Reinforcements appear on a given roll. This is the method used by DBM to determine the appearance of flank marches. They appear on the turn after the owning player rolls a '6' on a D6. This method makes their appearance unpredictable, but the time frame in which the reinforcements appear is very variable, perhaps making them too unpredictable. It is possible that the reinforcements will never appear.
Reinforcements appear according to an increasingly easier random roll.
This is the method whereby they appear, for example, on a '6' on turn 1, a '5' or '6' on turn 2, a '4', '5' or '6' on turn 3 and so on, generally reaching a point where they automatically appear. What I tried to achieve with the 'Alan Roll' is a method of making their appearance of reinforcements unpredictable, but allowing them, on average, to appear around a certain time. On each turn the owning player rolls a dice and adds the score to the total of previous rolls. If the score exceeds the predetermined number then the reinforcements appear. Determining the initial number should be based on roughly when the reinforcements are expected to appear, and what type of die is going to be used to test for them.