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Do not always trust computers! Therefore the following positions is only simple reference bear-off positions, where I have been able to get an exact answer.
[ Simple cube handling | This might come as a surprise | Greedy Bear-off | Fill holes and unstack heavy points | Artificial holes | Avoid the gammon | Do not trust computer programs! | Practical computer programs ]
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The answer is double/drop! The 3 roll position
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The answer is double/take! The 4 roll position
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The answer is double/no redouble/take! The 5 roll position
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| 8 |
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The answer is no double/beaver! On the first roll there is only 5 marked losers and 10 rolls where you get doubled out. The beaver is marginal. If white moves 1 checker from the 24 to the 23 point he does not have a beaver.
| 2 |
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| 7 |
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The answer is double/take!
This is just a counting job.
19/36 rolls gets off.
This is a last roll
position (white has nothing to gain by recubing) which means that if blue has more than 50% he has a double.
| 12 |
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| 12 |
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The answer is double/take!
| 24 |
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| 24 |
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The answer is double/take!
| 43 |
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| 33 |
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The answer is double/take! Counting is not everything.
In normal
positions the rule of thumb is that trailing with 10% is a borderline cube decission.
| 10 |
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| 7 |
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The answer is double/no redouble/take! Crossovers are not everything.
This is close to a last roll
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| 9 |
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| 21 |
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The answer is 4/2 3/o no matter where the cube is. The interesting thing is that the play is not greedy and that it is a big mistake (blunder) to play the greedy alternative. This type of position is the only example where the greedy alternative is a significant mistake. A common rule is Bear-off greedy (maximize cross overs)!
| 9 |
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| 31 |
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The answer is 3/o 6/o no matter where the cube is. The blunder alternative 6/3 4/o is the worst legal play in this position. Bear-off greedy!
| 3 |
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| 12 |
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The answer is 1/o(2) 3/2(2). The greedy alternative 1/o(2) 2/o is clearly a tactical mistake. Blue has at best 1 roll left and has to maximize his chance of winning with that roll. 2-2 will win with the correct play and not with the greedy. This special tactical consideration is limmited to last roll positions like this. An even number of checkers will always result in greedy bear-off unless this type of consideration arise.
| 40 |
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| 40 |
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The answer is 3/1 6/o no matter where the cube is.
After you have beared off greedy fill empty holes.
To unstack a heavy point only comes in as a third priority.
The last rules have many counter examples.
See Artificial holes
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The answer is 3/o if it is a game with a cube (roller's, centered or opponent's). If the cube is the roller's or centered the roller just missed a double/take. In double match point (no cube) 2/1 2/o is equaly good! I have never seen a non trivial bear-off position where the cubes position makes a difference on the checker play.
| 9 |
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| 30 |
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The answer is 5/2 4/o no matter where the cube is. This is one of the few examples of a situation where greedy beeroff is a mistake. As you can see the position is extreem since the greedy Bear-off will create a position with two holes, and do nothing for the heavy point! On the other hand the correct play results in a position with an even number of checkers, no real holes, and an unstacked heavy point. It is not easy to come up with a position where the greedy alternative is wrong and if you do end in such a position the greedy alternative is almost never a big mistake (see Greedy Bear-off).
An artificial hole is a hole on the 3, 2 or 1 point where the 6, 4 or 2 point respectively is stacked.
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The answer is 1/o 2/o 6/5.
Gready of course but why slot the 5 point and not the 3 point?
The answer is that the 3 point is an artificial hole and the 5 point is a real hole.
If you roll a 3 next time you properbly will not have to waist any pips whereas if you roll a 5 and do not slot the point now you will have to move a checker to the 1 point.
Chekers on the low points will sometimes later be beared off with 5 or 6'es.
This means that you waist pips by stakking up the low points which is the result of not slotting real holes.
This knowlege is important since it is the reason behind a lott of plays.
Actually it is importent in all the above plays.
One play where it clearly playes an important role is the first cube handling under This might come as a surprise
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Look again at how 6-2 is played in this position:
| 40 |
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| 40 |
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As we saw 3/1 6/o was the answer. Why not play 4/2 instead of 3/1. The hole on the 2 point is more artificial than on the 1 point.
Surprisingly many mistakes are made when people are trying to avoid getting gammoned and the basic gameplan is quite simple.
To understand the gameplan in these types of positions you have to realize that you have a fixed (presently unknown) number of pips you can move at your disposal. To avoid getting gammoned you need to bring one checker off with thouse pips. To bring one checker off you need to have all your checkers in your homeland. So the idear is basicaly (with few exeptions) to waist the minimal number of pips bringing all your checkers in to your homeland.
To do that you need to focus on cross-overs. You make a cross-over when you bring a checker past or from the 7, 13 or even 19 point. Bearing a checker off or bringing a checker in from the bar is sometimes called a cross-over too.
The most important real cross-over you can make is bringing a checker to the 6-point. You waist no pips in acheaving your objective with a checker that is brought to your 6-point. If you can not bring a checker to your 6-point try maximizing your chance of bringing one there with your next roll. This is done by making the second type of crossover I mentioned (move past the 13-point) normaly without stacking points. If this is not possible try to make some other cross-over. Sometimes it is even correct to waist a pip or two doing this. You normaly do not want to copy your rolls unless the gammon risk is very high and you need doublerolls.
Finaly you need to take a good look at positions with only one or two rolls left. At this point in a game you should be able to look at all posible rolls and minimize your gammon risk. Ed has made a page where example 1 and 4 illustrates this in a fun way.
So the idear is to maximize cross-overs with the objective to bring checkers to the 6-point and look for tactics at the end.
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| 206 |
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The answer is no double/drop. If you manage to reach a position where your opponent have one checker on the bar against a closed board and have a crunched up board it is marginaly too good. Therefore this position is too good since there is no exchange of rolls where white escapes and therefore no marked gainer.
Never commit your self to play a computers side in a money game. Your opponent can play with the strategy to provoke a position where he has a forward rolling outside prime. If he can establish that he will double, and e.g. Snowie 3.1 will beaver! Snowie will then double and he will beaver. This will mean that if he can provoke a position like this the cube will easily reach 512. He can loose many doubled gammons for that price. Computers do not understand the value of an outside prime!
You can create backgammon boards on the internet using Backgammon Board Component Images. An easy way to construct an internet backgammon board is supplied by Claes Norreen.
Here you can find a very practical LaTeX STY-file for creating LaTeX documents about Backgammon positions or matches.
Last ofcause there is Gnu Backgammon.
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