Under the suggested new rule, team wins if either
(i) scores 0 or 1; the total chance of this is
or if
(ii) scores some , and then team scores at least The collective chance of this is
Overall, is the sum of all these quantities. That is
Notice that we can write the infinite sum in this expression as
You can now use the fact that
if to evaluate Then you can work out which after some simplification turns out to be