Help devising a formula
Hi, this is way too complex for my meagre mathematical capabilities but wondered if anyone could help.
Your team regularly enters competitions. These competitions consist of a string of tasks done in a certain order. You know how many tasks need to be completed to win the competition but not which tasks will be involved. Once you complete one task you find out what the next task is. There is a pool of 10 tasks which can come up; once a task has been completed the same task cannot then come up in that particular competition. The number of tasks in any competition is set (and known to the players), but varies between competitions (it is always 10 or less).
The number of people in your team also varies between competitions (from 1 to 12). Each player has the possibility of doing 3 tasks per day. When given a task they have the choice of completing it or holding it. It is only possible to have one task at a time, so if a task is held no further tasks are allocated to that player until they chose to complete the outstanding task. If the task is completed that player has the opportunity of earning another task (up to a maximum of 3 tasks per day). Tasks are allocated to players entirely at random and may include tasks which have already been completed in that particular competition. It is possible for the same task to be allocated to more than one player.
Is should also be noted that the players in a team all play at different times throughout the day, with no guarantee of when a particular team member will be playing.
Is it possible to devise a formula the players could use to help them decide when it is better to complete a task (in the hope of gaining something more useful) or hold it (in the hope it becomes useful later) based on: the number of tasks in a competition, the number of uncompleted tasks in the competion, and the number of players participating?
I have racked my brains on this one but to no avail. Can anyone help, or will I have to admit defeat? Thanks for wading through all that anyway & apoligies if I have inadverantly posted in the wrong place.