Backgammon – Playing to win

Backgammon is without a doubt a far more fascinating game than most of the modern players realize. It has been around for many years, the instructions are easy to follow which means anyone can play Backgammon.

Backgammon is a game that should be taken very seriously if you plan to play it for money. Although many gamblers presume that backgammon is just like any other gambling game, backgammon is in fact very much a game of skill.

The main goal of the game is for each player to get all their game pieces, (checkers) onto the home board and then to remove all the pieces off the Backgammon board, (bear off). The first player to achieve this is the winner of the game.

The movement of the pieces is dictated by the number of spots on each of the two dice rolled. As in chess or checkers only one player can move his pieces at a time and to determine who moves first, each player takes one dice and rolls it onto the right side of his board on the playing surface.

The player with the higher number plays both numbers and moves either one checker or two separate checkers the corresponding number of spaces equivalent to the spots on each die. In case of a tie, each player rolls one dice again until there are different numbers for each player.

The players will first roll the dice before every move. The player moves with whatever consists with the roll of the dice. If he rolls a 5 and 2, then he will move seven slots. You can break the moves up between two game pieces. In other words, he can move one five spaces and the other piece two. If the same number would appear on both dice rolled, then the active player would be allowed double what the number is. For example, if he rolls a 5-5, then the roller is allowed four moves of five, instead of two moves of five.

The checkers must always be moved forward around the board according to the numbers shown on the dice. The numbers on the two dice constitute separate moves. For example, if a player rolls 4 and 6, he may move one checker four spaces to an open point and another checker six spaces to an open point, or he may move the one checker a total of ten spaces to an open point, but only if one of the intermediate points (either four or six spaces from the starting point) is also open. The bar is not counted as a space.

The checkers are always moved around the board from a player’s outer board to his inner or homeboard.

A checker may be moved only to an open point, one that is not occupied by two or more opposing checkers. A checker may move to a point if it is occupied by only one of the opponent’s checkers. In this case the opposing checker is hit and placed on the bar.

The Bear Off is the final stage of the game when you remove your checkers from your home board. You cannot start this process until all 15 of your checkers have made it to your homeboard.
After all your checkers (or men as they are also known) are in the home board, you may bear them off according to the numbers on the dice you throw. You must use your entire roll, so if you roll a 5 and have no checkers on the 6pt or 5pt, you must take a checker off of the next highest point with checkers on it.
If you roll a 5 and have no checkers on the 5pt but you do have a checker on the 6pt, you must move the checker on your 6pt five spaces to the 1pt. You do not have to bear a checker off if you have another legal move which can be useful when your opponent is on the bar or still owns a point in your board.

If your opponent hits a blot while you are bearing off, you must enter that checker and bring it all the way around back to your home board before you can continue to bear off checkers. The first player to bear off all 15 checkers wins the game!

Backgammon Software – Do you need it?

Quite frankly, the answer to this question is yes ! Over the last 10 years, the standard of play in backgammon has improved tremendously, largely due to the availability of software programs such as Snowie, BGblitz, GNU-backgammon and Jellyfish.

Owning one of these programs is imperative if you are serious about raising your own standard of play. This will allow you to help analyze games , and understand the probabilities and mathematics behind the game.

You do have to take it reasonably seriously though. You have to not just play, but you also have to think about what the program is doing and why. Often cube decisions and checker plays have a lot to do with the match score. If you do not understand, for example, why the program will play very aggressively for a gammon in some situations and not seem to care about gammons in others, or why the programs doubling decisions are very different depending on match score, then you will not get the most value of of using the software.

If you like to play online for money, these programs will help you judge your actual ability. Take their ratings very seriously. If you are able to play with a Snowie error rate in 5 point matches or longer of under 5.0, you will be able to compete with the strongest players online. If you are in the 5-10 range, you will probably be ok, but I would not suggest playing for high stakes against strong players. If your Snowie error rate is over 10, we recommend you to stick to free play until your skill level improves.

Only recently I started using Snowie to analyze all my games. If you play backgammon at one of the leading backgammon servers such as ???? you will be able to export your games and analyze them later. As there are always thousands of players online I have no problem fnding a game and I analyze every game I play. This has resulted in my standard of play improving remarkably over the last 6 months and I am positive that if you take the same approach yours will too.

‘Hope to see you online !’

David

Reference positions in backgammon – Part I

One of the most useful tools a backgammon player can have is the reference position. A reference position is no more than a studied position that is close enough to a position that will arise in a game. The player can then use the reference position to make a decision should a related position come up.

We will begin with the simplest of reference positions :

referenceposition-1-1

Both players need three rolls here to remove all their checkers. Any double thrown will save a roll. The side who’s turn it is to play has been calculated to win 78.8% of their games. Also the other player can never offer a worthwhile redouble. The side taking the double in a real money game needs 25% without use of the cube. This situation calls for a double and pass.

Here is a position that is very closely related. If black fails to roll a double this is what will happen. Black is 74.5% to win the game.

referenceposition-1-2

But take a look at this play:

referenceposition-1-3

It is possible to calculate Blacks chances of winning here.

White is very likely thinking that the position is the same for a lot of rolls. If Black rolls 11 it will be as good as any double unless he rolls a 21 next and white throws doubles. Its a very small difference.

If White rolls 22 it will not save him a roll letting White stay in the game with about 25% chance of winning 3% of the time. This gains White about 0.7% wins.

If Black rolls a 21 things change drastically. Instead of being 25.5% favorite to win White becomes 100% favorite. White will double and black will drop. Black will roll 21 5.6% at any given time so this gains me 75% of 5.6% which is 4.2%.

In total with ownership of the cube included white gains 5% in wins from 21.2 to 26.2% and is now able to take the double.

Before we leave the subject of reference positions, let’s show just a few more racing positions.

referenceposition-1-4

In this position both players need 2 rolls. The side whos turn it is is 86.1% favorite to win the game. if you take 1296 rolls (36 for each side) the player throwing the dice first will win on the first throw 216 times. The opposing player will roll doubles 180 of the last 1080 rolls. This means that the player throwing second will win 180/1296 times or 13.9% of the time. This matters because there might well be a situation where you are playing White and trailing 5-1 in a best of 9 series and your opponent has the cube and doubles to 4.

You can also take a black checker and place it on your 3 or 4 point. As you have seen you can always calculate your odds of winning if you know what the odds are n the reference position.

referenceposition-1-5

A position which requires 4 rolls for each player leaves the side who’s turn it is roll 74.5% favorite to win.In a money game this translates into a double and a take. You should double in this situation because most of the time neither side will roll a double and then your opponent will have a pass next turn ensuring you get maximum cube value.

referenceposition-1-6

A 5 roll position will leave the players who’s turn it is favorite 71.7% of the time. You should not double in this position as both players will not roll a double the majority of the time leaving you with a better double on the next turn.

Backgammon Position #14 – The Gammon Factor

backgammon-position-14-1

This position is a typical blitz. White has been aggressively attacking black who now finds himself on the bar facing a four-point home board. White doubles. Should Black take the double?

Let us evaluate by using our four basic criteria:

The Race: – black trails by 13 pips in a long race. Black has chances of winning the race.

Position: – White has the better home board but black has only one checker back to white’s two. Black’s position is a little inflexible and having a third checker out of play on his 3-pt certainly does not help. I would estimate the position element as being the same for both players.

Threat: – White’s big threat is to close black out and then black will not be able to move again until the bear-off. On the other hand black threatens to escape his back checker when it will be white who has to escape his men. White’s threat is immediate and obvious so advantage to white.

Opponent: – In this sort of position it does help to know your opponent. Will he play the blitz aggressively? Does he understand the blitz? If he is a cautious player you have more room to take.

Overall then, advantage to white and certainly a double as the position is highly volatile. Can black take the double?

The answer is no and the reason is that when black loses, over 40% of the time that he does so, he will lose a gammon and four points. He will win more than the 25% of time but he doesn’t win often enough to offset the gammon losses.

Luckily there is a rule of thumb for these gammonish positions

Divide your expected gammon loss by 2 and add the figure to the “normal” take percentage of 25%. So if you expect to lose a gammon 20% of the time (i.e. when you lose the game one fifth of those losses will be gammons) then add 10% to the 25% to give 35%. If you can win the game 35% of the time then you can take otherwise you have to drop.

As you can see from the rollout data below black can win from this position about 30% of the time but he loses a gammon about 43% of the time (31.9 expressed as a percentage of 70.3). We can see that Black is nowhere near a take and he must pass the double. Many would be deceived by the closeness of the race and black’s sound structure and take but that would be to overlook the key to the position – the gammon rate!

backgammon-position-14-2

This article only looks at the very basics of the gammon factor – we will take a more detailed look in subsequent articles.

Backgammon Position #12 – A simple ending?

backgammon-position-12-a-simple-ending-1

Black was hoping for a double to clear his mid-point but luck has deserted him and now he has to play this 43. After discarding the horrible 13/9, 4/1 there are only two plays: (a) 13/6 and (b) 13/9, 13/10. Surely not too difficult a problem and one that most people would get right in live play? Unfortunately this statement is not true as I have used this position many times with pupils and a fair percentage get it wrong. There is a very large difference in equity between the two plays. One of the plays is a blunder – Do you know which one?

Here are the typical arguments for both plays

Play (a) is clearly correct. We get one checker to safety and we are then playing with only one blot. If it is hit (twenty four numbers out of thirty-six do hit next turn) then we may be able to scramble it home. White may well double before he rolls but with only one blot I think we can take. If we make play (b), get hit and then fan, having the other blot means we can’t take a double next turn. Play (b) is less shots (twenty-one) but far more dangerous.

Play (b) is clearly correct. We leave only twenty-one shots versus twenty-four shots with play (a). Even if one checker does get hit most of our entering numbers will safety the other blot. The two blots are really an illusion – it’s minimizing the number of shots that counts. Also, with only twenty-one shots I don’t think white can double.

So which argument do you personally prefer?

As I stated above the decision is not close (see the Snowie evaluation) and in fact play (b) is the clear winner. The vital factor is minimizing the number of shots. Look at it this way – play (a) increases white’s hitting chances by 14% – that’s a huge percentage in backgammon terms. Too many players are deceived by the fact that play (b) exposes two blots and they choose play (a).

As with all positions in backgammon it is crucial to understand the dynamics of a position and then choose a game plan that meets the requirements of the position. Here that plan is to get home while leaving as few shots as possible. Note also that with both plays if white misses black will double him out.

I have had some pupils double from the white side after play (b) because of two blots. This is a huge error as white only a marginal favourite and when he misses, as we have already seen, he cannot take a redouble. Even after play (a) white is not strong enough to double

backgammon-position-12-a-simple-ending-2

This is an very good reference position because this type of problem occurs time and time again.

Backgammon Position #11

In this article we are taking a look at a relatively simple bear-off position. Should black double? Should white take if doubled?

bearing-off-in-backgammon-01
In bear-offs we are unable to use our Race/Threat/Position/Opponent criteria to evaluate the position. We should still factor in the opponent but most of what we do know about bear-offs we know through study and the accumulation of a number of reference positions.

For example we know that a 3-roll vs 3-roll ending as shown below means a double for black and a drop for white.

bearing-off-in-backgammon-02

White wins only 21.2% of the time which nowhere near the 25% he needs to take. Also white never gets to redouble.

In the 4-roll vs 4-roll position shown below the cube action is now double/take:

bearing-off-in-backgammon-03

White now wins about 27% of the time and occasionally gets to use the cube to good effect. However beware. If we change this position by one pip to:

bearing-off-in-backgammon-04

The cube action reverts to double/drop. This is because double ones no longer result in bearing off four men and white may also throw four successive 1’s and on the last turn will not be able to bear-off his last checker. Small differences can mean a lot in backgammon.

When we make judgements in a bear-off we mentally refer to positions such as the ones above and compare. In our first position both sides have five checkers each so initially we might think it is a 3-roll vs 3-roll position and use that benchmark. But black in particular may well take 4 rolls (for example look what happens if black roll 42 followed by 42). It looks as if it is roughly a 3½ roll vs 3-roll position. This should give you the answer that white will have a comfortable take.

bearing-off-in-backgammon-05

Does black have a double? Barely – the position is volatile enough that by next turn black may well have lost his market so he must double now. Snowie confirms this:

C.Bray 2007

Backgammon Position #10

In this article we shall continue to look at the complexities of doubling by studying the position illustrated above. But before we do that we should take another look at the basic skills that you need to play backgammon well.

These are ;

Pattern Recognition – backgammon is to complex to analyse every position anew. You have to rely on your knowledge of the game that you have built up over time. When you are faced with a problem you call upon your experience and your mental model of the game. You make use of your store of reference positions so you can make a reasonable assessment of any new problem that you face. Without that storel of previous positions the game would be impossible and this explains why it will take a number of years to become a good player – you need to invest time building your reference library.

Arithmetic – it is impossible to become a good player without being able to do the basic arithmetic involved when calculating pip counts (although when playing backgammon online this is done for you) and counting shots. Good match players have to be able to make the match equity calculations.

Psychology – it is important to always remember that you are playing another human being. He/she will make errors of judgement and can be subject to psychological pressure particularly in situations where there is a threat of a gammon.

Of these factors the most important one is pattern recognition, making it critical to build your library of reference positions as quickly as you can . One way to do that is by studying and reading and that is why articles like this one can accelerate your learning. So what about this position? Should black double? Should white take?

backgammon-position-10

Let us use our key criteria to examine the position:

The Race.

Black is 7 pips ahead before the roll of the dice. A small advantage to black but there is a long way to go yet.

The Position.

Both sides have two point home boards. Black’s is better because he has the 4-pt rather than the 2-pt. He also has his 8-pt and his bar-point and is only one point away from having a five point prime. White has lost his 8-pt but has his mid-point. Black has slotted his opponent’s 5-pt whilst white’s three checkers are in danger of being hemmed in. Whilst white’s structure is weak all his checkers are still in play so he should be able to improve his position. Overall – a fairly large advantage to black.

The Threat.

Black is threatening to immediately make both 5 points. If he can make his own 5-pt he will have be in a very powerful position – having virtually won the game. White has no immediate threats but one good roll, for example a small double, could improve his position. Overall the advantage lies with black.

The Opponent. This is a unknown in this particular position so we will assume both players will make ‘normal’ cube decisions.

Black is ahead in all three of the key elements so he should double. Does white have enough chances so that he can venture a take?

This is where the reference library and experience come in. Many players would give this up as white but in fact he has just enough structure to make this a take. A big point is that he holds an anchor in his opponent’s home board. This will give him chances throughout the game and save him from being gammoned (at least for a lot of the time). Those who have seen this type of position before will know it is a take. Those trying to work it out from first principles may well pass. Thus here we see the advantage of experience.

The Snowie rollouts confirm that black must double and that white has a close but correct take.

Backgammon Position #9

In this article we are going to continue to take a look at the world of doubling. Black has just managed to hit with a lucky shot by playing 24/13* and white has danced. In the actual game from which this position was taken black redoubled and white very dropped quickly being outraged at the way the game went.

backgammon-position-9

This leads us to the first important lesson. There is no place for emotion when playing backgammon. If you allow emotion to creep into your game you will end up losing games quickly and often. This maybe easier to say then to do, but trust me you will rarely see a top backgammon player showing signs of emotion.

Now let us take a look at this position objectively using our criteria from the last article and evaluate both black’s and white’s doubling decisions.

Remember the four things you need to consider when doubling:

The Race.

White is 26 pips ahead before the roll. This is a big advantage to white.

The Position.

Both sides have four point boards. In fact has black a 4½ point board and is threatening to make it a five point board. Any 6 or 4, a total of 27 rolls will allow him to make that fifth point. White is on the bar but note that black’s last checker still has to escape. Overall the advantage lies with black.

The Threat.

Black has 27 good numbers and so he has a significant threat. However note that if he does not cover the blot white is favourite to enter and can then attack the black checker on his 1-pt (if it has not escaped). Advantage black.

The Opponent.

It is important to remember that unless you are playing a computer you have to take your opponent into consideration. How will he/she react to being doubled? Is he/she someone who drops takes or conversely takes drops? We have already seen that white did drop this redouble in the actual game.

Also remember that the generally accepted view is that you should consider doubling if you are ahead in two of the first three elements and use the fourth element to help you make your final decision.

Here black is ahead in two of the three elements and we know that white may drop the redouble. It is crystal clear that in practical terms black should redouble.

What about the take/drop? White should analyse as follows:

  • Even if black makes his 4-pt I will still re-enter immediately one time in three. With my lead in the race and my four point home board I am certainly still in the game.
  • On the 9 rolls he fails to make the point. I get a direct shot on three numbers (55, 52 and 25) and I am also favourite to enter immediately. Given my lead in the race these nine misses by black are very good for me.
  • The gammon threat is minimal.
  • All in all I think I can expect to win at least 25% of the time from here.
  • I take.

Key Points

  • Do not let emotion get in the way of your ability to analyse the game.
  • Do take the time to see if you can win the position (at least) 25% of the time.
  • Always evaluate the gammon threat.

Snowie evaluates the position as no double and take but it is unable to evaluate the human factor. In practical terms this is a definite redouble. However, as we have seen it is a comfortable take and in fact dropping, as white did, is a major mistake.

Backgammon Position #8

In this article we are taking a look at a pretty simple problem but one that many people (including myself) get wrong.

backgammon-position-8-1

What should blacks play be ? There are three options

(A) 20/14, 7/3

(B) 7/1*, 7/3

(C) 20/10

Before reading further take at few minutes to decide how you would play the roll and why.

Now let us look at the relative merits of each option:

(A) frees one checker out from behind white’s mini prime (note that 9 of black’s numbers will not let him move any of the checkers on his 21-pt). It also creates a five-point prime against white’s single back checker. On the downside any 6 by white will be a winning roll as he holds the doubling cube and can probably play on for a gammon without much risk. White does have some horror numbers in 55, 54 and 44 and 22 isn’t great.

(B) also creates a five-point prime but has the bonus advantage of putting white on the bar against a five-point board. The negative side of this play is the fact that there are still three black checkers partially trapped on white’s 4-pt.

(C) This will solve the problem of the three trapped checkers by freeing one of them. It gives white some additional bad numbers. Now 64 and 61 also leave black with a direct shot. The downside of this play is that if white rolls a 2 he will have a winning position unless black manages to re-enter immediately.

So which is the right play to make ? As with many decisions in backgammon it is a question of balancing the risk against the possible reward. You need to balance your experience with detailed analysis.

I personally got this wrong by playing (B)

backgammon-position-8-2
There are two key points to note about (A) & (C):

  • They both results in allowing a back checker to escape. Computer analysis has taught us the importance of escaping from behind even a small prime.
  • They will both allow white to leave another blot exposed with quite a few numbers. This will in turn lead to black winning more gammons – a factor that most people will have overlooked when doing their analysis.

(A) is the better option because, it is much easier for black to make a full prime after this roll than (C); it will win more gammons and it loses fewer gammons. In fact (C)wins it by a massive margin, just check the rollout numbers in the picture above.

C.Bray 2007

Backgammon Position #7

This week we take a look at the complex world of doubling. There are four things we need to consider when doubling:

backgammon-position-7-1

The Race. Backgammon is primarily a race so normally winning the race means winning the game. There are some obvious exceptions eg, when you have checkers trapped behind an opponent’s prime but the race is a good guide.

The Position. Who has the best static features in the position? By this i mean things like home board points, anchors in your opponent’s board, primes or potential primes and the number of blots.

The Threat. Do you have threats and in particular do you have threats, which if carried out, would mean that your opponent would no longer take next turn? A threat would include things like hitting a blot, making a key point in your home board, or extending/completing a prime.

The Opponent. Unless you are playing a computer you will need to take your opponent into consideration. How will he/she react to being doubled? Is he/she someone who drops takes or conversely takes drops?

The generally accepted view is that you should consider doubling if you are ahead in two of the first three elements and use the fourth element to help you make your final decision.

In the chouette from which this position was taken, white had erroneously played a 62 by moving 15/9, 3/1*. This minimised black’s shots to 15 instead of 18 after the correct 15/9, 15/13 but it exposed three blots instead of one.

Let us evaluate the position.

The Race

Black is behind by 20 pips before the roll. Advantage lies with white.

The Position

Black has the stronger home board of the two and an anchor in white’s home board. White’s position is something of a mess with there being too many checkers on his 1-pt and 2-pt. Advantage to black

The Threat

White has three vulnerable blots and if black hits one of them he may well pick up at least one of the other two. Black will win a lot of gammons because of his strong home board. Note also that white won’t be able to redouble black even if he should stay on the bar. The position is highly volatile as after nearly any hit by black white would be dropping next turn. Advantage black

The Opponent

Not a big factor in this position as white is a good player who makes well-balanced cube decisions.

The key question is whether black will win enough gammons after hitting to make up for the fact that he is not favourite to hit from the bar. This can really only be judged from experience as it is nearly impossible to do so over the board.

In the chouette the team correctly judged that they would win enough gammons and doubled. White correctly took, black rolled 12, hit the blot on white’s 1-pt, picked up the other two and won a gammon.

The Snowie rollout above shows that both black and white made the right cube decisions.

backgammon-position-7-2

Note that had white played his 62 correctly, 15/9, 15/13, and you then applied the criteria above you would find that black would not have had a double.

The key lessons are :

  • Do not expose unnecessary blots when your opponent has a strong home board.
  • Learn to use the criteria above to make your doubling decisions.