You always have a simple 50% strategy:
Whatever the opponent chooses, there are exactly 3 good spin results and 3 bad ones for you.
Your opponent always has a simple 50+% strategy:
Doing otherwise is always worse, or equal at best; there are no possible bullet configurations where there are more than 3 "good" spin results for the player going first.
My parents' blood types can be one of four scenarios, which are equally-likely since they are not conditioned on my own blood type (clarified in comments):
How likely is it for me to have inherited the different possibilities, under each of these parental scenarios?
Multiplying by 4 to turn these into integers instead of percentages, we get the following ...
As JNF says, your mother must have AB parents and be BB herself.
Applying the final point directly to your father, before taking into account information from your own blood type your priors for his genotype are
OO: $0.25$, AB: $0.25$, AA: $0.125$, AO: $0.125$, BB: $0.125$, BO: $0.125$.
Thus the probabilities of a given allele from your father (again ...
I think that where you're getting confused is in the framing of the question. The question is asking for the fewest number of candies we need to take in order to guarantee that 7 candies share a colour.
The scenario you gave results in 7 candies sharing a colour after picking 13 candies out. However, if I can find a scenario where after picking 13 or more ...