diff --git a/game_state.h b/game_state.h
index a6f5abd..60eee5f 100644
--- a/game_state.h
+++ b/game_state.h
@@ -43,6 +43,7 @@ constexpr std::array<std::string, 6> suit_initials{"r", "y", "g", "b", "p", "t"}
 struct Card {
   suit_t suit;
   rank_t rank;
+  bool was_in_initial_hand;
 
   Card &operator++();
   const Card operator++(int);
@@ -84,12 +85,26 @@ struct CardMultiplicity {
   auto operator<=>(const CardMultiplicity &) const = default;
 };
 
+template<typename T>
+struct InnerCardArray {
+    template<size_t N>
+    using array_t = std::array<T, N>;
+};
+
+template<>
+struct InnerCardArray<bool> {
+    template<size_t N>
+    using array_t = std::bitset<N>;
+};
+
 template <suit_t num_suits, typename T> struct CardArray {
     using value_type = T;
 
     CardArray() = default;
     explicit CardArray(value_type default_val);
 
+    void fill(value_type val);
+
     const value_type &operator[](const Card &card) const;
 
     value_type &operator[](const Card &card);
@@ -97,7 +112,8 @@ template <suit_t num_suits, typename T> struct CardArray {
     auto operator<=>(const CardArray &) const = default;
 
 private:
-    std::array<std::array<T, starting_card_rank>, num_suits> _array {};
+    using inner_array_t = typename InnerCardArray<T>::template array_t<starting_card_rank>;
+    std::array<inner_array_t , num_suits> _array {};
 };
 
 enum class ActionType {
@@ -195,6 +211,14 @@ private:
 
     static constexpr uint8_t no_endgame = std::numeric_limits<uint8_t>::max();
 
+    // This will save the card positions of all cards that are in the draw pile when we start backtracking
+    CardArray<num_suits, boost::container::static_vector<player_t, max_card_duplicity>> _card_positions_draw;
+    // This will indicate whether cards that were in hands initially still are in hands
+    CardArray<num_suits, bool> _card_positions_hands;
+
+    // A list of cards (set up once upon initialization) of all good cards that were in starting hands
+    std::array<boost::container::static_vector<Card, hand_size>, num_players> _good_cards_in_initial_draw_pile;
+
     // further statistics that we might want to keep track of
     uint8_t _pace{};
     uint8_t _score{};
diff --git a/game_state.hpp b/game_state.hpp
index 9320866..f4d45a5 100644
--- a/game_state.hpp
+++ b/game_state.hpp
@@ -37,14 +37,19 @@ namespace Hanabi {
     }
 
     template<suit_t num_suits, typename T>
-    CardArray<num_suits, T>::CardArray(T default_val) {
-        for(size_t suit = 0; suit < num_suits; suit++) {
+    void CardArray<num_suits, T>::fill(T val) {
+        for (size_t suit = 0; suit < num_suits; suit++) {
             for (rank_t rank = 0; rank < starting_card_rank; rank++) {
-                _array[suit][rank] = default_val;
+                _array[suit][rank] = val;
             }
         }
     }
 
+    template<suit_t num_suits, typename T>
+    CardArray<num_suits, T>::CardArray(T default_val) {
+        fill(default_val);
+    }
+
     template<suit_t num_suits, typename T>
     const T& CardArray<num_suits, T>::operator[](const Card &card) const {
         return _array[card.suit][card.rank];
@@ -247,6 +252,7 @@ namespace Hanabi {
 
     template<suit_t num_suits, player_t num_players, hand_index_t hand_size>
     void HanabiState<num_suits, num_players, hand_size>::normalize_draw_and_positions() {
+        // Note that this function does not have to be particularly performant, we only call it once to initialize.
         const Card trash = [this]() -> Card {
             for(suit_t suit = 0; suit < num_suits; suit++) {
                 if(_stacks[suit] < starting_card_rank) {
@@ -257,25 +263,44 @@ namespace Hanabi {
         }();
 
         CardArray<num_suits, std::uint8_t> nums_in_draw_pile;
-        std::uint8_t num_trash_in_draw_pile = 0;
         for(const auto [card, multiplicity] : _draw_pile) {
             if (_stacks[card.suit] > card.rank) {
                 nums_in_draw_pile[card] += multiplicity;
             } else {
-                num_trash_in_draw_pile++;
+                nums_in_draw_pile[trash] += multiplicity;
             }
         }
 
+        // Prepare draw pile
         _draw_pile.clear();
         for(suit_t suit = 0; suit < num_suits; suit++) {
             for(rank_t rank = 0; rank < starting_card_rank; rank++) {
-                Card card {suit, rank};
+                Card card {suit, rank, false};
                 if (nums_in_draw_pile[card] > 0) {
                     _draw_pile.push_back({card, nums_in_draw_pile[card]});
+                    if(!is_trash(card)) {
+                        _card_positions_draw[card].clear();
+                        _card_positions_draw[card].resize(nums_in_draw_pile[card], draw_pile);
+                    }
                 }
             }
         }
-        _draw_pile.push_back({trash, num_trash_in_draw_pile});
+
+        // Prepare cards in hands
+        for(player_t player = 0; player < num_players; player++) {
+            for(Card& card : _hands[player]) {
+                if(!is_trash(card)) {
+                    if(std::count(_good_cards_in_initial_draw_pile[player].begin(), _good_cards_in_initial_draw_pile[player].end(), card) > 0) {
+                        // This card is already in hand, so just replace the second copy by some trash
+                        card = trash;
+                    } else {
+                        _good_cards_in_initial_draw_pile[player].push_back(card);
+                        card.was_in_initial_hand = true;
+                    }
+                }
+            }
+        }
+        _card_positions_draw.fill(draw_pile);
     }
 
     template<suit_t num_suits, player_t num_players, hand_index_t hand_size>
diff --git a/main.cpp b/main.cpp
index b088764..18d86d6 100644
--- a/main.cpp
+++ b/main.cpp
@@ -40,7 +40,18 @@ namespace Hanabi {
 
 }
 
+#define CHECK(test, condition) if (!(condition)) { std::cerr << "Test " << (test) << " failed." << std::endl; }
+
+void test() {
+    {
+        auto game = Download::get_game("1005195", 43);
+        auto res = game->backtrack(1);
+        CHECK("1005195", res == static_cast<double>(7) / 8);
+    }
+}
+
 int main(int argc, char *argv[]) {
+  test();
   if(argc == 3) {
       std::string game (argv[1]);
       std::string turn (argv[2]);