Backgammon Cube Handling in Races

Cube Handling in Races

Forum Archive : Cube Handling in Races

One checker model

From:   Kit Woolsey
Address:   kwoolsey@netcom.com
Date:   24 February 1998
Subject:   Re: Doubling in a LONG races and Medium races
Forum:   rec.games.backgammon
Google:   kwoolseyEowGwv.KG8@netcom.com

Hugh Sconyers wrote: > Anyone interested in the equities for the one checker race should download > BG Interface from www.realtime.com/~sconyers . The interface allows you to > look up one checker races for all pipcounts from 1 to 300. The interface > is free. The 10% mentioned above is conservative, as you can see from the > following examples from BG Interface: > > Roller's Pipcount 70 > Opponent's Pipcount 80 > > CPW .779192 > > Equities: > Cubeless .558384 > Roller's Cube .872846 > Centered Cube .855556 > Opponent's Cube .494483 > > Double from Center > Redouble > Take > > --------------------------- > > Roller's Pipcount 70 > Opponent's Pipcount 81 > > CPW .794301 > > Equities: > Cubeless .588602 > Roller's Cube .900131 > Centered Cube .886554 > Opponent's Cube .529958 > > Double from Center > Redouble > Take > > ---------------------- > > For the medium and long races of one checker the following works really > well for Takes, Doubles and Redoubles, but not perfectly: > > TAKES: > > X = Roller's Pipcount - Opponent's Pipcount > Y = 10% of Roller's Pipcount (Round Y to nearest integer ex: for 79 Y = > 8, for 75 Y = 7) > > if X <= Y + 3 then Take > if X > Y + 3 Pass > > for ex: > > 75 vs 85 > > X = 85 -75 = 10 > Y = 7 > X <= 7 + 3 hence Take > > 75 vs 86 > X = 86 -75 = 11 > Y = 7 > X > 7 + 3 hence Pass > > 79 vs 90 > X = 90 - 79 = 11 > Y = 8 > X <= 8 + 3 hence Take > > 79 vs 91 > X = 91 - 79 = 12 > Y = 8 > X > 8 + 3 hence Pass > > __________________________ > > DOUBLES from CENTER: > > X = Roller's Pipcount - Opponent's Pipcount > Y = 10% of Roller's Pipcount (Y NOT rounded: for 79 Y = 7, for 73 Y = 7) > if X >= Y - 1 then double from center > > for ex: > > 90 vs 97 > X = 97 -90 = 7 > Y = 9 > X < 9 - 1 hence do not Double from center > > 90 vs 98 > X = 98 - 90 = 8 > Y = 9 > X >= 9 -1 hence do Double from center > > 71 vs 76 > X = 76 - 71 = 5 > Y = 7 > X < 7 - 1 hence do not Double from center > > 71 vs 77 > X = 77 - 71 = 6 > Y = 7 > X >= 7 -1 hence do Double from center > > ----------------------------------------- > REDOUBLES: > > X = Roller's Pipcount - Opponent's Pipcount > Y = 10% of Roller's Pipcount (Y NOT rounded: for 79 Y = 7, for 73 Y = 7) > if X > Y then redouble > > 46 vs 50 > X = 50 - 46 = 4 > Y = 4 > X <= Y hence do not Redouble > > 46 vs 51 > > X = 51 - 46 = 5 > Y = 4 > X > 4 hence Redouble > > ------------------------- > > For people who like rules in english: > > If your lead in a race is greater than or equal to 10% of your pipcount > less 1 then Double from the center. > > If your lead in race is greater than 10% of your pipcount then Redouble. > (The above percentages are not rounded.) > > If you are behind no more than 10% of your opponent's pipcount plus 3 > pips then Take. (This percentage is rounded and .5 is rounded down.) > > ex: > > roller's pipcount = 80 > > opponent's pipcount: is between 1 and 86, then no Double > opponent's pipcount: is 87, then Double from center but don't Redouble and > is a take > opponent's pipcount: > 88 and < 91, then Double and Redouble and is a take > opponent's pipcount: > 92, then Double and Redouble and Pass > > These are the rules I use in money play to decide on the proper cube > action. In matches you have to make adjustments for the match score. > They seem to work well. Keep in mind these racing rules are for race > with no hitting chances. If there are hitting chances then doubling > ,redoubling and take points change. Also, these rules come from looking > at races with one only checker, but imo one checker races are close to > backgammon races. An excellent discussion of the one checker model. However, I do not agree that the one checker race is close to a normal backgammon race. For the one checker race, obviously there is no wastage. Not so in a normal backgammon race. When you roll those double 4's, 5's, or 6's, while they are certainly nice numbers to roll, they do lead to some wastage. Since the trailer often needs those big doubles to overcome the racing deficit, the wastage when he rolls the big doubles will hurt him. The leader will also waste when he rolls the big doubles, but it won't matter to him since the big doubles will only extend his lead. Consequently, I believe the one checker model makes things rosier for the trailer than they actually are. As a test, I examined the following position. X (on roll), has 5 men on the 6 point, 4 on the 5 point, 3 on the 4 point, 2 on the 3 point, and 1 on the 2 point. 70 pips exactly, and the optimal bearoff structure for 70 pips and 15 checkers. O has the same position, except the checker on the 2 point was moved back to the 12 point, giving him 80 pips. I then gave this to jellyfish to roll out, 12960 times. It should be noted that on level 5 (where the rollouts were done) jellyfish won't always play O's first roll correctly (for example, it plays a 4-2 12/8, 4/2 rather than the proper 12/6), but the cost of this error is relatively small. Once the outfield checker is home, the program will play each side equally well or badly. Results: X won 80% of the games. This is far from the 77.9% in the one checker variation, and makes what would be a borderline take (in the one checker game) a big pass in real life. I'm sure the difference is because of the wastage for O when he rolls big doubles. Moving the outfield checker to the 11 point cut X's win percentage down to 78.5%, and moving it to the 10 point cut it further to 76.5% -- now a take, according the jellyfish using the cube (and it would also appear to be a take from Sconyer's results). Thus, for races of this length it appears that the 1 checker model makes the trailer appear to be about 1 1/2 or 2 pips better than he actually is. What about longer races? Here the wastage effect shouldn't be so serious, since if O rolls his big doubles early he can play them with no wastage. I tried tossing a couple of the checkers on the low points into the outfield, making the pip count 96 to 85 (increasing the pip difference from 10 to 11 to compensate for the longer race). Here, the rollout gave X 79.2% wins. Moving O one pip closer (95 to 85) the rollout gave X 77.7% wins, which is probably a borderline take/pass. My conclusion is that the one checker model favors the trailer, and the shorter the race the more it favors the trailer. It can be used profitably, but only if you make a 1 or 2 pip adjustment (depending on the length of the race). As always, other factors such as smoothness, men off, crossovers, etc. play an important role -- this model only works if the other factors are equal or have already been appropriately compensated for. Kit

Hugh Sconyers writes:

This does not seem like a 'fair' test, since one side has a checker in the outerboard. In addition, the one checker model and the rules listed above are NOT trying to predict equities, but ARE trying to predict cube decisions. I rolled this out 12960 times using Jellyfish on level 7 got X winning 79.2% of the games with a sd of .002. I don't consider either the 1.2% difference I got or Kit 2.1% a major difference given the position. I ran a simulation of the same position 30,000 times using my CD-ROM databases of 10 checkers vs 10 checkers ( needs 9 vs 9 also). The following where the results: CPW .791737 Equities: Cubeless .583476 Roller cube .764600 Center cube .721350 Opponent cube .517574 Lets look at a similar positions where the EXACT answer is know for all cube position: side on roll has 4-6 3-5 2-4 1-3 pipcount of 50 and his opponent has the same: EXACT answer: one checker 50 vs 50: one checker 50 vs 51 CPW .618189 .608351 .633297 Equities: Cubeless .236377 .216702 .266594 Roller cube .455154 .425768 .491951 Center cube .363817 .331952 .411079 Opponent cube .124417 .104259 .162208 Clearly, for this position the EXACT equities results are the same as the one checker equities, but close imo. But the cube decisions are the same for this position and one checker of 50 vs 50 (and for 50 vs 51). Also, note that for the one checker model this position understates the advantage of the side on roll, but by adding just ONE pip to the non-roller position the one checker model OVER-estimates the chances of side on roll!!!!!! In addition, for this position 50 vs 50 is much closer to right than 50 vs 51 and the rules listed predicted the correct cube decisions for this position. imo and also many others, one Jellyfish's weakest part is in races. Jellyfish makes plays that also no 'expert' would agree with. The arguement that these plays cancel out is just not correct. I agree with Kit that is most cases the one checker model favors the trailer when looking at equity, but when trying to decide takes, passes, double and redoubles I think the rules listed above get very close to the correct answers. I have a program running now that will find the 'best rules' for takes, passes, doubles and redoubles by looking at know exact results and the one checker model. It is running on PII-333 and looks like it will only take 2 years ..... lol Hugh

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