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Difficulty in explaining wastage/overage

Posted By: Sam Pottle
Date: Wednesday, 15 January 2025, at 8:25 a.m.

In Response To: Difficulty in explaining wastage/overage (Jason Lee)

This is great--it illustrates the nature (and challenge!) of teaching. Students are not all the same. They vary in which ideas will be easy for them, and in what sort of mental models of the subject they bring to you. So keep trying different things.

For wastage, you could try the old exercise where you give Gabriel 15 checkers on his six point, and you get three checkers each on your four through eight points. You bear in/off simultaneously, sharing dice rolls. If you can get him to sit still long enough to play through the exercise a few times, he should notice that you often win, but he almost never wins. (Sometimes you finish bearing off simultaneously.)

This lesson is a bit indirect; the stack side loses *because* it ends up stacking on the low points. A somewhat more direct lesson would be to start both sides with the unstacked position. Here you win because you're making better checker plays, but sadly you don't win as often, so you might need a lot of trials to make the point.

For overage, does Gabriel understand why the naive takepoint in an unlimited game is 25%? You probably need to get him thinking in terms of risk-reward tradeoffs here.

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