diff --git a/src/allmain.c b/src/allmain.c
index de1fb1557..1ca917a74 100644
--- a/src/allmain.c
+++ b/src/allmain.c
@@ -132,14 +132,13 @@ boolean resuming;
                         moveamt = youmonst.data->mmove;
 
                         if (Very_fast) { /* speed boots or potion */
-                            /* average movement is 1.67 times normal */
-                            moveamt += NORMAL_SPEED / 2;
-                            if (rn2(3) == 0)
-                                moveamt += NORMAL_SPEED / 2;
-                        } else if (Fast) {
-                            /* average movement is 1.33 times normal */
+                            /* gain a free action on 2/3 of turns */
                             if (rn2(3) != 0)
-                                moveamt += NORMAL_SPEED / 2;
+                                moveamt += NORMAL_SPEED;
+                        } else if (Fast) {
+                            /* gain a free action on 1/3 of turns */
+                            if (rn2(3) == 0)
+                                moveamt += NORMAL_SPEED;
                         }
                     }
 
diff --git a/src/mon.c b/src/mon.c
index 35966e381..f387655e7 100644
--- a/src/mon.c
+++ b/src/mon.c
@@ -582,6 +582,7 @@ mcalcmove(mon)
 struct monst *mon;
 {
     int mmove = mon->data->mmove;
+    int mmove_adj;
 
     /* Note: MSLOW's `+ 1' prevents slowed speed 1 getting reduced to 0;
      *       MFAST's `+ 2' prevents hasted speed 1 from becoming a no-op;
@@ -592,21 +593,24 @@ struct monst *mon;
     else if (mon->mspeed == MFAST)
         mmove = (4 * mmove + 2) / 3;
 
-    if (mon == u.usteed) {
-        if (u.ugallop && context.mv) {
-            /* average movement is 1.50 times normal */
-            mmove = ((rn2(2) ? 4 : 5) * mmove) / 3;
-        }
-    } else if (mmove) {
-        /* vary movement points allocated to slightly reduce predictability;
-           random increment (avg +2) exceeds random decrement (avg +1) by
-           a small amount; normal speed monsters will occasionally get an
-           extra move and slow ones won't be quite as slow */
-        mmove += rn2(5) - rn2(3); /* + 0..4 - 0..2, average net +1 */
-        if (mmove < 1)
-            mmove = 1;
+    if (mon == u.usteed && u.ugallop && context.mv) {
+        /* increase movement by a factor of 1.5; also increase variance of
+           movement speed (if it's naturally 24, we don't want it to always
+           become 36) */
+        mmove = ((rn2(2) ? 4 : 5) * mmove) / 3;
     }
 
+    /* Randomly round the monster's speed to a multiple of NORMAL_SPEED. This
+       makes it impossible for the player to predict when they'll get a free
+       turn (thus preventing exploits like "melee kiting"), while retaining
+       guarantees about shopkeepers not being outsped by a normal-speed player,
+       normal-speed players being unable to open up a gap when fleeing a
+       normal-speed monster, etc.*/
+    mmove_adj = mmove % NORMAL_SPEED;
+    mmove -= mmove_adj;
+    if (rn2(NORMAL_SPEED) < mmove_adj)
+        mmove += NORMAL_SPEED;
+
     return mmove;
 }