diff --git a/common/dice/dice.go b/common/dice/dice.go
index 150a76134..39d771aed 100644
--- a/common/dice/dice.go
+++ b/common/dice/dice.go
@@ -25,7 +25,7 @@ func RollDeterministic(n int, seed int64) int {
 
 // RollUint16 returns a random uint16 value.
 func RollUint16() uint16 {
-	return uint16(rand.Intn(65536))
+	return uint16(rand.Int63() >> 47)
 }
 
 func RollUint64() uint64 {
diff --git a/common/dice/dice_test.go b/common/dice/dice_test.go
index 09b1dd4d3..05b364967 100644
--- a/common/dice/dice_test.go
+++ b/common/dice/dice_test.go
@@ -30,3 +30,21 @@ func BenchmarkIntn20(b *testing.B) {
 		rand.Intn(20)
 	}
 }
+
+func BenchmarkInt31(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		_ = uint16(rand.Int31() >> 15)
+	}
+}
+
+func BenchmarkInt63(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		_ = uint16(rand.Int63() >> 47)
+	}
+}
+
+func BenchmarkIntn(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		_ = uint16(rand.Intn(65536))
+	}
+}