Board Thread:News and Announcements/@comment-26581304-20150906194347/@comment-26871289-20150914042037

Caltain, you may have more insight into the actual algorithm used than I do. I still think it's theoretically possible to have at least 2 different approaches:

1. M% of all breeding attempts that could yield Z4 will instead yield Rare Z4 regardless of the combo used. In this case the likelihood of each possible outcome of the base case (without Rares) would be reduced by M% to account for the M% probability of Rare Z4. Under this algorithm it would be better to pick the combo with the lowest average cost of failure because there's an M% chance of success no matter which combo you choose. The lowest cost certainly wouldn't be Rare Z4 + Z4 as the failures would always cost 24 hours (or 18 with enhanced structures). The possibility of breeding outcomes like X1 and Y3 are actually favorable because they lower the time cost of the (1-M)% of attempts that aren't the desired Rare Z4.

2. N% of Z4 breeding "successes" will instead yield Rare Z4. This is the approach you describe. If the base probability of breeding Z4 (without Rares) is P%, then the probabilities of Z4 and Rare Z4 would be P*(1-N) and P*N respectively. Where other outcomes are available, their probabilities would remain unchanged and would sum up to 1-P. Under this algorithm it's best to maximize P at 100% by breeding Rare Z4 + Z4 because it actually increases overall chance of success by precluding nonproductive outcomes like X1 and Y3.

Whether BBB uses approach #1 or approach #2, it's also possible that the probabilities M and N are not constant, but rather are set depending on the breeding combo the player uses. BBB could set M1, M2, ..., Mx or N1, N2, ..., Nx such that the average time for one success (accounting for the average cost of failures) is approximately equal regardless of the combo employed. If BBB does this, then the difference between the two algorithms is fairly moot. And it would be probably be fairly difficult to identify the (marginally) optimal combo without either seeing the code or gathering copious data.

Even though there's the possibility of algorithm #1, I also suspect the actual implementation is algorithm #2. My evidence is only anecdotal, but nevertheless I always breed target Rare + target whenever the combo is available to me. I suppose this means that I doubt that BBB dials in the percentages for each possible combo. Though I'm uncertain whether any of this can definitively determined, I've enjoyed kicking around these ideas with you.