#### The game of Backgammon

1) Rules of the game

Backgammon is the game of Man-Errger-Dich-Nicht for big players. But it is the two-player variant. So two players try to move all their checkers around the board. On the way, you can also throw out your opponent’s stones and the first player to finish wins.

The small differences to Mensch-Ärger-Dich-Nicht:

- Each of the two players has 15 pieces (Mensch-Ärger-Dich-Nicht: 4).
- There are a total of 24 prongs, which are the squares on which the checkers may stand.
- The backgammon board is also called backgammon board or just board.
- The board is divided into 4 sections of 6 squares each.
- The checkers of both parties move in opposite directions.
- The winner is the first player to roll all the checkers. A Diced Stone
- The dice may only be rolled when all 15 (or, to be more precise, all remaining; more about this later) stones have arrived in the player’s own home field.
- The own home board is the last quadrant seen in the direction of movement for each player, i.e. the last 6 squares.
- Each square on the board may be occupied by more than one stone.
- However, the colour of the stones on a square must be uniform. There can never be two stones of different colours on the same square.
- The game is played with two dice.
- The number of points on each die must be completed with one stone of the party on the roll and must be executable (two exceptions later).
- Stones of one colour standing alone on a square may be captured by the opponent. To do this, the number of points on a die must move a stone exactly to the square of the stone to be captured (you cannot capture if you only pass one stone).
- If both dice show the same number (a double), then you may and must place each number four times (may or must is only called that because it can be advantageous or disadvantageous depending on the situation).
- If there are two or more stones of one colour on a square, the opponent may not enter the square at all (if there are two or more on a square, they are always of one colour; worth mentioning only because there is a Turkish variant of the game where you can “catch” stones of the opponent by placing one of your own on top).
- If the two dice show different numbers, each number on the dice must be drawn once. In doubles, each number must be drawn twice, so the number rolled must be drawn four times. So if both dice show a 3, a total of four threes must be drawn. The stone with which you want to move is freely selectable. However, each roll must be completely executable. You cannot add up the number of dice and only execute the sum (this special rule is really best explained by the example: You roll a 3 and a 5. You may very well draw the sum of the 8 dice with one stone. But at least the 3 or the 5 in the first half of the move must be a square not occupied by the opponent with two or more stones. If there is a single opponent’s stone on the 3 or on the 5, it may be captured. If there is a single stone on both 3 and 5, one of the two must be captured. Otherwise you have the choice of capturing or not capturing. If both squares, the 3 and the 5, are blocked, i.e. occupied by two or more opposing stones, the stone in question cannot move at all, even if the square 8 points away were free). However, you may also move the two numbers with two different stones. With doubles you may also move with up to 4 different stones; but you may also make all 4 moves with one stone or any combination. The basic rule for this is also: Every single number must be executable, i.e. there must not be two or more of the opponent’s stones on any of the squares to be entered.
- Every number rolled must be moved, if this is possible. If, however, one cannot legally move a remaining 6, for example, the number on this die is forfeited (but the other may or must still be moved, analogous to above). So you don’t have to move incomplete numbers, but may not move them at all.
- Captured stones land on the bar. The bar is a fictitious 25th point (for the opposing party even a 26th point) on the board. In most cases, a board actually has a “bar” in the middle of the board, where the stones can stand as long as they are not in use. But it remains a “fictitious” point, it is not specifically marked; many players hold the stones in their hands before rolling the dice).
- The rolling of the dice for stones on the bar is analogous to the normal move. The stone starts its move on the first point in the opponent’s home square. There it would (can) start with a 1. However, the square that the stone to be rolled intends to enter must be free, i.e. not occupied by two or more opposing stones. So if you actually roll 3 and 5 again and the opponent has “occupied” these two squares with two or more of his own stones, the stone cannot enter in this roll. The move is then forfeited completely. The special rule to be observed when rolling the dice is that the stone on the bar must be moved before any other stone may/could/must be moved. Since there can be more than one, all the stones on the bar must be rolled first before any other stone can be moved.
- The special rules for rolling the dice state that you must, of course, draw all the numbers on the dice, if possible. However, if you can no longer move a 6 because all the checkers are further ahead, you may also use the 6 to move a checker from the 5 or the 4, as long as there are no more checkers placed higher.
- Another special rule for the dice: You have to have all 15 stones in your home field before you can start dicing. However, it happens often enough that the opponent also has stones in this field. It may even be that the opponent still has stones on the bar that still have to be rolled. In all these cases, one speaks of there being “still contact”. This means that theoretically one more stone can be hit and have to start again from the beginning. IIn contrast: If there is no more contact, which also happens often enough, the game is then called a pure race: whoever throws higher wins. There can be no more hitting. So as long as there is contact, it is still possible to be beaten. That applies to both parties, of course. It is just that it is usually the only chance for the party far behind in the race to still win the game by striking. So if the trailing party then manages to capture a stone because it was left open when the dice were rolled (almost always unintentionally, but it happens), then this stone has to be transported around the whole board again. It has to be rolled in and start its journey home. The special rule now: the party whose stone has been captured, even if it has already rolled some stones, may only continue with the roll when the captured stone is also back in its own home square. So the correct rule is not “The dice can be rolled when all 15 stones of a party are in their home square” but like this: Whenever all the stones of a party still in play are in its own home field, stones may be rolled.”
- Another special feature and almost the eponym for the game: There are gammons and backgammons. A gammon is a game where one party has played out all its stones and the other has not yet played out a single stone. If this happens, the game counts double. That is, the number on the doubling cube is multiplied by 2. A very special form of gammon is backgammon. In this gammon, too, one party has played all its checkers and the other has not played any. But in backgammon, the loser still has at least one checker in the opponent’s home board, i.e. in the rearmost quadrant. Sometimes you deliberately take the risk of leaving a checker at the very back in order to be able to intercept and beat your opponent after all. Other times, however, you are so helpless that even with the best will in the world you can’t get the pieces out of the back. The factor then increases. In backgammon, the number on the doubling cube is multiplied by 3.

Those were the basic rules for now. Another basic rule is the starting position. The checkers do not all start from the rearmost point (which, according to the explanation above, would be the opponent’s bar), but are placed on certain points. The distribution is 2-5-3-5. In total, that is 15 stones distributed over four points. The first point, the one with the two stones, is actually the point furthest away from your own home field, the 24-point. This is the point on which you would roll a 1 from the bar. The next occupied point is the so-called “midpoint”. This is the reversal point on the board, but the 5 stones placed there would still have to pass each other. It is the point that is 13 squares away from one’s own cube point. Then there are 3 stones on your own 8-point and 5 stones on the 6-point. So, the checkers are all facing each other in a backgammon board that has been opened up and made symmetrical in this way.

2) Gameplay

The game is played like this: Both players roll one die. If the dice show the same number, the game is repeated. Otherwise, the player who rolled the higher number starts. And with the move that is shown on both dice together. You a 4, the opponent a 3, you must make the move 4-3. Then both players roll both dice alternately.

The following rules apply: In the tournament, the dice are rolled from a cup. The dice must be shaken audibly. Then the dice are rolled on the right side of the player’s own board. Both dice must then roll and touch at least one board. Then they must come to rest on a free area of the board. Then you have to make the move legally. As soon as you pick up the dice from the board, the move is considered finished and can no longer be changed. However, as long as the dice are on the board, you can touch the pieces and move them back and forth. This is in contrast to chess, where the rule “touched led” applies.

3) The doubling cube

There is also the doubling cube. Both parties can use it to double the stake (in the tournament: the score) that is being played for. There are also a few noteworthy rules. Both parties have access to the cube if the cube is in the middle, i.e. the game is undoubled so far. As soon as one side has doubled, the cube lies on the opponent’s side and is no longer accessible to the player who doubled. From this point on, only the party that has the cube on its side may double.

You may always double before you roll the dice, provided you have access to the dice. After doubling, the doubled party also has a few options: The normal ones are called Accept or Decline (the one special rule of the Beaver is explained in the chapter “Beaver-Dirk” and only applies to money play). If the doubled player rejects a doubling, the winner of course only gets the number of units originally shown on the doubling cube. So if you double from 4 to 8 and the opponent refuses, you get credited with 4 units, points.

4) Strategies

Since backgammon, even after explaining all these rules, still remains a racing game (that would be, so to speak, primitively expressed: whoever rolls higher wins), one must of course, in order to counteract this effect, develop strategies that at least challenge the principle.

One problem that unites both parties is the problem of bringing the two stones at the very back “home”. On the one hand, the reason is that these stones are at the very back, of course. On the other hand, they are also the furthest away from their own stones, namely a total of 11 fields to the next own point, the midpoint. The other 13 stones are “connected” to each other, to be reached by a single roll of a die.

So in order to move these stones around, you usually have to move them around alone. This makes them lose their protection and they can be hit as well as captured later.

One strategy, therefore, is to “free” one’s own stones that are far behind and, if possible, not to leave the opponent’s stones free. To do this, it is often very effective to “build” your own points. The squares “over-occupied” with 5 stones can unite their surplus stones in such a way that they form new points. Points are the squares occupied by 2 stones. So if you build up a lot of points in front of the opponent’s stones with the 13 stones on your own side of the board, it gradually becomes more and more difficult for them to free your own stones. Points built up in front of the opponent’s pieces in a row are also called a “prime”. There are two- to seven-point primes. However, the most effective is of course the six-point prime (you don’t need seven, but it doesn’t hurt either). It is impossible for the opponent to overcome it. You need at least twelve of your own stones. A six-prime cannot be skipped, because no single die can show more than a 6.

In principle, there are two possible dream goals: To completely wall in the opponent’s stones and to free your own stones. This is achieved when you build up six points in a row in front of the opponent’s stones. At this point, the height of your own cubes becomes largely irrelevant. The simple element of “race” has been successfully combated with “strategy”. However, if one’s own stones have not yet been freed, an exciting game often results. The type is also called “prime against prime”. Both try to get their own stones out and not to release the opponent’s. The opponent’s stones are not released. But since one has to move forward, it often results that one of the two has to break his prime, i.e. give up the rearmost points. The problem connected with this is also called the “timing problem”. One has to move forward even though one takes damage from it.

The absolute dream, however, is when the six-prime lies the entire home field of one’s own. Imagine: You manage to move one or more of your opponent’s pieces onto the bar and your own home square is double occupied by your own pieces on all squares! The opponent can then save himself the trouble of rolling the dice. He would not be able to make a single move because he could not start with a single number. Then you can keep rolling the dice until you roll out your own stones (remember: 12 stones are enough to build the prime in your own home field, 6 fields are occupied by at least two stones each, 6*2 = 12. So the other three stones can or must be brought home first. The height of one’s own rolls has the smallest possible influence: it is indifferent.

5) Winning strategy

To use the term “winning strategy” here is, of course, nonsense. There is not one winning strategy. There are good players and not so good players. There are good moves and not so good moves. And even at that, judgement is not absolutely reliable. It is currently spoken of by the backgammon computer and accepted by the world’s elite. But whether there is not a better possible move here and there is not finally clarified by this either.

There are also the terms “diversification” and “duplication”, which could at least be understood by a beginner. If possible, “diversification” should be applied to one’s own moves and “duplication” to the opponent’s moves. After all, the meaning of the words is certainly not difficult even for non-English speakers. You diversify your own throws, you duplicate for your opponent. Diversifying allows you to make many good throws. You have a 5 that you could use here, you could do something with a 2 and the 4 would be helpful here. You could also use 6s and 1s in an emergency. For the opponent you make it look different, if possible. It’s best if he doesn’t have any good throws at all. But if he has an obviously good number, then you put a stone in another place on the board so that he could hit it with the same number. If he then had the number, he wouldn’t even know where to move it first. But maybe he doesn’t even have it yet. And so on.

Why I included this has only one reason: self-congratulation. I’m explaining my own “winning strategy”. I would also smoothly add “but please don’t tell anyone” if I hadn’t already published it at this moment. But this “winning strategy” still doesn’t deserve the name. It is more a behaviour at the board, which I would like to get rid of here.

But I also have to mention something very important again: In the moneygame, in the everyday business of being a backgammon pro, which I would have liked to be once (I was too bad for it and put the idea that I was a pro to the file), I was absolutely unsuccessful. I completely neglected all my ridiculous theories about winning strategy, unless you know of a better reason why I was so unsuccessful. I simply could not win. In the moneygame, the fact that you had to pay immediately for every unlucky lost game was decisive for me. And I probably played the following game under the aspect of wanting to win back the money now. That’s typical loser behaviour. It is important to make good moves and not to play according to the current score. But that only serves as a transition to the…

6) Tournament Backgammon

This was the discipline that suited me. Sure, anything you succeed at, you imagine you’re good at. But there was still a good reason why I liked it so much. At some point in the tournament, you paid the entry fee. After that, the money was worth something. That value changed with every move, with every game won or lost, with every match won or lost. But the change was only in the equity itself. One did not have to reach into one’s pocket, nor could one fill up the pocket. The equtiy was a fictitious value. Only after the last throw in the last own game of the tournament the value was realised. You got a prize or not, or the amount was fixed. From the tennis world, I still know the phrase “I hope to score the last point in the match”. That was the funny equivalent of winning the match. So in backgammon you could also hope to make the last throw of the tournament yourself. The last stone was thrown, the opponent could, according to Gentleman, only congratulate him. And: if you had made it, you certainly had a prize. Because: something must have been at stake. And one won.

The consequence of this for me was once again to be found in psychology, plus the use of the Pauli ladder. By psychology I said to myself: as long as I’m not eliminated or the match is not over, it’s pointless to get angry. I don’t know yet what the final outcome will be. Imagine losing a very unlucky game, getting angry about it, but continuing to play the match and winning it! First of all, the opponent would then have every reason to be angry himself. But not so much about the lost match as about the reaction after the unfortunate loss: “You’re whining all the time about how unlucky you are and in the end you win the match.

So you don’t know who will win the match until the last throw, which is made by yourself or your opponent. After the last throw, you do know, but it’s too late to get angry now, so what’s the point? But whoever wants to can get annoyed, I wouldn’t care either and also for the chances. Unless you transport that frustration to the next tournament. Here, too, neither frustration nor anger are the true factors influencing the chances of winning a match. The real influencing factor is, of course, the loss of concentration due to anger, and consequently the changed decisions, which, on balance, can simply turn out worse as a result. A worse move results in worse chances of winning and in the sequence of many bad moves perhaps the decisive change in the odds to one’s own disadvantage, the loss of the match.

So during a tournament match I simply didn’t get angry. And after the elimination it was too late, so I refrained from it as well. That was the psychological part. The “Pauli leader” part had merely led to internalisation. And that was indeed the case. I just couldn’t get angry any more. The principle was too clear and obvious to me. A lost match simply doesn’t matter, no matter how unlucky. Maybe you win the match afterwards and have turned this misfortune into happiness. After all, what could be better than to accommodate bad luck in such a way that it does no harm?

The advantage of not being angry was that my full concentration was always on the execution of the next move, on the next decision. Of course, that often depended on the score of the match. Of course, if you are behind in the match, you sometimes have to make different, riskier decisions. Conversely, if you are leading, you have to make somewhat “safer” decisions. But that had nothing to do with bad luck. It was just a strategy adapted to the score.

One last secret I’d like to spill now and today: There is a natural tension that every player feels at the board and during a match, at least the serious player. One is anxious about one’s own throws and about the opponent’s throws. Well, in order to be able to execute one’s own throws, one must of course inevitably look at one’s own dice. But practically all players also look at the opponent’s dice. And that was my starting point.

Of course, there are two very obvious reasons for this. One is that you simply want to know what your opponent is rolling. That’s the expression of tension part. The other is an intuitive part: if I don’t look to see what he has rolled, after all, he can just hit a stone and pick up the dice even though he hasn’t hit at all. Or a similar cheating attempt. He draws a dream roll that he didn’t have at all. You have to “keep an eye on your opponent”, in the true sense of the word.

Now came my creation: I didn’t look at what the opponents rolled. That was my greatest “secret of success”, as I like to imagine. No way that the opponents didn’t ask themselves at some point why I wasn’t looking. Or even wondering what would happen if they simply made a different throw than the throws indicated. On top of that, of course, my behaviour can simply be described as downright “cool”. And I know that it simply irritated my opponents. The thought: “Doesn’t he want to know what I rolled?” must simply have an impact. “Doesn’t he take me seriously?” But it’s also enough to say, “Everyone’s looking at what I roll. Why isn’t he?” The concentration is on something other than the optimal execution of the move. And I can’t see anything “unfair” about it to this day. I managed to fool my opponent into thinking that I was not interested in his throw.

I readily confess that I did look briefly when I picked up the dice. My confidence was great, but perhaps not great enough for that. Especially in important games. I could see what the man had bet. I registered the change of position without looking at the dice. I could then check when I picked up the dice: He moved 5-3. Did he also roll 5-3? Of course, the problem of checking is not necessary if the opponent has made a move that is very disadvantageous for him. Why check then? He will certainly have rolled that too.

By the way, there was even another consequence or a certain behaviour that I perfected. If the opponent had executed one of his throws incorrectly, which sometimes happens unintentionally, I just looked at the board for a while after the incorrect execution and did nothing. Because a rule says that if the opponent makes a wrong move, you can object to it but you don’t have to. So you have the choice whether to leave the position as it is or to demand the correct execution of the move. But this consequence has also led to uncertainty on the part of the opponents. The first reaction is always irritation. But many then reacted in such a way that they noticed their mistake and then quickly wanted to correct the wrong move, shortly after picking up the dice. I then had to additionally object to this behaviour because it was not “rule-compliant” (I had the choice whether the move was valid or not), which led to further uncertainty.

All in all, I claim, at least with regard to my tournament successes in backgammon, that I used the means of psychology, which I had ignored (unsuccessfully) all my life in chess, as a matter of course. I was unsuccessful in the money game for the same reasons as in chess: there I always just made my own legs.

However, I concede that with your experience there is also an easier judgement about my “successes”: “The guy has simply had soup and is puffing himself up here like this.” There is nothing to add to that, except “add” and “nothing”.