To go a bit off-track based on your final sentence: my high school physics teacher would do any numerical calculation that came up first in his head, as an esti

To go a bit off-track based on your final sentence: my high school physics teacher would do any numerical calculation that came up first in his head, as an estimate, and only then use a calculator or write on the board. Usually the estimate was within ±10-20% of the correct value even for long combinations of numbers with a bunch of decimals. Cube roots didn't come up, but square roots did. The point of that was to show the use of approximations and of having an idea how much a result should be, to guard against calculator typos and the like. I think that has some metaphorical relevance for the chess example.