Backgammon Lesson – 6

Beginners Please – Lesson 6

by Paul Money – September 2006

Welcome beginners! In a sense, we are all beginners at this game, as at all levels you will find players with gaps in their knowledge. I like to think of this as learning together rather than me teaching you.

Once you have learned to play, most people like to have a small wager on the game. It does add to the excitement and helps to keep the mind focused. A word of advice though, you have to find the right level of stake for you. It should be affordable, but meaningful. A very good guide is to decide on the maximum amount of money that you can afford to lose in a session and play for 1% of that per point. If a $100 loss for the evening is a painful, but affordable for you, play for a $1 a point.

Online, the amount of money that you can lose in a single game is set to a level that you decide beforehand. This is a very good plan and I would like to see it done in live play too.

A lot of live social play comes in the form of chouettes. A chouette is a group of players, somewhere between three and six is a good number, who all play on the same board. One player, known as “the box”, plays against the rest who play as a team, with a “captain” making the plays and having the final say on the play. If the box wins, the captain is demoted and another player takes his place. If the box loses, he goes to the bottom of the team, the captain becomes the new box and the next player in the team becomes the captain. Each player has their own doubling cube, which is fun!

Chouette rules vary so widely that I will not list them all here, but the basis remains the same, one player playing against a team. In some chouettes, all the players may advise the captain from the start, in others, they may only advise once their cube has been turned, but the consultation is a big part of the fun and also of course, the learning process.

Opportunities to use the cube can occur from the second roll onward and a missed opportunity can cost you a lot of money, so as you are shaking your dice (or before you click your mouse) just remind yourself where the cube is and ask yourself, “Should I double now?”

Let’s take a look at a money game – how should we play this opening 5-1 roll?

The only two plays tried these days are 24/23, 13/8 and 13/8, 6/5. The move of 24/18 had a short vogue and café players sometimes try 13/7, but neither of these is a realistic contender. Playing 24/23, 13/8 is probably the best play for beginners. It tends to lead to simpler games and it also avoids having to make the “When should I split?” decision later on, when it is more difficult. The 13/8, 6/5 move leads to more complex games, usually starting with a blot-hitting contest. Its main attraction for the best players is that it unstacks a checker from each of their tallest points. They like plays that do this because it leads to much greater flexibility, leading to more good rolls next turn. Weak players faced with a very strong opponent, such as the robot players that can be found on most servers, complain that the bots roll suspiciously well. They do roll well, but it isn’t suspicious. Good play leads to better dice!

When I said that slotting with the 1 led to more difficulty, this is the sort of thing that I had in mind. When Red makes the 5pt on the opening roll with a 3-1, it is well known (and worth remembering if you didn’t know) that a 6-2 response calls for White to play 24/18, 13/11. Because Red has seized the best point, White must play aggressively to try and exchange hits or grab an anchor on the bar point. Here, where Red is only threatening to make his 5pt, White must select the quieter 24/16! This is because of the 13 great numbers to hit and cover that Red will have if White stays on the 18pt. Playing 24/16, reduces these numbers to 6 and is to be preferred. A nice, little known play, worth remembering.

Anyway, let’s say that White makes the common small mistake and plays 24/18, 13/11 and Red throws 5-5, played of course, 8/3(2), 6/1*(2). Worse still, White dances. This leaves the position below with Red on roll. What is the correct cube action for both sides?

These positions after one player has been pounded with 5-5 and danced are usually the earliest chances that we see for a double. Let’s look closely at what is happening here. The first thing to note is that this is a money game, so invariably in live play, although not always online, the Jacoby rule is in effect. This is a rule invented in the 1960’s by celebrated gamesman and early theorist Oswald Jacoby. It is quite simple and just says that neither player may win a gammon (double) or backgammon (triple) unless the cube has been turned. Its object is to cut out tedious games where one side is playing on and trying to win a gammon with the cube in the middle.

These games are only tedious for one side by the way! This rule is never used in match play. It means that it is of no use for Red to play on and trying to win a gammon. If this was a match and Red could win an undoubled gammon, should he play on here? Actually no. He does of course have strong gammon threats, but not quite strong enough to make playing on correct and he should turn the cube now. White must pass. In 100 games, Red wins around 68 of them, of which 43 or so will be gammons. White’s 32 wins and around 7 gammons of her own are not enough to justify a take. Adding up for both sides Red can expect 43 games of 4 points (172) and 25 of 2 points (50) for a plus of 222. White can expect 7 of 4 points (28) and 25 of 2 points (50), totaling 78 for her side. In 100 games, Red scores 222-78= 144 points, an average of 1.44 points per game. Clearly White does a lot better to pass and just pay 1 point.

You may have noticed that the above figures, which are in themselves only estimates, also conveniently omit several key features. They leave out backgammons. There won’t be many of these here, perhaps only 1 or 2% for Red at the most, so we normally don’t bother to take account of them. The figures also assume that all the games will be played to the end without another cube turn, in other words the statistics and the equity that we derive from them are cubeless.

This is for the sake of simplicity, but in fact White will do a good bit better than these figures in practice, because she will have access to the cube. Her cubeful equity will be much better than her cubeless equity. Red has to go on from here and win the game without the cube. White will still have chances to win the game, even when Red is 99% favourite to win. The reverse isn’t true. White has only to get into the 75-80% region and she can win the game with the cube.

A third factor that the robots can’t take into account yet, is that there is still a considerable amount of difficult play in this game, certainly with the checkers and perhaps with the cube as well. If White felt that she was a much more skilful player for example, or that her side was easier to play, she would be entitled to take those factors into consideration if the decision to take or pass was relatively close. She might also have watched Red play before and noted that he doesn’t play this position at all well, or that he is the sort of player who will weakly pass a 4 cube later. Here the decision isn’t very close actually, it’s a big pass. For now, don’t worry too much about the value of cube ownership or different skill levels. You will have your hands full as it is just trying to get a reasonable estimate of what the cubeless figures might be like.

How did I get those figures? I just asked GnuBG to estimate them for me and they are probably correct to within 1% or so. How might you or I estimate them in practice? Actually I wouldn’t try. It is what we call a reference position, one where I already know that the correct action is double/pass. This position, with small variations, occurs often enough to be worth remembering. If Red is better off in some respect, it might be worth his while in a match to consider playing on for a gammon. If White is better off, she can sometimes take this sort of thing. Here is an example:

The sequence of events was much the same. Red rolled 5-1 and slotted, White rolled 6-3 and ran out, Red rolled 5-5 and White danced. Red doubles of course, but White can just about take this. Red has fewer numbers that hit and cover because some of his threes are duplicated. The threes that he needs to hit, he needs to cover as well.

All these come under the general category of blitz positions. A blitz is where the defender (White) is under attack, usually without an anchor and the attacker (Red) is trying to put as many checkers as possible on the bar and close his board. For the attacker they represent a fairly easy cube decision, you double the first time that White flunks, either staying on the bar or entering awkwardly. For the defender, they are a nightmare, almost invariably facing a very tough take/pass decision. While the attacker has only two points made in board, they are usually takes and often not even correct doubles.

With four points made and a man on the bar, they are usually passes and sometimes too good to double. With three points made and a man on the bar, it usually boils down to the size of the threat to hit more blots and make more points. Note here that although Red is an underdog to hit and only a small favourite to make a fourth point, his double is still very powerful, so watch out if he is stronger than this. A whole book would barely suffice to scratch the surface of blitz play, with cube and with checkers, so we will have to move on for the moment. Even when you are an advanced player you are going to find these tough!

In general, when should we consider giving the cube in the early and middle parts of games? Years ago, I gave a seminar where this question was asked. Mark Adkins provided the answer for me, “Whenever something good happens”. Is this too simplistic? Not really, arriving at an optimal doubling point is sometimes a matter of edging forward, gradually getting closer to our prey, but very much more often it is a matter of a Great Leap. We hit and make a point, we throw the number that escapes our last checker, we throw an excellent double that makes ground on both sides of the board and in each case, our opponent makes a poor reply. When this Great Leap occurs is a good time to take stock of what is actually happening.

Later on, you will probably begin to think of things in terms of how often you can win and how many gammons, but a good and simple way to start is to use PRAT. This delightful acronym stands for Position, Race and Threats. You must ask yourself, “How do I stand in each area of the game? Is my position superior? How do I stand in the race? What threats do I have to improve on the next sequence of rolls?” If you feel that you have an advantage in two of these categories, you may well have enough for an initial double. An advantage in all three areas usually indicates a very strong double, perhaps even a pass.

Another infallible rule is known as the Woolsey Rule, named after Kit Woolsey, the great player, writer and theorist. It goes, “If I was in my opponent’s shoes and was doubled in this position, would I be certain that it was a take. If there is some doubt as to whether it is or not, then it must be a double!”

Of course if you are certain that it is a take, it might still be a double, it might not, but any doubt at all is enough to justify turning the cube. Pound for pound, this is about the strongest advice that you are ever going to get about doubling. Memorise it.

That’s enough to take on board for one lesson. We will expand on all this another time. Now here is another of the handy charts that I have made for you, laying out responses to an opening play.

Note: The moves suggested above are the #1 results of rollouts, however, sometimes other possible moves for a dice roll may have been listed as very close or as a reasonable alternate.

Learning these charts by heart is practically impossible. You might like to go through them and note those plays that you don’t know, then transfer them to file cards. Flicking through them in a spare moment can often lodge some information into the brain. When faced with a decision that you are not sure of in a match or money game, make a mental note to look it up afterwards and do it! Making a mistake is fine, but making a mistake again and again is just plain stupid.

For your homework this time, I want you to log onto your favourite backgammon server and spend an hour watching two strong players. Try to get a feel for the sort of position that they are doubling, or even considering doubling. If they are nice people, they might even respond to polite questions seeking information. Backgammon players are a pretty decent set on the whole!