diff --git a/README.md b/README.md
index 0ee7365..dd7c936 100644
--- a/README.md
+++ b/README.md
@@ -67,10 +67,10 @@ On the first 20000 seeds, we have these scores and win rates (average ± standar
 
 |         |   2p    |   3p    |   4p    |   5p    |
 |---------|------------------|------------------|------------------|------------------|
-| cheat   | 24.8594 ± 0.0036 | 24.9785 ± 0.0012 | 24.9720 ± 0.0014 | 24.9557 ± 0.0018 |
-|         | 90.59 ± 0.21 % | 98.17 ± 0.09 % | 97.76 ± 0.10 % | 96.42 ± 0.13 % |
-| info    | 22.5194 ± 0.0125 | 24.7942 ± 0.0039 | 24.9354 ± 0.0022 | 24.9220 ± 0.0024 |
-|         | 12.58 ± 0.23 % | 84.46 ± 0.26 % | 95.03 ± 0.15 % | 94.01 ± 0.17 % |
+| cheat   | 24.8209 ± 0.0041 | 24.9781 ± 0.0012 | 24.9734 ± 0.0014 | 24.9618 ± 0.0017 |
+|         | 88.40 ± 0.23 % | 98.14 ± 0.10 % | 97.83 ± 0.10 % | 97.03 ± 0.12 % |
+| info    | 22.5217 ± 0.0125 | 24.7946 ± 0.0039 | 24.9356 ± 0.0022 | 24.9223 ± 0.0024 |
+|         | 12.55 ± 0.23 % | 84.48 ± 0.26 % | 95.05 ± 0.15 % | 94.04 ± 0.17 % |
 
 ## Other work
 
diff --git a/src/game.rs b/src/game.rs
index a037f0b..4e92989 100644
--- a/src/game.rs
+++ b/src/game.rs
@@ -654,6 +654,11 @@ impl GameState {
                     TurnResult::Hint(results)
                 }
                 TurnChoice::Discard(index) => {
+                    assert!(
+                        self.board.hints_remaining < self.board.hints_total,
+                        "Tried to discard while at max hint count"
+                    );
+
                     let card = self.take_from_hand(index);
                     debug!("Discard card in position {}, which is {}", index, card);
                     self.board.discard.place(card.clone());
diff --git a/src/strategies/cheating.rs b/src/strategies/cheating.rs
index fe24cd2..fd9bc94 100644
--- a/src/strategies/cheating.rs
+++ b/src/strategies/cheating.rs
@@ -163,6 +163,11 @@ impl PlayerStrategy for CheatingPlayerStrategy {
             return TurnChoice::Play(index);
         }
 
+        // cannot discard while at max hint count
+        if view.board.hints_remaining == view.board.hints_total {
+            return self.throwaway_hint(view);
+        }
+
         // discard threshold is how many cards we're willing to discard
         // such that if we only played,
         // we would not reach the final countdown round
diff --git a/src/strategies/examples.rs b/src/strategies/examples.rs
index a944a50..6f3f3eb 100644
--- a/src/strategies/examples.rs
+++ b/src/strategies/examples.rs
@@ -41,29 +41,27 @@ pub struct RandomStrategyPlayer {
 impl PlayerStrategy for RandomStrategyPlayer {
     fn decide(&mut self, view: &BorrowedGameView) -> TurnChoice {
         let p = rand::random::<f64>();
-        if p < self.hint_probability {
-            if view.board.hints_remaining > 0 {
-                let hint_player = view.board.player_to_left(&self.me);
-                let hint_card = rand::thread_rng()
-                    .choose(view.get_hand(&hint_player))
-                    .unwrap();
-                let hinted = {
-                    if rand::random() {
-                        // hint a color
-                        Hinted::Color(hint_card.color)
-                    } else {
-                        Hinted::Value(hint_card.value)
-                    }
-                };
-                TurnChoice::Hint(Hint {
-                    player: hint_player,
-                    hinted,
-                })
-            } else {
-                TurnChoice::Discard(0)
-            }
-        } else if p < self.hint_probability + self.play_probability {
+        if p < self.play_probability {
             TurnChoice::Play(0)
+        } else if view.board.hints_remaining == view.board.hints_total
+            || (view.board.hints_remaining > 0 && p < self.play_probability + self.hint_probability)
+        {
+            let hint_player = view.board.player_to_left(&self.me);
+            let hint_card = rand::thread_rng()
+                .choose(view.get_hand(&hint_player))
+                .unwrap();
+            let hinted = {
+                if rand::random() {
+                    // hint a color
+                    Hinted::Color(hint_card.color)
+                } else {
+                    Hinted::Value(hint_card.value)
+                }
+            };
+            TurnChoice::Hint(Hint {
+                player: hint_player,
+                hinted,
+            })
         } else {
             TurnChoice::Discard(0)
         }
diff --git a/src/strategies/information.rs b/src/strategies/information.rs
index c56652f..8a98b33 100644
--- a/src/strategies/information.rs
+++ b/src/strategies/information.rs
@@ -889,9 +889,9 @@ impl InformationPlayerStrategy {
             self.find_useless_cards(&view.board, &public_info.get_player_info(me));
         let useless_indices = self.find_useless_cards(&view.board, &private_info);
 
-        // NOTE When changing this, make sure to keep the "discard" branch of update() up to date!
-        let will_hint = if view.board.hints_remaining > 0
-            && public_info.someone_else_needs_hint(view)
+        // NOTE When changing this, make sure to keep the "discard" branch of update_wrapped() up to date!
+        let will_hint = if view.board.hints_remaining == view.board.hints_total
+            || (view.board.hints_remaining > 0 && public_info.someone_else_needs_hint(view))
         {
             true
         } else if view.board.discard_size() <= discard_threshold && !useless_indices.is_empty() {