diff --git a/include/game_state.hpp b/include/game_state.hpp
index a48cb42..5cab931 100644
--- a/include/game_state.hpp
+++ b/include/game_state.hpp
@@ -215,6 +215,7 @@ namespace Hanabi
       }
     } else {
       _num_strikes++;
+      assert(_num_strikes <= max_num_strikes);
       _num_copies_left[played_card]--;
     }
 
@@ -646,6 +647,7 @@ namespace Hanabi
       // If we misplayed, then we lost the card and have to regain it now
       _num_copies_left[last_action.discarded]++;
       _num_strikes--;
+      assert(_num_strikes >= 0);
     }
     CHECK_DRAW_PILE_INTEGRITY;
   }
@@ -1033,8 +1035,9 @@ namespace Hanabi
     }
 
     // Check for discards now
-    if (_pace > 0 and _num_clues < max_num_clues)
+    if (_pace > 0 and (_num_clues < max_num_clues or _num_strikes < max_num_strikes))
     {
+      bool const play_card_instead_of_discarding = _num_clues == max_num_clues;
       // This will hold the index of trash to discard
       std::uint8_t const invalid_index = std::numeric_limits<std::uint8_t>::max();
       std::uint8_t discard_index = invalid_index;
@@ -1068,7 +1071,7 @@ namespace Hanabi
 
       // Discard if we found trash now
       if (discard_index != invalid_index) {
-        probability_t const probability_discard = check_play_or_discard(discard_index, false);
+        probability_t const probability_discard = check_play_or_discard(discard_index, play_card_instead_of_discarding);
 
         best_probability = std::max(best_probability, probability_discard);
         if (best_probability == 1)
@@ -1081,7 +1084,7 @@ namespace Hanabi
         // sacrifice cards in hand
         for(hand_index_t index = 0; index < hand_size; ++index) {
           if(!is_critical(hand[index])) {
-            probability_t const probability_sacrifice = check_play_or_discard(index, false);
+            probability_t const probability_sacrifice = check_play_or_discard(index, play_card_instead_of_discarding);
 
             best_probability = std::max(best_probability, probability_sacrifice);
             if (best_probability == 1)
@@ -1176,7 +1179,8 @@ namespace Hanabi
   template<suit_t num_suits, player_t num_players, hand_index_t hand_size>
   std::uint64_t HanabiState<num_suits, num_players, hand_size>::unique_id() const
   {
-    unsigned long id = 0;
+    // Encode strikes first, since they will often be zero.
+    unsigned long id = _num_strikes;
 
     // encode all positions of cards that started in draw pile
     ASSERT(_relative_representation.card_positions_draw.size() == _relative_representation.good_cards_draw.size());
@@ -1259,6 +1263,9 @@ namespace Hanabi
     std::vector<std::uint64_t> ret;
     std::vector<Card> cards;
 
+    // encode strikes first
+    ret.push_back(_num_strikes);
+
     // encode all positions of cards that started in draw pile
     ASSERT(_relative_representation.card_positions_draw.size() == _relative_representation.good_cards_draw.size());
     for (size_t i = 0; i < _relative_representation.card_positions_draw.size(); i++)