Let's say I have 50 addresses which have an average of 0.5 BTC. Some have two or three times the average balance, while others have less than 0.1% of the average. Many times per day an address is selected to either receive or send some amount of coins, fueling the inequality.
What's an efficient, cost-effective method of rebalancing a large number of addresses such that each contains roughly the average balance?
(Assume the algorithm to select a keypair with which to transact is fixed and cannot be modified for argument sake.)