I need a formula for a betting app I am writing. It concerns multiple bets ie doubles and trebles. For a bet of 4 selections where all the selections are runners there are 6 doubles AB AC AD BC BD CD and 4 trebles ABC ABD ACD BCD. Now if any selection fails to run for whatever reason then the bet still stands so long as one of the selections involved still runs. So, if 2 selections fail to run, say A and B the doubles are changed thus :-
AB void
AC – C
AD – D
BC –C
BD –D
CD unchanged
The trebles are changed thus
ABC –C
ABD –D
ACD-CD
BCD-CD
If three of the selections fail to run, then all bets where those selections would have been included are altered in a similar manner. I need to be able to compute the changed multiples ie doubles trebles singles etc for all selections from 4 to 8. For the life of me I can’t figure it out. I wonder if anyone would be kind enough to provide a solution. Many thanks.