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WASTAGE AND VARIANCE

Posted By: Tom Keith
Date: Tuesday, 19 October 2010, at 2:01 p.m.

In Response To: WASTAGE AND VARIANCE (Ray Kershaw)

I don't have examples, but I can give a sense of the type of position that produces high wastage or high volatility.

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Wastage refers to the number of pips you expect to "waste" when bearing off your final checkers. Perhaps the highest wastage position is having all 15 of your checkers on the ace point because all your rolls other than 1-1 will waste pips. (And since you have an odd number of checkers your last roll will always waste a whole number.)

Any position that has many checkers on low-numbered points will be high in wastage. Gaps can also lead to wastage. For example, if you have a gap on your five point any 5's you roll will force you to move checkers from your six point to your ace point, and generally more than one checker on your ace point is wasteful.

Low wastage positions are "triangular" in appearance, with the most checkers on your six point and progressively fewer checkers on lower numbered points. The lowest wastage 15-checker position is the so-called "Trice Triangle", which has 7 checkers on the six point, 5 checkers on the five point, and 3 checkers on the four point.

Wastage is tied to the concept of "effective pip count" (aka "Trice count"). Your effective pip count (EPC) is the number of rolls you expect to use to take all your checkers off multiplied by 49/6 (the average pips per roll). EPC = normal pip count + wastage.

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Variance (or volatility) is a measure of how rapidly the equity of a position changes from one turn to the next. Volatility increases as you near the end of the game and bear more of your checkers off. It can be very high once you get down to just a couple checkers remaining.

High volatility forces you to double earlier than you would normally because it leads to more and bigger market losers. An extreme example of high volatility is: [You have a checker on 2 and 5; opponent has a checker on 1 and 2.] If you bear off both checkers (19/36), you win the game. If you miss (17/36), opponent wins the game.

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Note that wastage is a one-sided concept—your wastage is independent of your opponent's checkers. Volatility is a two-sided concept—it depends on the arrangement of both your checkers and your opponent's.

If you are thinking about doubling, wastage and volatility are both bad from an equity point of view. However it's interesting that high wastage forces you to double later and high volatility forces you to double earlier.

Messages In This Thread

• WASTAGE AND VARIANCE
  Ray Kershaw -- Tuesday, 19 October 2010, at 11:49 a.m.
  • WASTAGE AND VARIANCE
    Maik Stiebler -- Tuesday, 19 October 2010, at 1:03 p.m.
    • WASTAGE AND VARIANCE
      Bob Koca -- Tuesday, 19 October 2010, at 7:05 p.m.
      • WASTAGE AND VARIANCE
        Maik Stiebler -- Tuesday, 19 October 2010, at 7:40 p.m.
  • WASTAGE AND VARIANCE
    Tom Keith -- Tuesday, 19 October 2010, at 2:01 p.m.
    • WASTAGE AND VARIANCE
      Maik Stiebler -- Tuesday, 19 October 2010, at 2:23 p.m.
      • WASTAGE AND VARIANCE
        Tom Keith -- Tuesday, 19 October 2010, at 2:56 p.m.
  • WASTAGE AND VARIANCE
    Timothy Chow -- Tuesday, 19 October 2010, at 3:02 p.m.