diff --git a/mctx/_src/search.py b/mctx/_src/search.py
index e844c73..7b9a74e 100644
--- a/mctx/_src/search.py
+++ b/mctx/_src/search.py
@@ -270,8 +270,12 @@ def body_fun(loop_state):
     action = tree.action_from_parent[index]
     reward = tree.children_rewards[parent, action]
     leaf_value = reward + tree.children_discounts[parent, action] * leaf_value
+    # Accumulate in at least float32 before returning to the tree's dtype.
+    value_dtype = jnp.promote_types(tree.node_values.dtype, jnp.float32)
     parent_value = (
-        tree.node_values[parent] * count + leaf_value) / (count + 1.0)
+        tree.node_values[parent].astype(value_dtype) * count
+        + leaf_value.astype(value_dtype)) / (count.astype(value_dtype) + 1.0)
+    parent_value = parent_value.astype(tree.node_values.dtype)
     children_values = tree.node_values[index]
     children_counts = tree.children_visits[parent, action] + 1
 
diff --git a/mctx/_src/tests/backward_precision_test.py b/mctx/_src/tests/backward_precision_test.py
new file mode 100644
index 0000000..25169af
--- /dev/null
+++ b/mctx/_src/tests/backward_precision_test.py
@@ -0,0 +1,136 @@
+# Copyright 2021 DeepMind Technologies Limited. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ==============================================================================
+"""Finite search averages for low-precision values and integer visit counts."""
+
+from absl.testing import absltest
+from absl.testing import parameterized
+import jax
+import jax.numpy as jnp
+import mctx
+from mctx._src import search
+import numpy as np
+
+
+def one_edge_tree(dtype, old_value, reward, visits):
+  root = mctx.RootFnOutput(
+      prior_logits=jnp.zeros((1, 2)),
+      value=jnp.array([old_value], dtype),
+      embedding=jnp.zeros((1, 1)),
+  )
+  tree = search.instantiate_tree_from_root(
+      root, 1, root_invalid_actions=jnp.zeros((1, 2)), extra_data=None
+  )
+  return tree.replace(
+      parents=tree.parents.at[0, 1].set(0),
+      action_from_parent=tree.action_from_parent.at[0, 1].set(0),
+      children_index=tree.children_index.at[0, 0, 0].set(1),
+      children_rewards=tree.children_rewards.at[0, 0, 0].set(reward),
+      node_visits=tree.node_visits.at[0, 0]
+      .set(visits)
+      .at[0, 1]
+      .set(visits - 1),
+      children_visits=tree.children_visits.at[0, 0, 0].set(visits - 1),
+  )
+
+
+class BackwardPrecisionTest(parameterized.TestCase):
+
+  @parameterized.product(
+      dtype=[jnp.float16, jnp.bfloat16, jnp.float32],
+      use_jit=[False, True],
+      case=[
+          (60000.0, 60000.0, 1),
+          (60000.0, -60000.0, 3),
+          (100.0, 200.0, 70000),
+      ],
+  )
+  def test_backup_matches_wide_reference_without_changing_storage(
+      self, dtype, use_jit, case
+  ):
+    old, reward, count = case
+    tree = one_edge_tree(dtype, old, reward, count)
+    stored_old = float(tree.node_values[0, 0])
+    stored_reward = float(tree.children_rewards[0, 0, 0])
+    expected = (stored_old * count + stored_reward) / (count + 1)
+    operation = jax.jit(search.backward) if use_jit else search.backward
+    result = operation(tree, jnp.array([1]))
+    self.assertEqual(result.node_values.dtype, dtype)
+    self.assertTrue(bool(jnp.isfinite(result.node_values).all()))
+    tolerance = (
+        0.008
+        if dtype == jnp.bfloat16
+        else 0.001
+        if dtype == jnp.float16
+        else 1e-6
+    )
+    np.testing.assert_allclose(
+        result.node_values[0, 0], expected, rtol=tolerance
+    )
+    self.assertEqual(int(result.node_visits[0, 0]), count + 1)
+    self.assertEqual(int(result.children_visits[0, 0, 0]), count)
+    np.testing.assert_array_equal(result.parents, tree.parents)
+    np.testing.assert_array_equal(
+        result.children_rewards, tree.children_rewards
+    )
+
+  @parameterized.product(use_jit=[False, True], initial=[0.0, 60000.0])
+  def test_public_muzero_preserves_finite_high_reward_averages(
+      self, use_jit, initial
+  ):
+    dtype = jnp.float16
+    root = mctx.RootFnOutput(
+        prior_logits=jnp.zeros((1, 2)),
+        value=jnp.array([initial], dtype),
+        embedding=jnp.zeros((1, 1)),
+    )
+
+    def recurrent(params, key, action, embedding):
+      del params, key, action
+      return (
+          mctx.RecurrentFnOutput(
+              reward=jnp.full(1, 60000.0, dtype),
+              discount=jnp.zeros(1, dtype),
+              prior_logits=jnp.zeros((1, 2)),
+              value=jnp.zeros(1, dtype),
+          ),
+          embedding,
+      )
+
+    def policy():
+      return mctx.muzero_policy(
+          None,
+          jax.random.PRNGKey(0),
+          root,
+          recurrent,
+          num_simulations=4,
+          dirichlet_fraction=0.0,
+          max_depth=1,
+          qtransform=lambda tree, node: jnp.zeros_like(
+              tree.children_prior_logits[node]
+          ),
+      )
+
+    result = (jax.jit(policy) if use_jit else policy)()
+    self.assertTrue(bool(jnp.isfinite(result.search_tree.node_values).all()))
+    np.testing.assert_allclose(
+        result.search_tree.node_values[0, 0],
+        (initial + 4 * 60000.0) / 5,
+        rtol=0.002,
+    )
+    np.testing.assert_allclose(jnp.sum(result.action_weights, axis=-1), 1.0)
+
+
+if __name__ == '__main__':
+  absltest.main()