Abstract
Cricket teams are usually listed on the scoreboard in expected batting order, and although captains can choose to send in any of the remaining batsmen when a wicket falls, they rarely depart from the usual batting order. By optimizing a simplified model using dynamic programming, this paper shows that in all forms of cricket significant increases in expected score result if captains allow a variable batting order and base their decision on the state of the game, rather than using a set batting order.