Believing in Kammic efficacy seems to be a prerequisite in the teachings, which applies to the three types of kamma: white, black and neither white nor black. Linguistically, efficacy is rooted in the idea of efficiency, which is relevant to what achieves ends with the least amount of time and energy. Dibba cakkhu is a supramundane ability that seems to confirm kammic efficacy both in worldly and spiritual matters.
In worldly matters, dibba cakkhu is explained in the following terms:
How does the idea of "efficacy" translates into worldly matters that makes believing in kammic efficacy plausible? Imagine there is a shop or government agency where people are queuing up waiting for their turn at the desk, then a sexy woman appears and the lustful employee decides to give her a "special treatment" with the hope of impressing her or some other fantasy. Here where beauty becomes advantageous in terms of time and energy. Same thing can be said about money, which buys the time and energy of others, sparing pain and allowing for more sensual pleasure by the owner. It is described "efficient" to the extent that it works as a general rule, except for the "leakage" of impermanence, which prevents it from reaching "fullness" metaphorically speaking.With clairvoyance that is purified and superhuman, they see sentient beings passing away and being reborn—inferior and superior, beautiful and ugly, in a good place or a bad place. They understand how sentient beings are reborn according to their deeds: ‘These dear beings did bad things by way of body, speech, and mind. They spoke ill of the noble ones; they had wrong view; and they acted out of that wrong view. When their body breaks up, after death, they’re reborn in a place of loss, a bad place, the underworld, hell. These dear beings, however, did good things by way of body, speech, and mind. They never spoke ill of the noble ones; they had right view; and they acted out of that right view. When their body breaks up, after death, they’re reborn in a good place, a heavenly realm.’ And so, with clairvoyance that is purified and superhuman, they see sentient beings passing away and being reborn—inferior and superior, beautiful and ugly, in a good place or a bad place. They understand how sentient beings are reborn according to their deeds. This is the second knowledge that they attain. Ignorance is destroyed and knowledge has arisen; darkness is destroyed and light has arisen, as happens for a meditator who is diligent, keen, and resolute.
In terms of spiritual currency, or kamma that is neither white or black (the N8FP) it promises fullness by somehow eliminating the leakage of impermanence, or by using impermanence in a way that achieves an end that is certain. A sotapanna has his reward in the spiritual currency of seven lives maximum, before attaining fullness of some sort (arahntship). Dibba cakkhu was equally used by the Buddha to identify people with little dust in their eyes, which again establishes the link between kammic efficacy and the Buddhist path.
It seems that kammic efficacy is inseparable from kammic manifestations in the realm of the sense in advantageous ways and that include Buddhas, except that these advantages are not easy to understand neither in the case of the arahant, nor in the case of the worldling. In the case of the arahant, the 32 signs of a great man are used to identify Arahants by mystics, and in some suttas in DN, they kept on looking for the 32nd sign until the Buddha revealed it to them! It is indeed unclear what advantages "long fingers" would provide a Buddha. In the case of worldling, the perceived advantages might turn into curses, leading to more attachments to what is impermanent, which could lead to more pain than one who lacked these advantages all along.
Finally, the whole thing does not provide solid basis as to what our belief in kammic efficacy should be based on. Take our self-congratulatory talk as an example, how lucky we are to be born as humans and encountering the Buddha's teachings, which should be based on wholesome kamma done in the past. It would have been in service of faith to have Buddhists more attractive that other sects, but a simple look at monasteries and Buddhist countries would reveal that they are pretty average, at least based on how they look.
So, in light of the above, how best to understand kammic efficacy?