diff --git a/src/backend/bootstrap/bootstrap.c b/src/backend/bootstrap/bootstrap.c
index 5c0fe9b715b..cded57e045a 100644
--- a/src/backend/bootstrap/bootstrap.c
+++ b/src/backend/bootstrap/bootstrap.c
@@ -202,6 +202,14 @@ AuxiliaryProcessMain(int argc, char *argv[])
 
 	MyStartTime = time(NULL);
 
+	/*
+	 * Initialize random() for the first time, like PostmasterMain() would.
+	 * In a regular IsUnderPostmaster backend, BackendRun() computes a
+	 * high-entropy seed before any user query.  Fewer distinct initial seeds
+	 * can occur here.
+	 */
+	srandom((unsigned int) (MyProcPid ^ MyStartTime));
+
 	/* Compute paths, if we didn't inherit them from postmaster */
 	if (my_exec_path[0] == '\0')
 	{
diff --git a/src/backend/tcop/postgres.c b/src/backend/tcop/postgres.c
index cf4d4ec356b..47651c4ceac 100644
--- a/src/backend/tcop/postgres.c
+++ b/src/backend/tcop/postgres.c
@@ -3620,6 +3620,14 @@ PostgresMain(int argc, char *argv[],
 		MyProcPid = getpid();
 
 		MyStartTime = time(NULL);
+
+		/*
+		 * Initialize random() for the first time, like PostmasterMain()
+		 * would.  In a regular IsUnderPostmaster backend, BackendRun()
+		 * computes a high-entropy seed before any user query.  Fewer distinct
+		 * initial seeds can occur here.
+		 */
+		srandom((unsigned int) (MyProcPid ^ MyStartTime));
 	}
 
 	SetProcessingMode(InitProcessing);