Backgammon Cube Handling in Races

Cube Handling in Races

Forum Archive : Cube Handling in Races

Calculating winning chances

From:   OpenWheel
Address:   none
Date:   29 November 2005
Subject:   Bearoff calculation techniques.
Forum:   GammOnLine

Can someone steer me in the right direction as to how to figure my winning chances in some lopsided bearoffs, such as one like the following that came up for me today? X leads 9-point match: 6-0 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ 58 | O O O O O O | | O | | O O O O O O | | | | O O | | | | | | | | | | | | | | | | | | | | X X | | | | X X | | | | X X X | | | +---+ 40 | X X X X X | | | | 2 | +---+---+---+---+---+---+---+---+---+---+---+---+---+ +---+ 1 2 3 4 5 6 7 8 9 10 11 12

Raccoon writes:

I'll address the lopsided race, not adjusting for stacks and gaps and wastage. (1) For almost any race length, if you trail by 4 pips on roll, your GWC is about 50%. (2) For almost any race length, Leader's pipcount + 10% + 2 = about 78% GWC. (3) The value of each additiona pip beyond that declines quickly. Example: You trail on roll 50-46. You have about 50% GWC. You lead on roll 40-46. 40+4+2 = 46 -> you have about 78% GWC Going from 50-46 to 40-46, 10 pips better, gained you 28% GWC, so each pip was worth on average 2.8% GWC. Additional pips are worth much less than 2.8%. You could figure 40-46 = 78%, 40-50 = 85% (each additional pip being worth about 1.75%) and then I'd just add another 1% for each additional pip, so 40-58 comes to about 94% GWC. Of course you'd make an adjustment for the wasted pips. Check out Tom Keith's "Value of a pip" table at http://www.bkgm.com/rgb/rgb.cgi?view+1203 The table covers a range of leads from -14 to +10 and shows the average value of a pip at various race lengths. By going up and down the columns you can see how each pip's value changes depending on how close the race is.

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