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Difficulty in explaining wastage/overage

Posted By: Nack Ballard
Date: Monday, 6 January 2025, at 9:24 p.m.

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

I don't think it's just Gabriel (unless she is super-stubborn). As a teacher, I can definitely relate. At first, I (too) found it a challenge to get the light bulb to turn on with some beginning and low intermediate students.

Your gift certificate analogy (though I think it can be improved) seems like a good idea. However, if you want to relate wastage directly to backgammon, I suggest trying something like this:

"You can only play as many pips as the dice gods give you. You are absolutely right that having four checkers on the 1pt is better than having four checkers on the 6pt -- in a vacuum. However, that is not the choice given to you. You don't get extra pips handed to you for nothing (in order to get to the ace point). [You might have to reiterate this several times in different ways.]

"The choice given to you is more like this:

"You, as White, have eight checkers remaining (that add up to 68 pips): four on the 11pt and four on the 6pt. [See diagram below.] You roll double 5s. Which of these three moves is "better" (will eventually get all of your checkers off the board with the fewest number of rolls on average):

(a) playing all four 5s from 11pt to 6pt,
(b) playing two 5s from 11pt to 1pt, or
(c) playing all four 5s from 6pt to 1pt?"

If her instinct is to prefer (b) or (c) or she thinks it shouldn't matter (e.g., "it depends on what I roll!"), offer to play two sides of the board, with (a) on your side, simultaneously with random, identical dice. I don't think it will take long for the concept of pip wastage to dawn and imprint on her. For added context, you could ring a bell or say "ding" whenever she bears off from the 1pt with a larger number.

I've encountered the argument, "Well, maybe "a" because it gets the checkers IN!" (which deflects from the issue). In that case, move White's 11pt checkers back to the 12pt or change the roll to double 4s, and ask the question afresh.

Nack





White is Player 2

score: 0
pip: 68
Unlimited Game
Jacoby Beaver
pip: 0
score: 0

Blue is Player 1
XGID=--------------d----d------:0:0:-1:00:0:0:3:0:10
White on roll, cube action?

eXtreme Gammon Version: 2.10

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