt(t, epsilon)
+}
+
+/// Indices of the first pair of teams sharing a rank, if any.
+///
+/// A tie is only representable when the draw probability is positive: with
+/// `p_draw == 0.0` the truncation margin collapses to zero and the two-sided
+/// tie update evaluates `0/0`. Callers use this to reject such events before
+/// they reach inference.
+pub(crate) fn first_tied_pair(ranks: &[u32]) -> Option<(usize, usize)> {
+    for (i, a) in ranks.iter().enumerate() {
+        for (j, b) in ranks.iter().enumerate().skip(i + 1) {
+            if a == b {
+                return Some((i, j));
+            }
+        }
+    }
+
+    None
+}
+
+/// As `first_tied_pair`, but over the engine's internal `f64` outputs.
+///
+/// Ranks reach the engine already converted to descending `f64` outputs, and
+/// `Game` decides a tie by exact equality of those values — so this mirrors
+/// the comparison inference itself performs.
+pub(crate) fn first_tied_output(outputs: &[f64]) -> Option<(usize, usize)> {
+    for (i, a) in outputs.iter().enumerate() {
+        for (j, b) in outputs.iter().enumerate().skip(i + 1) {
+            if a == b {
+                return Some((i, j));
+            }
+        }
+    }
+
+    None
+}
+
 pub(crate) fn sort_time<T: Copy + Ord>(xs: &[T], reverse: bool) -> Vec<usize> {
     let mut x: Vec<(usize, T)> = xs.iter().enumerate().map(|(i, &t)| (i, t)).collect();
 

src/outcome.rs

@@ -57,9 +57,11 @@ impl Outcome {
 
     /// Explicit per-team continuous scores with a per-event noise override.
     ///
-    /// `sigma` must be `> 0.0`; debug-asserts otherwise.
+    /// `sigma` must be `> 0.0`. Constructing an `Outcome` with a non-positive
+    /// or NaN sigma is allowed; the value is rejected with
+    /// `InferenceError::InvalidParameter` when the event is ingested, so
+    /// callers get an error rather than a panic.
     pub fn scores_with_sigma<I: IntoIterator<Item = f64>>(scores: I, sigma: f64) -> Self {
-        debug_assert!(sigma > 0.0, "score_sigma must be > 0.0 (got {sigma})");
         Self::Scored {
             scores: scores.into_iter().collect(),
             sigma: Some(sigma),
@@ -169,9 +171,15 @@ mod tests {
         }
     }
 
+    /// Construction accepts any sigma; the value is validated at ingestion so
+    /// callers receive an `InferenceError` rather than a panic. See
+    /// `tests/degenerate_inputs.rs::scored_event_rejects_non_positive_sigma`.
     #[test]
-    #[should_panic(expected = "score_sigma must be > 0.0")]
+    fn scores_with_sigma_defers_validation_to_ingestion() {
-    fn scores_with_sigma_rejects_zero() {
+        let o = Outcome::scores_with_sigma([3.0, 1.0], 0.0);
-        let _ = Outcome::scores_with_sigma([3.0, 1.0], 0.0);
+        match o {
+            Outcome::Scored { sigma, .. } => assert_eq!(sigma, Some(0.0)),
+            Outcome::Ranked(_) => panic!("expected Scored variant"),
+        }
     }
 }

tests/degenerate_inputs.rs

@@ -0,0 +1,195 @@
+//! Degenerate, boundary, and error-path coverage.
+//!
+//! These run in both debug and release: the defects they pin were all
+//! guarded only by `debug_assert!`, so a debug-only suite never saw them.
+
+use trueskill_tt::{
+    ConstantDrift, ConvergenceOptions, Game, GameOptions, Gaussian, History, InferenceError,
+    Outcome, Rating,
+};
+
+type R = Rating<i64, ConstantDrift>;
+
+fn rating() -> R {
+    R::new(
+        Gaussian::from_ms(25.0, 25.0 / 3.0),
+        25.0 / 6.0,
+        ConstantDrift(25.0 / 300.0),
+    )
+}
+
+fn assert_finite(g: Gaussian, what: &str) {
+    assert!(
+        g.mu().is_finite() && g.sigma().is_finite(),
+        "{what} must be finite, got mu={} sigma={}",
+        g.mu(),
+        g.sigma()
+    );
+}
+
+#[test]
+fn record_draw_without_draw_probability_is_rejected() {
+    let mut h = History::default();
+    let err = h.record_draw(&"a", &"b", 1).unwrap_err();
+    assert!(matches!(
+        err,
+        InferenceError::TieWithoutDrawProbability { .. }
+    ));
+}
+
+#[test]
+fn builder_draw_without_draw_probability_is_rejected() {
+    let mut h = History::default();
+    let err = h
+        .event(1)
+        .team(["a"])
+        .team(["b"])
+        .draw()
+        .commit()
+        .unwrap_err();
+    assert!(matches!(
+        err,
+        InferenceError::TieWithoutDrawProbability { .. }
+    ));
+}
+
+#[test]
+fn draw_with_positive_draw_probability_is_finite() {
+    let mut h = History::builder().p_draw(0.25).build();
+    h.record_draw(&"a", &"b", 1).unwrap();
+    let report = h.converge().unwrap();
+
+    assert_finite(h.current_skill("a").unwrap(), "drawn competitor skill");
+    assert_finite(h.current_skill("b").unwrap(), "drawn competitor skill");
+    assert!(report.log_evidence.is_finite());
+    assert!(report.converged);
+}
+
+#[test]
+fn game_ranked_rejects_tie_without_draw_probability() {
+    let a = [rating()];
+    let b = [rating()];
+    let teams: Vec<&[R]> = vec![&a, &b];
+    let err = Game::ranked(&teams, Outcome::draw(2), &GameOptions::default()).unwrap_err();
+    assert!(matches!(
+        err,
+        InferenceError::TieWithoutDrawProbability { .. }
+    ));
+}
+
+/// `Outcome::winner(w, n)` ties every loser, so any n >= 3 free-for-all hits
+/// the tie path even though the caller never asked for a draw.
+#[test]
+fn winner_of_three_or_more_requires_draw_probability() {
+    let a = [rating()];
+    let b = [rating()];
+    let c = [rating()];
+    let teams: Vec<&[R]> = vec![&a, &b, &c];
+
+    let err = Game::ranked(&teams, Outcome::winner(0, 3), &GameOptions::default()).unwrap_err();
+    assert!(matches!(
+        err,
+        InferenceError::TieWithoutDrawProbability { .. }
+    ));
+
+    let opts = GameOptions {
+        p_draw: 0.1,
+        ..GameOptions::default()
+    };
+    let game = Game::ranked(&teams, Outcome::winner(0, 3), &opts).unwrap();
+    for team in game.posteriors() {
+        for skill in team {
+            assert_finite(skill, "3-team winner posterior");
+        }
+    }
+}
+
+#[test]
+fn full_ranking_without_ties_needs_no_draw_probability() {
+    let a = [rating()];
+    let b = [rating()];
+    let c = [rating()];
+    let teams: Vec<&[R]> = vec![&a, &b, &c];
+    let game = Game::ranked(&teams, Outcome::ranking([0, 1, 2]), &GameOptions::default()).unwrap();
+
+    for team in game.posteriors() {
+        for skill in team {
+            assert_finite(skill, "strict ranking posterior");
+        }
+    }
+}
+
+#[test]
+fn empty_history_converges_trivially() {
+    let mut h = History::default();
+    let report = h.converge().unwrap();
+    assert_eq!(report.iterations, 0);
+    assert!(report.converged);
+}
+
+#[test]
+fn empty_event_stream_then_converge() {
+    let mut h = History::default();
+    h.add_events(std::iter::empty()).unwrap();
+    let report = h.converge().unwrap();
+    assert_eq!(report.iterations, 0);
+}
+
+#[test]
+fn empty_history_queries_do_not_panic() {
+    let h = History::default();
+    assert!(h.learning_curves().is_empty());
+    assert!(h.learning_curve("nobody").is_empty());
+    assert!(h.current_skill("nobody").is_none());
+}
+
+#[test]
+fn single_event_history_converges() {
+    let mut h = History::default();
+    h.record_winner(&"a", &"b", 1).unwrap();
+    let report = h.converge().unwrap();
+    assert!(report.converged);
+    assert_finite(h.current_skill("a").unwrap(), "single-event skill");
+}
+
+#[test]
+fn scored_event_rejects_non_positive_sigma() {
+    let mut h = History::builder().score_sigma(2.0).build();
+    let err = h
+        .event(1)
+        .team(["a"])
+        .team(["b"])
+        .scores_with_sigma([3.0, 1.0], f64::NAN)
+        .commit()
+        .unwrap_err();
+    assert!(matches!(
+        err,
+        InferenceError::InvalidParameter {
+            name: "score_sigma",
+            ..
+        }
+    ));
+}
+
+#[test]
+fn convergence_reports_are_finite_across_many_teams() {
+    let opts = GameOptions {
+        p_draw: 0.1,
+        convergence: ConvergenceOptions::default(),
+        ..GameOptions::default()
+    };
+    let holders: Vec<[R; 1]> = (0..12).map(|_| [rating()]).collect();
+    let teams: Vec<&[R]> = holders.iter().map(|t| t.as_slice()).collect();
+    let game = Game::ranked(&teams, Outcome::ranking(0..12), &opts).unwrap();
+
+    assert!(
+        game.log_evidence().is_finite(),
+        "12-team log-evidence must be finite, got {}",
+        game.log_evidence()
+    );
+    for team in game.posteriors() {
+        for skill in team {
+            assert_finite(skill, "12-team posterior");
+        }
+    }
+}