diff --git a/src/game.rs b/src/game.rs
index 852d44f..76c9e61 100644
--- a/src/game.rs
+++ b/src/game.rs
@@ -102,24 +102,51 @@ impl Default for GameOptions {
     }
 }
 
-/// Owned variant of `Game` returned by public constructors.
+/// One match, fitted on its own.
 ///
-/// Unlike `Game<'a, T, D>` (which borrows its result/weights slices from
-/// History's internal state), `OwnedGame<T, D>` owns the team ratings, so it
-/// can be returned freely from public constructors. The inference inputs
-/// themselves are not retained — nothing reads them back.
+/// Rate a single match against ratings you already hold and read the updated
+/// beliefs straight back. There is no history behind it: nothing is stored,
+/// nothing propagates backward, and the priors you hand in are the only
+/// evidence used. That makes it the wrong tool for the thing this crate exists
+/// for — [`History`](crate::History) is what infers skill *through time*,
+/// revising past estimates as later matches arrive, and a sequence of `Game`s
+/// chained by hand is a forward-only filter, not the same answer.
 ///
-/// A fitted single match, and nothing more: see [`Game`] for why that is not
-/// the same as a step of a [`History`](crate::History).
+/// Reach for it when a history would be overkill or unavailable: a one-off
+/// matchup, replaying a rating step from stored numbers, checking the engine
+/// against a reference, or a caller that keeps its own persistence and only
+/// wants the update rule.
+///
+/// ```
+/// use trueskill_tt::{ConstantDrift, Game, GameOptions, Gaussian, Outcome, Rating};
+///
+/// let strong: Rating = Rating::new(Gaussian::from_ms(30.0, 3.0), 1.0, ConstantDrift::new(0.0));
+/// let weak: Rating = Rating::new(Gaussian::from_ms(20.0, 3.0), 1.0, ConstantDrift::new(0.0));
+///
+/// // The underdog wins.
+/// let game = Game::ranked(
+///     &[&[weak], &[strong]],
+///     Outcome::winner(0, 2),
+///     &GameOptions::default(),
+/// )?;
+///
+/// let posteriors = game.posteriors();
+/// assert!(posteriors[0][0].mu() > weak.prior().mu(), "the winner gained");
+/// assert!(posteriors[1][0].mu() < strong.prior().mu(), "the loser lost");
+///
+/// // An upset is improbable, and `log_evidence` says so.
+/// assert!(game.log_evidence() < 0.5_f64.ln());
+/// # Ok::<(), trueskill_tt::InferenceError>(())
+/// ```
 #[derive(Debug)]
 #[must_use]
-pub struct OwnedGame<T: Time, D: Drift<T>> {
+pub struct Game<T: Time, D: Drift<T>> {
     teams: Vec<Vec<Rating<T, D>>>,
     pub(crate) likelihoods: Vec<Vec<Gaussian>>,
     pub(crate) log_evidence: f64,
 }
 
-impl<T: Time, D: Drift<T>> OwnedGame<T, D> {
+impl<T: Time, D: Drift<T>> Game<T, D> {
     pub(crate) fn new(
         teams: Vec<Vec<Rating<T, D>>>,
         result: Vec<f64>,
@@ -131,7 +158,8 @@ impl<T: Time, D: Drift<T>> OwnedGame<T, D> {
 
         // `Game` takes the teams by value and is dropped here, so take the vec
         // back out of it rather than handing it a clone.
-        let g = Game::ranked_with_arena(teams, &result, &weights, p_draw, convergence, &mut arena);
+        let g =
+            GameRef::ranked_with_arena(teams, &result, &weights, p_draw, convergence, &mut arena);
 
         Self {
             teams: g.teams,
@@ -149,7 +177,7 @@ impl<T: Time, D: Drift<T>> OwnedGame<T, D> {
     ) -> Self {
         let mut arena = ScratchArena::new();
 
-        let g = Game::scored_with_arena(
+        let g = GameRef::scored_with_arena(
             teams,
             &scores,
             &weights,
@@ -204,27 +232,15 @@ impl<T: Time, D: Drift<T>> OwnedGame<T, D> {
     }
 }
 
-/// One match's factor graph, fitted on its own.
+/// The borrowing form of [`Game`], used only inside the crate.
 ///
-/// Rate a single match against ratings you already hold and get the updated
-/// beliefs straight back. There is no history behind it: nothing is stored,
-/// nothing propagates backward, and the priors you hand in are the only
-/// evidence used. That makes it the wrong tool for the thing this crate exists
-/// for — [`History`](crate::History) is what infers skill *through time*,
-/// revising past estimates as later matches arrive, and a sequence of `Game`s
-/// chained by hand is a forward-only filter, not the same answer.
-///
-/// Reach for `Game` when a history would be overkill or unavailable: a
-/// one-off matchup, replaying a rating step from stored numbers, checking the
-/// engine against a reference, or a caller that keeps its own persistence and
-/// only wants the update rule.
-///
-/// The type is mostly a namespace. Its constructors — [`Game::ranked`],
-/// [`Game::scored`], [`Game::one_v_one`], [`Game::free_for_all`] — return an
-/// [`OwnedGame`], because `Game<'a, …>` borrows the result and weight slices
-/// that `History` keeps internally and so cannot be handed out.
+/// `History` keeps each event's result and weight slices in its own storage
+/// and sweeps them thousands of times, so the inference core borrows them
+/// rather than copying. That borrow is the whole difference between this and
+/// [`Game`]; it is why this type cannot be handed to a caller, and why it is
+/// not part of the public API.
 #[derive(Debug)]
-pub struct Game<'a, T: Time = i64, D: Drift<T> = crate::drift::ConstantDrift> {
+pub(crate) struct GameRef<'a, T: Time = i64, D: Drift<T> = crate::drift::ConstantDrift> {
     teams: Vec<Vec<Rating<T, D>>>,
     result: &'a [f64],
     weights: &'a [Vec<f64>],
@@ -234,7 +250,7 @@ pub struct Game<'a, T: Time = i64, D: Drift<T> = crate::drift::ConstantDrift> {
     pub(crate) log_evidence: f64,
 }
 
-impl<'a, T: Time, D: Drift<T>> Game<'a, T, D> {
+impl<'a, T: Time, D: Drift<T>> GameRef<'a, T, D> {
     pub(crate) fn ranked_with_arena(
         teams: Vec<Vec<Rating<T, D>>>,
         result: &'a [f64],
@@ -476,11 +492,12 @@ impl<'a, T: Time, D: Drift<T>> Game<'a, T, D> {
         self.likelihoods = likelihoods;
     }
 
-    /// Updated skill belief for every competitor, as `[team][member]` in the
-    /// order the teams and members were passed in — prior times this match's
-    /// likelihood, exactly as [`OwnedGame::posteriors`].
-    #[must_use]
-    pub fn posteriors(&self) -> Vec<Vec<Gaussian>> {
+    /// As [`Game::posteriors`].
+    ///
+    /// Test-only: inference reads `likelihoods` directly, and `GameRef` is not
+    /// public, so the only callers are this module's own goldens.
+    #[cfg(test)]
+    pub(crate) fn posteriors(&self) -> Vec<Vec<Gaussian>> {
         self.likelihoods
             .iter()
             .zip(self.teams.iter())
@@ -492,16 +509,9 @@ impl<'a, T: Time, D: Drift<T>> Game<'a, T, D> {
             })
             .collect::<Vec<_>>()
     }
-
-    /// Natural log of how probable this outcome was under the priors, summed
-    /// over the diff chain's links — as [`OwnedGame::log_evidence`].
-    #[must_use]
-    pub fn log_evidence(&self) -> f64 {
-        self.log_evidence
-    }
 }
 
-impl<T: Time, D: Drift<T>> Game<'_, 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
@@ -525,6 +535,12 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         Ok(())
     }
 
+    /// Fit one match from an ordinal result.
+    ///
+    /// `teams` is `[team][member]`, and `outcome` ranks those teams in the
+    /// same order. Read the result with [`posteriors`](Game::posteriors) and
+    /// [`log_evidence`](Game::log_evidence).
+    ///
     /// # Errors
     ///
     /// - `InvalidParameter` if `options.convergence` is out of range — an
@@ -542,7 +558,7 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         teams: &[&[Rating<T, D>]],
         outcome: crate::Outcome,
         options: &GameOptions,
-    ) -> Result<OwnedGame<T, D>, crate::InferenceError> {
+    ) -> Result<Self, crate::InferenceError> {
         options.convergence.validate()?;
         Self::validate_teams(teams)?;
         if !(0.0..1.0).contains(&options.p_draw) {
@@ -581,7 +597,7 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         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(
+        Ok(Self::new(
             teams_owned,
             result,
             weights,
@@ -590,6 +606,12 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         ))
     }
 
+    /// Fit one match from continuous scores.
+    ///
+    /// Unlike [`ranked`](Game::ranked), the *size* of each adjacent gap is
+    /// evidence: beating a team by ten says more than beating them by one.
+    /// How much more is set by `options.score_sigma`.
+    ///
     /// # Errors
     ///
     /// - `InvalidParameter` if `options.score_sigma` is not strictly positive
@@ -602,7 +624,7 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         teams: &[&[Rating<T, D>]],
         outcome: crate::Outcome,
         options: &GameOptions,
-    ) -> Result<OwnedGame<T, D>, crate::InferenceError> {
+    ) -> Result<Self, crate::InferenceError> {
         options.convergence.validate()?;
         Self::validate_teams(teams)?;
         if options.score_sigma <= 0.0 || options.score_sigma.is_nan() {
@@ -638,7 +660,7 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         }
         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(
+        Ok(Self::new_scored(
             teams_owned,
             scores,
             weights,
@@ -647,7 +669,24 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         ))
     }
 
-    /// Convenience wrapper over [`Game::ranked`] for two single-competitor teams.
+    /// Two single-competitor teams: the common case, without the nesting.
+    ///
+    /// Returns a `Game` like every other constructor. It used to return
+    /// `(Gaussian, Gaussian)` — the posteriors alone — which made it the one
+    /// member of the family you could not ask for
+    /// [`log_evidence`](Game::log_evidence). Call `.posteriors()` for the old
+    /// shape:
+    ///
+    /// ```
+    /// # use trueskill_tt::{ConstantDrift, Game, GameOptions, Gaussian, Outcome, Rating};
+    /// # let a: Rating = Rating::new(Gaussian::from_ms(25.0, 8.0), 4.0, ConstantDrift::new(0.0));
+    /// # let b = a;
+    /// let game = Game::one_v_one(&a, &b, Outcome::winner(0, 2), &GameOptions::default())?;
+    /// let post = game.posteriors();
+    /// let (a_post, b_post) = (post[0][0], post[1][0]);
+    /// # let _ = (a_post, b_post);
+    /// # Ok::<(), trueskill_tt::InferenceError>(())
+    /// ```
     ///
     /// # Errors
     ///
@@ -659,12 +698,12 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         b: &Rating<T, D>,
         outcome: crate::Outcome,
         options: &GameOptions,
-    ) -> Result<(Gaussian, Gaussian), crate::InferenceError> {
-        let game = Self::ranked(&[&[*a], &[*b]], outcome, options)?;
-        let post = game.posteriors();
-        Ok((post[0][0], post[1][0]))
+    ) -> Result<Self, crate::InferenceError> {
+        Self::ranked(&[&[*a], &[*b]], outcome, options)
     }
 
+    /// A free-for-all: every competitor is their own one-member team.
+    ///
     /// # Errors
     ///
     /// Wraps each competitor in a one-member team and delegates to
@@ -673,7 +712,7 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         competitors: &[&Rating<T, D>],
         outcome: crate::Outcome,
         options: &GameOptions,
-    ) -> Result<OwnedGame<T, D>, crate::InferenceError> {
+    ) -> Result<Self, crate::InferenceError> {
         let teams: Vec<Vec<Rating<T, D>>> = competitors.iter().map(|p| vec![**p]).collect();
         let team_refs: Vec<&[Rating<T, D>]> = teams.iter().map(|t| t.as_slice()).collect();
         Self::ranked(&team_refs, outcome, options)
@@ -703,7 +742,7 @@ mod tests {
         );
 
         let w = [vec![1.0], vec![1.0]];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![vec![t_a], vec![t_b]],
             &[0.0, 1.0],
             &w,
@@ -731,7 +770,7 @@ mod tests {
         );
 
         let w = [vec![1.0], vec![1.0]];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![vec![t_a], vec![t_b]],
             &[0.0, 1.0],
             &w,
@@ -759,7 +798,7 @@ mod tests {
         );
 
         let w = [vec![1.0], vec![1.0]];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![vec![t_a], vec![t_b]],
             &[0.0, 1.0],
             &w,
@@ -793,7 +832,7 @@ mod tests {
         ];
 
         let w = [vec![1.0], vec![1.0], vec![1.0]];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             teams.clone(),
             &[1.0, 2.0, 0.0],
             &w,
@@ -810,7 +849,7 @@ mod tests {
         assert_ulps_eq!(b, Gaussian::from_ms(31.311358, 6.698818), epsilon = 1e-6);
 
         let w = [vec![1.0], vec![1.0], vec![1.0]];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             teams.clone(),
             &[2.0, 1.0, 0.0],
             &w,
@@ -827,7 +866,7 @@ mod tests {
         assert_ulps_eq!(b, Gaussian::from_ms(25.000000, 6.238469), epsilon = 1e-6);
 
         let w = [vec![1.0], vec![1.0], vec![1.0]];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             teams,
             &[1.0, 2.0, 0.0],
             &w,
@@ -867,7 +906,7 @@ mod tests {
         );
 
         let w = [vec![1.0], vec![1.0]];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![vec![t_a], vec![t_b]],
             &[0.0, 0.0],
             &w,
@@ -899,7 +938,7 @@ mod tests {
         );
 
         let w = [vec![1.0], vec![1.0]];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![vec![t_a], vec![t_b]],
             &[0.0, 0.0],
             &w,
@@ -935,7 +974,7 @@ mod tests {
         );
 
         let w = [vec![1.0], vec![1.0], vec![1.0]];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![vec![t_a], vec![t_b], vec![t_c]],
             &[0.0, 0.0, 0.0],
             &w,
@@ -972,7 +1011,7 @@ mod tests {
         );
 
         let w = [vec![1.0], vec![1.0], vec![1.0]];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![vec![t_a], vec![t_b], vec![t_c]],
             &[0.0, 0.0, 0.0],
             &w,
@@ -1024,7 +1063,7 @@ mod tests {
         ];
 
         let w = [vec![1.0, 1.0], vec![1.0], vec![1.0, 1.0]];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![t_a, t_b, t_c],
             &[1.0, 0.0, 0.0],
             &w,
@@ -1058,7 +1097,7 @@ mod tests {
         )];
 
         let w = [w_a, w_b];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![t_a.clone(), t_b.clone()],
             &[1.0, 0.0],
             &w,
@@ -1083,7 +1122,7 @@ mod tests {
         let w_b = vec![0.7];
 
         let w = [w_a, w_b];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![t_a.clone(), t_b.clone()],
             &[1.0, 0.0],
             &w,
@@ -1108,7 +1147,7 @@ mod tests {
         let w_b = vec![0.7];
 
         let w = [w_a, w_b];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![t_a, t_b],
             &[1.0, 0.0],
             &w,
@@ -1144,7 +1183,7 @@ mod tests {
         )];
 
         let w = [w_a, w_b];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![t_a, t_b],
             &[1.0, 0.0],
             &w,
@@ -1180,7 +1219,7 @@ mod tests {
         )];
 
         let w = [w_a, w_b];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![t_a, t_b],
             &[1.0, 0.0],
             &w,
@@ -1226,7 +1265,7 @@ mod tests {
         let result = vec![10.0, 0.0]; // a beat b by 10
         let weights = [vec![1.0], vec![1.0]];
         let mut arena = ScratchArena::new();
-        let g = Game::scored_with_arena(
+        let g = GameRef::scored_with_arena(
             teams,
             &result,
             &weights,
@@ -1246,7 +1285,7 @@ mod tests {
 
         // Tighter score_sigma should produce a stronger update.
         let mut arena2 = ScratchArena::new();
-        let g_tight = Game::scored_with_arena(
+        let g_tight = GameRef::scored_with_arena(
             vec![vec![prior], vec![prior]],
             &result,
             &weights,
@@ -1357,7 +1396,7 @@ mod tests {
         let w_b = vec![0.9, 0.6];
 
         let w = [w_a, w_b];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![t_a.clone(), t_b.clone()],
             &[1.0, 0.0],
             &w,
@@ -1392,7 +1431,7 @@ mod tests {
         let w_b = vec![0.7, 0.4];
 
         let w = [w_a, w_b];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![t_a.clone(), t_b.clone()],
             &[1.0, 0.0],
             &w,
@@ -1427,7 +1466,7 @@ mod tests {
         let w_b = vec![0.7, 2.4];
 
         let w = [w_a, w_b];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![t_a.clone(), t_b.clone()],
             &[1.0, 0.0],
             &w,
@@ -1459,7 +1498,7 @@ mod tests {
         );
 
         let w = [vec![1.0, 1.0], vec![1.0]];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![
                 t_a.clone(),
                 vec![R::new(
@@ -1480,7 +1519,7 @@ mod tests {
         let w_b = vec![1.0, 0.0];
 
         let w = [w_a, w_b];
-        let g = Game::ranked_with_arena(
+        let g = GameRef::ranked_with_arena(
             vec![t_a, t_b.clone()],
             &[1.0, 0.0],
             &w,
@@ -1505,7 +1544,7 @@ mod tests {
 
         // Capped at 1 iteration: cannot fully propagate down a 4-team chain.
         let mut arena = ScratchArena::new();
-        let g_capped = Game::ranked_with_arena(
+        let g_capped = GameRef::ranked_with_arena(
             teams.clone(),
             &result,
             &weights,
@@ -1520,7 +1559,7 @@ mod tests {
 
         // Same inputs, plenty of iterations: fully converged.
         let mut arena = ScratchArena::new();
-        let g_full = Game::ranked_with_arena(
+        let g_full = GameRef::ranked_with_arena(
             teams,
             &result,
             &weights,
@@ -1552,7 +1591,7 @@ mod tests {
         let weights = vec![vec![1.0]; 4];
 
         let mut arena = ScratchArena::new();
-        let g_undamped = Game::ranked_with_arena(
+        let g_undamped = GameRef::ranked_with_arena(
             teams.clone(),
             &result,
             &weights,
@@ -1564,7 +1603,7 @@ mod tests {
 
         // alpha=0.5 with extra iterations: should reach the same fixed point.
         let mut arena = ScratchArena::new();
-        let g_damped = Game::ranked_with_arena(
+        let g_damped = GameRef::ranked_with_arena(
             teams,
             &result,
             &weights,
diff --git a/src/history.rs b/src/history.rs
index b361780..e21a896 100644
--- a/src/history.rs
+++ b/src/history.rs
@@ -3053,8 +3053,8 @@ mod tests {
 
     use super::*;
     use crate::{
-        ConstantDrift, EPSILON, Event, Game, Gaussian, Member, Outcome, P_DRAW, Team,
-        arena::ScratchArena,
+        ConstantDrift, EPSILON, Event, Gaussian, Member, Outcome, P_DRAW, Team,
+        arena::ScratchArena, game::GameRef,
     };
 
     /// #17: a slice's footprint must be O(competitors in the slice), not
@@ -3170,7 +3170,7 @@ mod tests {
         let observed = h.time_slices[1].skills.get(a).unwrap().posterior();
 
         let w = [vec![1.0], vec![1.0]];
-        let p = Game::ranked_with_arena(
+        let p = GameRef::ranked_with_arena(
             h.time_slices[1].events[0].within_priors(
                 false,
                 &h.time_slices[1].skills,
diff --git a/src/lib.rs b/src/lib.rs
index 98eb14c..d727c0d 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -154,7 +154,7 @@ pub use drift::{ConstantDrift, Drift};
 pub use error::{InferenceError, UnknownKeys};
 pub use event::{Event, Member, Team};
 pub use event_builder::EventBuilder;
-pub use game::{Game, GameOptions, OwnedGame};
+pub use game::{Game, GameOptions};
 pub use gaussian::Gaussian;
 pub use history::{History, HistoryBuilder, Joint};
 use matrix::Matrix;
diff --git a/src/time_slice.rs b/src/time_slice.rs
index 5a5e1bd..1f81ab1 100644
--- a/src/time_slice.rs
+++ b/src/time_slice.rs
@@ -9,7 +9,7 @@ use crate::{
     arena::ScratchArena,
     color_group::ColorGroups,
     drift::Drift,
-    game::Game,
+    game::GameRef,
     gaussian::Gaussian,
     rating::Rating,
     storage::{CompetitorStore, SkillStore},
@@ -141,10 +141,15 @@ impl Event {
         let teams = self.within_priors(false, skills, competitors);
         let result = self.outputs();
         let g = match self.kind {
-            EventKind::Ranked => {
-                Game::ranked_with_arena(teams, &result, &self.weights, p_draw, convergence, arena)
-            }
-            EventKind::Scored { score_sigma } => Game::scored_with_arena(
+            EventKind::Ranked => GameRef::ranked_with_arena(
+                teams,
+                &result,
+                &self.weights,
+                p_draw,
+                convergence,
+                arena,
+            ),
+            EventKind::Scored { score_sigma } => GameRef::scored_with_arena(
                 teams,
                 &result,
                 &self.weights,
@@ -409,7 +414,7 @@ impl<T: Time> TimeSlice<T> {
                 let result = event.outputs();
 
                 let g = match event.kind {
-                    EventKind::Ranked => Game::ranked_with_arena(
+                    EventKind::Ranked => GameRef::ranked_with_arena(
                         teams,
                         &result,
                         &event.weights,
@@ -417,7 +422,7 @@ impl<T: Time> TimeSlice<T> {
                         self.convergence,
                         &mut self.arena,
                     ),
-                    EventKind::Scored { score_sigma } => Game::scored_with_arena(
+                    EventKind::Scored { score_sigma } => GameRef::scored_with_arena(
                         teams,
                         &result,
                         &event.weights,
@@ -724,7 +729,7 @@ impl<T: Time> TimeSlice<T> {
             let result = event.outputs();
             match event.kind {
                 EventKind::Ranked => {
-                    Game::ranked_with_arena(
+                    GameRef::ranked_with_arena(
                         teams,
                         &result,
                         &event.weights,
@@ -735,7 +740,7 @@ impl<T: Time> TimeSlice<T> {
                     .log_evidence
                 }
                 EventKind::Scored { score_sigma } => {
-                    Game::scored_with_arena(
+                    GameRef::scored_with_arena(
                         teams,
                         &result,
                         &event.weights,
diff --git a/tests/equivalence.rs b/tests/equivalence.rs
index 46db26b..592ea49 100644
--- a/tests/equivalence.rs
+++ b/tests/equivalence.rs
@@ -23,8 +23,10 @@ fn ts_rating(mu: f64, sigma: f64, beta: f64, gamma: f64) -> R {
 fn game_1v1_golden_matches_historical() {
     let a = ts_rating(25.0, 25.0 / 3.0, 25.0 / 6.0, 25.0 / 300.0);
     let b = ts_rating(25.0, 25.0 / 3.0, 25.0 / 6.0, 25.0 / 300.0);
-    let (a_post, b_post) =
-        Game::<i64, _>::one_v_one(&a, &b, Outcome::winner(0, 2), &GameOptions::default()).unwrap();
+    let post = Game::<i64, _>::one_v_one(&a, &b, Outcome::winner(0, 2), &GameOptions::default())
+        .unwrap()
+        .posteriors();
+    let (a_post, b_post) = (post[0][0], post[1][0]);
     // Historical golden from pre-T2 test_1vs1 (team 0 wins):
     assert_ulps_eq!(
         a_post,
diff --git a/tests/game.rs b/tests/game.rs
index 6681990..35905b5 100644
--- a/tests/game.rs
+++ b/tests/game.rs
@@ -32,10 +32,16 @@ fn game_ranked_1v1_golden() {
 fn game_one_v_one_shortcut() {
     let a = default_rating();
     let b = default_rating();
-    let (a_post, b_post) =
+    let game =
         Game::<i64, _>::one_v_one(&a, &b, Outcome::winner(0, 2), &GameOptions::default()).unwrap();
+    let post = game.posteriors();
+    let (a_post, b_post) = (post[0][0], post[1][0]);
     assert!(a_post.mu() > 25.0);
     assert!(b_post.mu() < 25.0);
+
+    // It returns a game like every other constructor, so evidence is askable.
+    // Two identical ratings make either result equally likely.
+    assert!((game.log_evidence() - 0.5_f64.ln()).abs() < 1e-12);
 }
 
 #[test]
@@ -118,8 +124,10 @@ fn one_v_one_honours_the_draw_probability_it_is_given() {
         p_draw: 0.25,
         ..GameOptions::default()
     };
-    let (a_post, b_post) = Game::<i64, _>::one_v_one(&a, &b, Outcome::draw(2), &options)
-        .expect("a draw is representable once p_draw is positive");
+    let post = Game::<i64, _>::one_v_one(&a, &b, Outcome::draw(2), &options)
+        .expect("a draw is representable once p_draw is positive")
+        .posteriors();
+    let (a_post, b_post) = (post[0][0], post[1][0]);
 
     // A symmetric draw leaves the means alone and sharpens both sides.
     assert!((a_post.mu() - b_post.mu()).abs() < 1e-9);
@@ -135,8 +143,10 @@ fn one_v_one_honours_convergence_options() {
         convergence: ConvergenceOptions::default(),
         ..GameOptions::default()
     };
-    let (a_post, _) = Game::<i64, _>::one_v_one(&a, &b, Outcome::winner(0, 2), &options).unwrap();
-    assert!(a_post.mu() > 25.0);
+    let post = Game::<i64, _>::one_v_one(&a, &b, Outcome::winner(0, 2), &options)
+        .unwrap()
+        .posteriors();
+    assert!(post[0][0].mu() > 25.0);
 }
 
 /// `Game` is a public entry point that does not pass through `History`'s