Complexities of karma accounting It is of certain interest to me how does buddhism view the mechanics of karma accounting. By accounting I mean the weighing of intentions and outcomes and adjustment of the karmic ledger of the reincarnated unit - without a "supercomputer" to calculate all the expected probabilities.

Consider this example from the book [https://www.amazon.com/Three-Levels-Spiritual-Perception-Commentary/dp/0861713680] "The three levels of spiritual perception" by Kunga Tenpay Nyima:

"... there is a story in the Jakata Tales of one of the earlier lives of the Buddha as a bodhisattva. In that rebirth he was a sailor. While crossing a river in a ferry, through his bodhisattva's prescience he realized that one of the passengers was planning to kill all five hundred people aboard the ship. Quick as a wink, he killed the person intending the evil act. By doing so, he saved not only the other passengers but also the person who was planning to kill them, preventing him from committing such a terrible sin. Even though he did this at the price of killing a living being himself, because his intention was so good, and was motivated by compassion, both for the other passengers and for the would-be killer, it was, on balance a meritorious action."

Note the complexity of this scenario, and also extend it a bit in your imagination with other people suspecting that the killing could take place, and also the killer himself still debating in his mind as to whether to proceed and sink the ship. The bodhisattva could also not be 100% sure that the deed will eventually take place - as Buddhism rejects complete determinism and fatalism. There were other passenger with their intentions and decisions to act or not to act, passengers whose karma was to be punished on this ship and by not dying on that day the balance could have been changed for the worse. Imagine there were future killers among the passengers, etc etc. 

There was a web of intentions, partial knowledge, and unknown outcomes. 


How does karma calculation proceed in this case without a supercomputer?
How can we, as individuals, choose the right course of action without knowing the outcome of this complicated karmic accounting?
How does karma calculation proceed in this case without a supercomputer?

The weather is complicated too. People literally use supercomputers to run numerical models/simulations of the atmosphere, to predict the rain and wind. In other words, it requires a super-computer to predict the weather.

On the other hand the weather happened by itself, resolved itself, even before super-computers were invented.

Similarly karma can proceed without a super-computer even though people cannot calculate it exactly.

One of the suttas (Acintita Sutta) says that one should not conjecture "the results of kamma".

How can we, as individuals, choose the right course of action

Karma isn't quite like the weather: unlike karma, the planet's weather is more-or-less unaffected by what one person does, so there's no feedback loop between one person's actions and the fruits of the weather.

I think there are many ways to choose the right course of action:


We get good advice (or teaching) from other people
The Dhamma gives us rules of heuristics about right courses of action (e.g. the precepts and other Buddhist ethics, and, the eightfold path, and so on)
The Dhamma gives us insight into which variables are important to monitor: for example greed and anger (craving and aversion) are important; lay (social) responsibilities and personal (family) responsibilities are important; mindfulness is important; good-will is important, and so is equanimity, generosity, and so on; renunciation is important, dispassion is important; etc.
We experience results of action.
Buddhism sometimes suggests some alternative to conventional thought (for example choosing a "middle way" instead of one extreme or the other; or for example non-action instead of action)


Incidentally I beware of taking the Jataka tales literally, or even as a good example of how to behave; for example it's difficult for me to accept that story as proof that it's sometimes right to kill somebody.

Also, one of the characteristics of an enlightened Buddha is that they are able to know more: including being able to see the workings of karma more clearly than other people can.
There are some Buddhist practices or paths which involve learning how to act is if we were enlightened -- see the answers which describe tantrayana in this topic -- but these may require a teacher.

To repeat, I think we should be reluctant to understand that Jataka story as meaning that it's sometimes alright and even benevolent or beneficial to kill people (which might be a doctrine e.g. of the Hindu Bhagavad Gita). On the other hand that story illustrates a point: that according to Buddhism, your "intention" matters -- karma is described as "intentional action". I suspect that maybe pre-Buddhist doctrine taught that "ritual action" (e.g. Brahmins tending household fires) was important, and the Buddha countered that with a new (Buddhist) doctrine about intention.