diff --git a/tests/queries/0_stateless/03165_optimize_row_order_during_insert_cardinalities.reference b/tests/queries/0_stateless/03165_optimize_row_order_during_insert_cardinalities.reference
new file mode 100644
index 00000000000..b466509a965
--- /dev/null
+++ b/tests/queries/0_stateless/03165_optimize_row_order_during_insert_cardinalities.reference
@@ -0,0 +1,38 @@
+Alex	1	63	0
+Alex	1	65	0
+Alex	1	239	0
+Alex	2	224	0
+Alex	4	83	0
+Alex	4	134	0
+Alex	4	192	0
+Bob	2	53	0
+Bob	4	100	0
+Bob	4	177	0
+Bob	4	177	0
+Nikita	1	173	0
+Nikita	1	228	0
+Nikita	2	148	0
+Nikita	2	148	0
+Nikita	2	208	0
+Alex	1	63	1
+Alex	1	65	1
+Alex	1	239	1
+Alex	2	128	1
+Alex	2	128	1
+Alex	2	224	1
+Alex	4	83	1
+Alex	4	83	1
+Alex	4	134	1
+Alex	4	134	1
+Alex	4	192	1
+Bob	2	53	1
+Bob	2	53	1
+Bob	2	187	1
+Bob	2	187	1
+Bob	4	100	1
+Nikita	1	173	1
+Nikita	1	228	1
+Nikita	2	54	1
+Nikita	2	54	1
+Nikita	2	148	1
+Nikita	2	208	1
diff --git a/tests/queries/0_stateless/03165_optimize_row_order_during_insert_cardinalities.sql b/tests/queries/0_stateless/03165_optimize_row_order_during_insert_cardinalities.sql
new file mode 100644
index 00000000000..fef280970ca
--- /dev/null
+++ b/tests/queries/0_stateless/03165_optimize_row_order_during_insert_cardinalities.sql
@@ -0,0 +1,11 @@
+-- Checks that RowOptimizer correctly selects the order for columns according to cardinality, with an empty ORDER BY.
+-- There are 4 columns with cardinalities {name : 3, timestamp": 3, money: 17, flag: 2}, so the columns order must be {flag, name, timestamp, money}.
+
+DROP TABLE IF EXISTS tab;
+
+CREATE TABLE tab (name String, timestamp Int64, money UInt8, flag String) ENGINE = MergeTree ORDER BY () SETTINGS allow_experimental_optimized_row_order = True;
+INSERT INTO tab VALUES ('Bob', 4, 100, '1'), ('Nikita', 2, 54, '1'), ('Nikita', 1, 228, '1'), ('Alex', 4, 83, '1'), ('Alex', 4, 134, '1'), ('Alex', 1, 65, '0'), ('Alex', 4, 134, '1'), ('Bob', 2, 53, '0'), ('Alex', 4, 83, '0'), ('Alex', 1, 63, '1'), ('Bob', 2, 53, '1'), ('Alex', 4, 192, '1'), ('Alex', 2, 128, '1'), ('Nikita', 2, 148, '0'), ('Bob', 4, 177, '0'), ('Nikita', 1, 173, '0'), ('Alex', 1, 239, '0'), ('Alex', 1, 63, '0'), ('Alex', 2, 224, '1'), ('Bob', 4, 177, '0'), ('Alex', 2, 128, '1'), ('Alex', 4, 134, '0'), ('Alex', 4, 83, '1'), ('Bob', 4, 100, '0'), ('Nikita', 2, 54, '1'), ('Alex', 1, 239, '1'), ('Bob', 2, 187, '1'), ('Alex', 1, 65, '1'), ('Bob', 2, 53, '1'), ('Alex', 2, 224, '0'), ('Alex', 4, 192, '0'), ('Nikita', 1, 173, '1'), ('Nikita', 2, 148, '1'), ('Bob', 2, 187, '1'), ('Nikita', 2, 208, '1'), ('Nikita', 2, 208, '0'), ('Nikita', 1, 228, '0'), ('Nikita', 2, 148, '0');
+
+SELECT * FROM tab SETTINGS max_threads=1;
+
+DROP TABLE tab;