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Short race cube, lop-sided score

Posted By: Ian Shaw
Date: Wednesday, 17 March 2010, at 2:15 p.m.

In Response To: Short race cube, lop-sided score (Ian Shaw)

I found it very tricky for two reasons: the position and the match score. Here's how I analysed it.

  • The position has six chequers a side but is far from a three-roll position.
  • I have trouble evaluating the efficiency of White's position. The empty three and five points cause wastage, but at least all odd numbers fill gaps, so it's maybe not as bad as it looks. I'm sure White wastes more than Blue, but by how much?
  • Rule 62/ Nack 57 would indicate that the last take for money is at (27-5)/7 = 3 pips. Does the rule even apply at quite such a low pipcount?
  • Assuming Rule 62 works. then if three pips is borderline for money (about 22% GWC) then I would allow 3% per pip in such a short race to get a Cubeless GWC of around 28%, less whatever I should allow for White's greater wastage.

    So how does that feed into the cube decision?

    Instinctively one would think that, trailing by 7 points, White should be taking more aggressively than for money. But I note that there are no gammons and Blue can still use 2, 4 or even 8 points, so maybe it's not so different after all.

    It's a longer match than I'm used to, so I'm struggling a bit with ME calculations.

  • Neil's numbers are 8-away = 6, 11-away = 5, 15-away = 4, 19-away = 3.5, so I interpolate to get 13-away = 4.5, 17-away = 3.75.
  • White's naive takepoint is:
    Take/Lose to -17 -8 = 16.25%
    Pass to -17 -9 = 20%
    Take/Win to -15 -10 = 30%

    White risks 3.75 to gain 10%, so takepoint = 3.75/13.75 = 15/55 = 3/11 = 27.27%. So, even though White is a long way behind in the match the takepoint is considerably higher than for money. This surprises me somewhat.

    The good news is that I can stop without considering the recube. I've estimated that I have something under 28% winning chances, but I'll surely have enough recube vig on a 4-cube to account for this.

    Double and take.

    *****************************************************

    As an exercise, I'll consider the recube to 4 in more detail.
    Blue take and Win to -6 -17 for 91% or so
    Blue pass to -10 -15 for 70%
    Blue take and lose to -10 -13 for 63.5%
    Blue risks 6.5 to gain 21, so the takepoint = 6.5/27.5 = 26/110 ≈ 23.4%

    I would guess that the recube efficiency is lower than the typical 0.7 because White's best chance is to roll a big set which would lose the market. So I'll go with 0.5 for the efficiency to simplify the math. Therefore, White's fully live takepoint would be 27.27 - (27.27 * 23.4 * 0.5) ≈ 27.3 - 3.6 = 23.7%

    Using the same estimate of 3% per pip, this result implies that White must drop almost 1 pip lower than for money.

    From this analysis, it looks like it pays to be cautious with the adage that the trailer can take deeper than for money, even on an initial cube when trailing in a match with a long way to go.

    (Alternatively, I've messed up the maths along the way: I've done it all in my head, as I would have to over the board.)

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