The computer will only consider moves to be complete in the case of multiple captures if the 'active' checker, that is, the checker that has already captured, has no further captures. Therefore it will not terminate multiple captures halfway because that would be illegal. We have described the algorithm in great detail in our research page. What we do is create a Vector of all the possible moves, and then consider these moves, calling the Minimax method recursively. The move consideration has all the checking inlined and does not consider spurious moves.
Illegal moves are, as far as possible, detected early and rejected.
Whenever possible, we have streamlined the engine. For example, redundant checking was present in the code to catch bugs, but these were later removed. Therefore, when the computer considers a position to generate a Vector of moves, it only looks once for forced captures, instead of doing so for every single considered walking move. An example of this may be crowning a new king, or the capture of two checkers. It sees that by forcing the player to make some other move, say by giving up one of its other checkers, it can forestall the first eventuality.