Astrology can help most tests, but has a chance of actually taking away a success from the roll, thought it is unlikely.
Ignoring the fiction and focusing only on the rules, is there any situation where accepting the astrology helping die actually reduces the chance of succeeding at a roll?
The factors one can play around with are: number of dice rolled, shade of the dice, obstacle, whether the roll is open or not. (Supposedly using deeds artha might also factor in. Feel free to consider it, also, if you feel like it.)
My intuition suggests that it would have to be a situation where one has a good probability of exactly matching the obstacle and little chance of missing it by only 1 success. However, achieving these at the same time seems difficult or maybe impossible. Rolling one white die with obstacle 1 does gain benefit from the astrology die, for example.
I am well aware that there are other reasons for not always helping everything with astrology; this is not the issue at hand. Let us focus on the probabilities, please.
I will accept an answer that gives a concrete case where the probability of failure with astrology is greater than without astrology, or a correct mathematical proof that such can never be the case. Extensive numerical calculations covering most possible cases might be accepted, also.
Please note that positive expected value of the astrology die does not constitute a proof.