diff --git a/src/uu/sort/src/sort.rs b/src/uu/sort/src/sort.rs
index 06bcc7ff8..aa4d483c0 100644
--- a/src/uu/sort/src/sort.rs
+++ b/src/uu/sort/src/sort.rs
@@ -1398,7 +1398,22 @@ fn compare_by<'a>(
         let settings = &selector.settings;
 
         let cmp: Ordering = match settings.mode {
-            SortMode::Random => random_shuffle(a_str, b_str, &global_settings.salt.unwrap()),
+            SortMode::Random => {
+                // check if the two strings are equal
+                if custom_str_cmp(
+                    a_str,
+                    b_str,
+                    settings.ignore_non_printing,
+                    settings.dictionary_order,
+                    settings.ignore_case,
+                ) == Ordering::Equal
+                {
+                    Ordering::Equal
+                } else {
+                    // Only if they are not equal compare by the hash
+                    random_shuffle(a_str, b_str, &global_settings.salt.unwrap())
+                }
+            }
             SortMode::Numeric => {
                 let a_num_info = &a_line_data.num_infos
                     [a.index * global_settings.precomputed.num_infos_per_line + num_info_index];
diff --git a/tests/by-util/test_sort.rs b/tests/by-util/test_sort.rs
index 16437d526..8573ce03f 100644
--- a/tests/by-util/test_sort.rs
+++ b/tests/by-util/test_sort.rs
@@ -235,6 +235,16 @@ fn test_random_shuffle_two_runs_not_the_same() {
     }
 }
 
+#[test]
+fn test_random_ignore_case() {
+    let input = "ABC\nABc\nAbC\nAbc\naBC\naBc\nabC\nabc\n";
+    new_ucmd!()
+        .args(&["-fR"])
+        .pipe_in(input)
+        .succeeds()
+        .stdout_is(input);
+}
+
 #[test]
 fn test_numeric_floats_and_ints() {
     test_helper(