diff --git a/src/statebag.py b/src/statebag.py
--- a/src/statebag.py
+++ b/src/statebag.py
@@ -31,6 +31,40 @@ def estimateDistance(diff):
 	return replacements+1 # ???
 
 
+## Update contents of diff1 by contents of diff2.
+def updateDiff(diff1,diff2):
+	res=[]
+	i=j=0
+	m=len(diff1)
+	n=len(diff2)
+	while i<m and j<n:
+		(r1,c1,action1,item1)=diff1[i]
+		(r2,c2,action2,item2)=diff2[j]
+		if (r1,c1)==(r2,c2):
+			merged=transformSingle(action1,item1,action2,item2)
+			if merged: res.append((r1,c1,*merged))
+			i+=1
+			j+=1
+		elif (r1,c1)<(r2,c2):
+			res.append(diff1[i])
+			i+=1
+		else:
+			res.append(diff2[j])
+			j+=1
+	if i<m: res.extend(diff1[i:])
+	else: res.extend(diff2[j:])
+	return res
+
+
+def transformSingle(action1,item1,action2,item2):
+	if action1=="+":
+		if action2!="-":
+			return ("+",item2)
+	elif action2=="-": return ("-",item2)
+	elif (action1=="*" and item1==item2) or (action1=="-" and item1!=item2): return ("*",item2)
+	return None
+
+
 class GameTreeNode:
 	def __init__(self,parent,color):
 		self.parent=parent
@@ -54,11 +88,11 @@ class BoardState:
 	def __init__(self,board):
 		self._board=tuple(tuple(x for x in row) for row in board)
 		self.nodes=(GameTreeNode(self,BLACK),GameTreeNode(self,WHITE))
-		self.diff2Prev=None
+		self.cachedDiff=[]
 		self._hash=None
 
-	def tryConnect(self,s):
-		diff=self-s
+	def tryConnect(self,s,diff=None):
+		if diff is None: diff=self-s
 		distEst=estimateDistance(diff)
 		if distEst>3: return # we couldn't find every such move sequence anyway without a clever algorithm
 		weightEst=s.getWeight()+2-distEst
@@ -114,11 +148,13 @@ class StateBag:
 		sn=BoardState(board)
 		if len(self._states)>0:
 			if sn==self._states[-1]: return None # no change
-			sn.diff2Prev=sn-self._states[-1]
+			sn.cachedDiff=sn-self._states[-1]
 		else: sn.setWeight(1)
 
+		diff=sn.cachedDiff
 		for s in reversed(self._states):
-			sn.tryConnect(s)
+			sn.tryConnect(s,diff)
+			diff=updateDiff(s.cachedDiff,diff)
 		self._states.append(sn)
 		return sn