Forum Archive : Strategy--Bearing Off

Wastage--Positions that minimize From:   Stig Eide Address:   stigei@james.stud.unit.no Date:   30 April 1996 Subject:   Re: 15 positions that minimize waste of pips in bear-off Forum:   rec.games.backgammon Google:   Pine.OSF.3.91.960428210340.13461A-100000@james.stud.unit.no Trice: > Your 2 2 2 3 3 3 distribution is good, given a 15 checker > position with a pip count of 48. (In fact, subject to these two > constraints, I believe it is optimal, but I'm going on memory.) It's close, but 1 2 3 4 3 2 is the optimal distribution. As pointed out by several, we can't control the pipcount. And then our initial posting with minimal pip-waste for 1-15 checkers left is not of much value, except for the 000357 position which should be the aim in the bear-in. As a consequence Eirik made a table of optimal boards for all possible combinations of pips and checkers left. Interested can get a postscript-file by emailing him: thaco@stud.unit.no Here's the optimal board for each pipcount, no matter how many checkers left. Interestingly, fewest checkers left is often not optimal: The 48-pip board 000008 (8 men at 6point) wastes 1.49 pips more than 000144. You can always transform pipwaste to expected rolls left: Just add the pipcount, and divide it with 8.1667. Enjoy.. 8-) 1:100000(7.17) 2:200000(6.17) 3:110000(5.17) 4:101000(4.62) 5:000010(4.30) 6:000001(4.21) 7:010010(5.05) 8:001010(5.26) 9:001001(5.32) 10:000101(5.11) 11:000011(5.01) 12:000002(5.23) 13:001101(5.40) 14:001011(5.40) 15:000111(5.31) 16:000021(5.45) 17:000012(5.47) 18:001111(5.67) 19:000211(5.79) 20:001012(5.73) 21:000112(5.53) 22:000022(5.65) 23:000013(5.85) 24:001112(6.06) 25:000212(6.05) 26:000122(5.89) 27:000113(5.97) 28:000023(6.05) 29:001122(6.21) 30:000222(6.25) 31:000132(6.23) 32:000123(6.15) 33:000114(6.33) 34:000024(6.38) 35:001123(6.37) 36:000223(6.38) 37:000133(6.36) 38:000124(6.39) 39:000034(6.55) 40:001133(6.56) 41:000233(6.53) 42:000224(6.55) 43:000134(6.51) 44:000125(6.62) 45:000035(6.74) 46:001134(6.66) 47:000234(6.63) 48:000144(6.69) 49:000135(6.67) 50:001234(6.77) 51:001144(6.81) 52:000244(6.76) 53:000235(6.75) 54:000145(6.78) 55:000136(6.83) 56:001235(6.86) 57:001145(6.87) 58:000245(6.82) 59:000236(6.88) 60:000146(6.89) 61:001245(6.92) 62:000345(6.93) 63:000255(6.94) 64:000246(6.91) 65:000156(6.99) 66:000147(7.00) 67:001246(6.98) 68:000346(6.98) 69:000256(6.98) 70:000247(7.00) 71:001346(7.05) 72:001256(7.04) 73:000356(7.03) 74:000347(7.05) 75:000257(7.04) 76:000248(7.09)-001356(7.09) 77:001347(7.11) 78:001257(7.09) 79:000357(7.07) 80:000267(7.11) 81:000258(7.11) 82:000249(7.18) 83:000159(7.22) 84:00014A(7.35) 85:00005A(7.48) 86:00004B(7.68) 87:00003C(7.99) 88:00002D(8.47) 89:00001E(9.19) 90:00000F(10.17) Where A,B,C,D,E and F represents 10,11,12,13,14 and 15 checkers. Stig Eide and Eirik Milch Pedersen   Did you find the information in this article useful?           Do you have any comments you'd like to add?

 

Strategy--Bearing Off

Greedy bearoff exception  (Stick+, Jan 2011) 

Playing for gammon  (Max Levenstein+, Aug 2011) 

Rules of thumb  (Rich Munitz+, Oct 2009) 

Wastage  (David Montgomery, Apr 1996) 

Wastage--Positions that minimize  (Stig Eide, Apr 1996) 

Which gaps to fill  (Kit Woolsey, Mar 1996) 

Winning the bearoff race  (Dave Flaks+, Jan 2001) 

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