diff --git a/include/haproxy/tools.h b/include/haproxy/tools.h
index 46fef67c5..ae900adfb 100644
--- a/include/haproxy/tools.h
+++ b/include/haproxy/tools.h
@@ -1055,4 +1055,20 @@ static inline int32_t ha_random()
 	return ha_random32() >> 1;
 }
 
+extern THREAD_LOCAL unsigned int statistical_prng_state;
+
+/* Xorshift RNGs from http://www.jstatsoft.org/v08/i14/paper.
+ * This has a (2^32)-1 period, only zero is never returned.
+ */
+static inline unsigned int statistical_prng()
+{
+	unsigned int x = statistical_prng_state;
+
+	x ^= x << 13;
+	x ^= x >> 17;
+	x ^= x << 5;
+	return statistical_prng_state = x;
+}
+
+
 #endif /* _HAPROXY_TOOLS_H */
diff --git a/src/debug.c b/src/debug.c
index 209199ab0..914c80de8 100644
--- a/src/debug.c
+++ b/src/debug.c
@@ -42,16 +42,6 @@
 volatile unsigned long threads_to_dump = 0;
 unsigned int debug_commands_issued = 0;
 
-/* Xorshift RNGs from http://www.jstatsoft.org/v08/i14/paper */
-static THREAD_LOCAL unsigned int y = 2463534242U;
-static unsigned int debug_prng()
-{
-        y ^= y << 13;
-        y ^= y >> 17;
-        y ^= y << 5;
-        return y;
-}
-
 /* dumps a backtrace of the current thread that is appended to buffer <buf>.
  * Lines are prefixed with the string <prefix> which may be empty (used for
  * indenting). It is recommended to use this at a function's tail so that
@@ -748,7 +738,7 @@ static struct task *debug_task_handler(struct task *t, void *ctx, unsigned short
 	t->expire = tick_add(now_ms, inter);
 
 	/* half of the calls will wake up another entry */
-	rnd = debug_prng();
+	rnd = statistical_prng();
 	if (rnd & 1) {
 		rnd >>= 1;
 		rnd %= tctx[0];
@@ -770,7 +760,7 @@ static struct task *debug_tasklet_handler(struct task *t, void *ctx, unsigned sh
 
 	/* wake up two random entries */
 	for (i = 0; i < 2; i++) {
-		rnd = debug_prng() % tctx[0];
+		rnd = statistical_prng() % tctx[0];
 		rnd = tctx[rnd + 2];
 
 		if (rnd & 1)
diff --git a/src/tools.c b/src/tools.c
index 1c43354bd..d3ee4265b 100644
--- a/src/tools.c
+++ b/src/tools.c
@@ -78,6 +78,12 @@ THREAD_LOCAL int itoa_idx = 0; /* index of next itoa_str to use */
 THREAD_LOCAL char quoted_str[NB_QSTR][QSTR_SIZE + 1];
 THREAD_LOCAL int quoted_idx = 0;
 
+/* thread-local PRNG state. It's modified to start from a different sequence
+ * on all threads upon startup. It must not be used or anything beyond getting
+ * statistical values as it's 100% predictable.
+ */
+THREAD_LOCAL unsigned int statistical_prng_state = 2463534242U;
+
 /*
  * unsigned long long ASCII representation
  *
@@ -5363,6 +5369,16 @@ size_t sanitize_for_printing(char *line, size_t pos, size_t width)
 	return pos - shift;
 }
 
+static int init_tools_per_thread()
+{
+	/* Let's make each thread start from a different position */
+	statistical_prng_state += tid * MAX_THREADS;
+	if (!statistical_prng_state)
+		statistical_prng_state++;
+	return 1;
+}
+REGISTER_PER_THREAD_INIT(init_tools_per_thread);
+
 /*
  * Local variables:
  *  c-indent-level: 8