diff --git a/src/PacketFilter.cc b/src/PacketFilter.cc
index 7b0ef0fbee..c1c496235d 100644
--- a/src/PacketFilter.cc
+++ b/src/PacketFilter.cc
@@ -18,7 +18,7 @@ void PacketFilter::AddSrc(const IPAddr& src, uint32_t tcp_flags, double probabil
 	{
 	Filter* f = new Filter;
 	f->tcp_flags = tcp_flags;
-	f->probability = uint32_t(probability * RAND_MAX);
+	f->probability = probability * static_cast<double>(zeek::max_random());
 	auto prev = static_cast<Filter*>(src_filter.Insert(src, 128, f));
 	delete prev;
 	}
@@ -27,7 +27,7 @@ void PacketFilter::AddSrc(zeek::Val* src, uint32_t tcp_flags, double probability
 	{
 	Filter* f = new Filter;
 	f->tcp_flags = tcp_flags;
-	f->probability = uint32_t(probability * RAND_MAX);
+	f->probability = probability * static_cast<double>(zeek::max_random());
 	auto prev = static_cast<Filter*>(src_filter.Insert(src, f));
 	delete prev;
 	}
@@ -36,7 +36,7 @@ void PacketFilter::AddDst(const IPAddr& dst, uint32_t tcp_flags, double probabil
 	{
 	Filter* f = new Filter;
 	f->tcp_flags = tcp_flags;
-	f->probability = uint32_t(probability * RAND_MAX);
+	f->probability = probability * static_cast<double>(zeek::max_random());
 	auto prev = static_cast<Filter*>(dst_filter.Insert(dst, 128, f));
 	delete prev;
 	}
@@ -45,7 +45,7 @@ void PacketFilter::AddDst(zeek::Val* dst, uint32_t tcp_flags, double probability
 	{
 	Filter* f = new Filter;
 	f->tcp_flags = tcp_flags;
-	f->probability = uint32_t(probability * RAND_MAX);
+	f->probability = probability * static_cast<double>(zeek::max_random());
 	auto prev = static_cast<Filter*>(dst_filter.Insert(dst, f));
 	delete prev;
 	}
@@ -113,5 +113,5 @@ bool PacketFilter::MatchFilter(const Filter& f, const IP_Hdr& ip,
 			return false;
 		}
 
-	return uint32_t(zeek::random_number()) < f.probability;
+	return zeek::random_number() < f.probability;
 	}
diff --git a/src/PacketFilter.h b/src/PacketFilter.h
index a485b604e8..c450120ee4 100644
--- a/src/PacketFilter.h
+++ b/src/PacketFilter.h
@@ -34,7 +34,7 @@ public:
 private:
 	struct Filter {
 		uint32_t tcp_flags;
-		uint32_t probability;
+		double probability;
 	};
 
 	static void DeleteFilter(void* data);
diff --git a/src/util.cc b/src/util.cc
index cccc65db8c..ff488226c3 100644
--- a/src/util.cc
+++ b/src/util.cc
@@ -1183,13 +1183,21 @@ bool have_random_seed()
 	return bro_rand_determistic;
 	}
 
+constexpr uint32_t zeek_prng_mod = 2147483647;
+constexpr uint32_t zeek_prng_max = zeek_prng_mod - 1;
+
+long int zeek::max_random()
+	{
+	return bro_rand_determistic ? zeek_prng_max : RAND_MAX;
+	}
+
 long int zeek::prng(long int state)
 	{
 	// Use our own simple linear congruence PRNG to make sure we are
 	// predictable across platforms.  (Lehmer RNG, Schrage's method)
 	// Note: the choice of "long int" storage type for the state is mostly
 	// for parity with the possible return values of random().
-	constexpr uint32_t m = 2147483647;
+	constexpr uint32_t m = zeek_prng_mod;
 	constexpr uint32_t a = 16807;
 	constexpr uint32_t q = m / a;
 	constexpr uint32_t r = m % a;
diff --git a/src/util.h b/src/util.h
index e30b7650e5..c699204915 100644
--- a/src/util.h
+++ b/src/util.h
@@ -604,7 +604,14 @@ long int prng(long int state);
  * Wrapper for system random() in the default case, but when running in
  * deterministic mode, uses the platform-independent zeek::prng()
  * to obtain consistent results since implementations of rand() may vary.
+ * @return  A value in the range [0, zeek::max_random()].
  */
 long int random_number();
 
+/**
+ * @return The maximum value that can be returned from zeek::random_number().
+ * When not using deterministic-mode, this is always equivalent to RAND_MAX.
+ */
+long int max_random();
+
 } // namespace zeek
diff --git a/src/zeek.bif b/src/zeek.bif
index 253e2d8822..1d09e4bddf 100644
--- a/src/zeek.bif
+++ b/src/zeek.bif
@@ -930,7 +930,7 @@ function hrw_weight%(key_digest: count, site_id: count%): count
 ##      provided by the OS.
 function rand%(max: count%): count
 	%{
-	auto result = bro_uint_t(double(max) * double(zeek::random_number()) / (RAND_MAX + 1.0));
+	auto result = bro_uint_t(double(max) * double(zeek::random_number()) / (zeek::max_random() + 1.0));
 	return zeek::val_mgr->Count(result);
 	%}
 
diff --git a/testing/btest/plugins/reader-plugin/src/Foo.cc b/testing/btest/plugins/reader-plugin/src/Foo.cc
index 6cae03ca18..a7e5021932 100644
--- a/testing/btest/plugins/reader-plugin/src/Foo.cc
+++ b/testing/btest/plugins/reader-plugin/src/Foo.cc
@@ -48,7 +48,7 @@ std::string Foo::RandomString(const int len)
 		// zeek::random_number() is not thread-safe; as we are only using one simultaneous thread
 		// here, this should not matter in this case. If this test ever starts showing
 		// random errors, this might be the culprit.
-		s[i] = values[zeek::random_number() / (RAND_MAX / sizeof(values))];
+		s[i] = values[zeek::random_number() / (zeek::max_random() / sizeof(values))];
 
 	return s;
 	}