diff --git a/spot/misc/game.cc b/spot/misc/game.cc
index ad9c9674b..1c3e21f06 100644
--- a/spot/misc/game.cc
+++ b/spot/misc/game.cc
@@ -159,8 +159,6 @@ namespace spot
 
       bool solve(const twa_graph_ptr &arena)
       {
-        ensure_parity_game(arena, "solve_parity_game()");
-
         // todo check if reordering states according to scc is worth it
         set_up(arena);
         // Start recursive zielonka in a bottom-up fashion on each scc
@@ -171,7 +169,17 @@ namespace spot
             if (!info_->is_useful_scc(c_scc_idx_))
               {
                 for (unsigned v: c_states())
-                  w_.set(v, false);
+                  {
+                    w_.set(v, false);
+                    // The strategy for player 0 is to take the first
+                    // available edge.
+                    if ((*owner_ptr_)[v] == false)
+                      for (const auto &e : arena_->out(v))
+                        {
+                          s_[v] = arena_->edge_number(e);
+                          break;
+                        }
+                  }
                 continue;
               }
             // Convert transitions leaving edges to self-loops
@@ -195,14 +203,6 @@ namespace spot
         // All done -> restore graph, i.e. undo self-looping
         restore();
 
-        if (!std::all_of(w_.has_winner_.cbegin(), w_.has_winner_.cend(),
-                           [](bool b)
-                           { return b; }))
-          {
-            for (unsigned n = 0; n < w_.has_winner_.size(); ++n)
-              std::cerr << "hw[" << n << "]=" << w_.has_winner_[n] << '\n';
-          }
-
         assert(std::all_of(w_.has_winner_.cbegin(), w_.has_winner_.cend(),
                            [](bool b)
                            { return b; }));
@@ -234,7 +234,7 @@ namespace spot
 
       void set_up(const twa_graph_ptr &arena)
       {
-        owner_ptr_ = arena->get_named_prop<std::vector<bool>>("state-player");
+        owner_ptr_ = ensure_parity_game(arena, "solve_parity_game()");
         arena_ = arena;
         unsigned n_states = arena_->num_states();
         // Resize data structures
@@ -333,7 +333,7 @@ namespace spot
               {
                 // The outgoing edges are taken finitely often
                 // -> disregard parity
-                if (subgame_[e.dst] != unseen_mark)
+                if (info_->scc_of(e.dst) != c_scc_idx_)
                   {
                     // Edge leaving the scc
                     change_stash_.emplace_back(arena_->edge_number(e),
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 6f5494e3b..94e4ac645 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -393,6 +393,7 @@ TESTS_python = \
   python/dualize.py \
   python/ecfalse.py \
   python/except.py \
+  python/game.py \
   python/gen.py \
   python/genem.py \
   python/implies.py \
diff --git a/tests/python/game.py b/tests/python/game.py
new file mode 100644
index 000000000..9d77c153d
--- /dev/null
+++ b/tests/python/game.py
@@ -0,0 +1,63 @@
+#!/usr/bin/python3
+# -*- mode: python; coding: utf-8 -*-
+# Copyright (C) 2020 Laboratoire de Recherche et Développement de
+# l'EPITA.
+#
+# This file is part of Spot, a model checking library.
+#
+# Spot is free software; you can redistribute it and/or modify it
+# under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 3 of the License, or
+# (at your option) any later version.
+#
+# Spot is distributed in the hope that it will be useful, but WITHOUT
+# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+# or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
+# License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+import spot
+
+g = spot.automaton("""HOA: v1 States: 9 Start: 0 AP: 2 "a" "b"
+acc-name: Streett 1 Acceptance: 2 Fin(0) | Inf(1) properties:
+trans-labels explicit-labels state-acc spot-state-player: 0 1 0 1 0 1
+0 1 1 --BODY-- State: 0 {1} [1] 1 [1] 3 State: 1 {1} [1] 2 State: 2
+{1} [0] 8 State: 3 {1} [1] 4 State: 4 {1} [0] 5 State: 5 {1} [0] 6
+State: 6 {1} [1] 7 State: 7 State: 8 {1} [0] 2 --END--""")
+
+assert spot.solve_parity_game(g) == False
+
+s = spot.highlight_strategy(g).to_str("HOA", "1.1")
+assert s == """HOA: v1.1
+States: 9
+Start: 0
+AP: 2 "a" "b"
+acc-name: Streett 1
+Acceptance: 2 Fin(0) | Inf(1)
+properties: trans-labels explicit-labels state-acc !complete
+properties: !deterministic exist-branch
+spot.highlight.states: 0 5 1 4 2 4 3 5 4 5 5 5 6 5 7 5 8 4
+spot.highlight.edges: 2 5 3 4 6 5 8 5 9 4
+spot.state-player: 0 1 0 1 0 1 0 1 1
+--BODY--
+State: 0 {1}
+[1] 1
+[1] 3
+State: 1 {1}
+[1] 2
+State: 2 {1}
+[0] 8
+State: 3 {1}
+[1] 4
+State: 4 {1}
+[0] 5
+State: 5 {1}
+[0] 6
+State: 6 {1}
+[1] 7
+State: 7
+State: 8 {1}
+[0] 2
+--END--"""