The simplest way I know of to do that is by a weighted linear combination. Both information gain and risk are quantifiable; one in bits and the other in probab

The simplest way I know of to do that is by a weighted linear combination. Both information gain and risk are quantifiable; one in bits and the other in probability (or log-odds which is also bits). Then the problem reduces to finding appropriate weights, which can be done with your favorite n-dimensional search algorithm. It may also be useful to consider how many remaining incorrect guesses there are in the game.