Thursday, October 8, 2009

Remember the old pedantic piece: It's not whether you win or lose; it's how you play the game?
Yeah, right. Not in this age of bottom lines and payoffs.
But actually the way you play the game, in most games, decides whether not you win or lose but in fact whether you stay in the game or not. A game is played by the rules, or it's not played at all.
You can't move a pawn backwards in chess; you can't jump your own man in checkers; you can't bid 1 heart after 2 diamonds. If you do, you're out of the game. Period. That's how games differ from life, and that's why children have to learn the discipline of accepting rules if they want to play games.

But the fascination of games has more to do with the way they are a reflection of life than the way they are different. Chess is a battle for power. Monopoly™ is a fight for real estate. Bridge is a challenge to fulfill a contract.

But what is Backgammon? It's more than a fight or a challenge. It treads on the unknowable; it operates both with mathematical certainty and mystic darkness. It is a search for the balance between the individual and the community.

A backgammon board is a set of 24 triangles in alternating colors. It’s on this playing field that the struggle of backgammon is engaged. It’s grand principle is: the more you win, the more advantage your opponent has.

The game is played with counters, 15 for each player. (Fig. 2) There is a diabolic ingenuity to the number 15. It is an odd number, that is, not divisible by 2. But it is precisely that number 2 that is crucial to the play. For if you have 2 counters on a given triangle, your opponent cannot move against you.

I am getting ahead of myself. What one must do to dominate and destroy the opponent is to move all one’s counters from their initial positions to one’s own inner court, thence off the board.

But I’d forgetten to explain “inner court.” The board is divided into four areas: the set of six triangles to the left of the player is known as the inner court; the set to the right known as the outer court. So that each player has an inner and outer court. And one must return all one’s counters to one’s own inner court, finally off the board.

One more little item: the counters may move only in one direction, clockwise. There is no going back. One cannot go home again. Or rather, one must go home, always.


Of the 15, five are already in one’s own inner court, fully a third of the game is practically given you. Another fifth (3 counters) are placed just outside, in your outer court.

How easy, you think, to put over half the counters into your own courts! But so for your opponent. Everything is the same; everything is balanced. And, of course, everything is artificial. Which is to say, little in "life" is as balanced or as equal. But it's what you expect from a game: artificiality. Rules, conventions, only a single opponent. Nothing like "life," with its hurly-burly, its unpredictability, its demand for the bottom line, its jungle battle for survival.

I’d fogotten to tell you that one moves counters only by throwing dice. Such a small item to forget, but there is the diabolism of those dice! One has such choice in this game with 15 counters. Each can be moved independently or in pairs. But the apparent choice is mitigated by those dice. If one, for instance, rolls a 6 and a 3, one has the choice of moving one counter 9 spaces (triangles) (always, remember, clockwise) or two counters, one 6 spaces and the other 3.

So the dice determine that there is a mathematical dimension to this struggle: the matter of combinations of twelve things taken two at a time. The mathematician will write in thus: 12C2 and will point out that the chances of any one combination coming up will be governed by an immutable relationship.

To begin with, then, the game presents a number of mathematical elements:

• the outer and inner courts - (6 positions in each of 4 courts)

• the 12C2 dice throws

• the ability to use both numbers separately or together

• the 15 counters

• the single, clockwise direction of the counter moves. Actually, while you are moving clockwise, your opponent moves counterclockwise (from your point of view).

The center of the game is the tension between the number six and the number five. There are six die faces just as there are six positions in each court. But there are 15 counters set up at the beginning of the game in the following pattern: 2,5,3,5 (working clockwise from your opponent's inner court to yours). No one can distribute 15 counters over 12 spaces equally; there is always some imbalance: the tension between 5 and 6. (In Arabic and Hebrew, the name of the game is "6 and 5.")

So really, the game is not so predictable. That imbalance keeps the players from easily resolving the problem of getting one's counters off the board. It's that one single counter, that extra one that creates all the trouble. Sorry; getting ahead of myself again.

During the first stages of the game, dice throws usually evoke rather conventional and easily predicted moves. For instance, a 6/5 combination will move a counter from position 1 to 12 Or a 5/2 will move a counter from position 12 to position 17.

But each time a counter is moved, the decision about how to use the next dice throw becomes less conventional, more judgemental. For instance even though a first throw of a 6/5 combination may well mean a 1-12 move, the second one, although still suggestive of that same move, will mean that your opponent's inner court is left unthreatened because you have no more counters in it. Thus he is freer to move individual counters as rapidly as he can into his own inner court.

That's an example of the balance of this game. If you have managed to move both counters out of his inner court (giving you what appears to be a distinct advantage) that move has allowed him greater safety in moving his own counters. The more you win, the more you lose. And since the setup is perfectly symmetrical, that princple is equally true for your opponent.

I mentioned earlier that if you have two counters on a given position, your opponent cannot move against you. But if you should need or want to move one of those counters and leave only one on a positon, your opponent can capture that counter (if one or both dice allow him to land on that poisition). Once he has captured it, the counter is out of play until a throw of your dice allows it to return to your opponent's inner court, furthest from your court. Then the counter must start its journey home all over again. So it's that pesky single counter, the one operating alone, that 15th, that creates the danger, the risk, the vulnerability.

It's the young or sickly gnu or zebra, for instance, being stalked by a predator. As long as the animal has the protection of the herd, the community, the predator will not touch him. But out in the open, somehow excluded from the gang, he is fair prey.

The trick in Backgammon is to find one's way home, maintaining at least pairs of counters for mutual safety. If you can get to your home court in pairs (6x2), then those three single pieces are just add-ons, so that three of the pairs become threesomes. And the risk and individuality of the loners disappear.

Maybe you want to call it the "herd instinct," the ghetto mentality, the wagons in a circle, community. It's there in all of us: that desire for protection, for the security of the known, the tried and true. It works against the loner, the single oddity, the risk-taker, the out-lier. It makes us delight in ritual and habit and schedule.

Elements of balance and imbalance are everywhere. Boxing has the same features. A boxer's balance, his ability to dance on the balls of his feet, shifting weight easily from one foot to the other not only makes him a difficult target for his opponent to hit; it also provides the jumping off point for him to land a good, solid blow to his opponent's midsection or head or finally to his jaw. And landing a real hit not only injures the opponent but also knocks him off balance so as to be a target for more blows.

Ballroom dancing also depends on balance. But in this case, both partners try to avoid imbalance so as to sweep their bodies in rhythm with the music's beat. Imbalance brings in the element of chaos, destroys the working together of the parts, makes harmony and sympathetic vibration break down.

Still, there is that feature of imbalance that makes an individual. Balancing, working in harmony with a larger structure, staying sensitive to the rhythms and sounds of your context is part of that communal protection racket. That 15th counter, the one that throws off the balance of pairs, is also the one that stands out from the crowd. It is the one that refuses to accept the pattern. It is the one that questions the conventional wisdom that supports the pattern. Throw something off balance and one immediately wants to justify it. So its value, its power, its popularity is imnmediately questioned.

Both balance and imbalance have their necessary functions.

But it is not only the odd man out that unbalances the game. The player is always subject to the whim of the dice. If, when one of your counters is out of play, your opponent has all his inner court positions filled (each with two counters = 12 counters, so he still has three outside) you cannot reenter the game.


Eventually, of course, that "closed" court must open by virtue of the fact of the dice throws. If 12 counters "lock up" the court, only three are left in play. When these three have arrived at one's inner court, the player is ready to start moving his counters off the board. And since you cannot reenter the game yet, he has all the dice throws. But that advantage will quickly become a disadvatange; the next dice throw will most probably open at least one of the six positions, and so you throw the dice, hoping to enter into the open position. If you are really lucky, the dice will allow you to enter a position where only one counter stands, thus capturing that counter and putting your opponent in the same condition you had just found yourself in, another kind of balance. All because of the unpredictability of the dice.

This unpredictability is not all mathematical, not all a matter of the randomness of the throw. There is something dark, something diabolical, in the pattern of dice throws. Every player has known the feeling of the dice "running" against him or in his favor. Sometimes it seems as though, no matter what one does, the dice throw in his favor or disfavor. That's the real diabolism in the game: there must be some force controlling those throws if they come out in someone's favor time and time again. I hesitate to give it a name: God, the Devil, Fate, Nemesis, The Force. We've all heard such names given to who knows what. Perhaps it is the same field from which the idea of a poem is born. It certainly is not perceivable by human senses.

There is, therefore, a dynamic relationship between luck (the apparently random throw of the dice) and judgement (the decision one makes to move counters), "dynamic" in the sense that the importance of one or the other is always changing.

This matter of judgement is, of course, the distinctly human dimension to the game. Judgement involves experience, intelligence, and the ability to observe and learn from that observation. One quickly enough learns the conventional moves, those that obtain in the early stages of the game. But there comes a certain point at which one's almost automatic use of convention fails to meet the situation successfully. When that condition occurs depends on both the throw of the dice and the judgement of the player.

But when it does occur, one has passed into the second stage of the game. When judgement becomes more important than convention, the player must design a strategy for winning. Should he move as many pieces as rapidly as possible toward his inner court? But if that isolates one or more pieces in the opponent's inner court, will that plan cripple him? Should he leave a pair in position 12 so as to allow those further away some protection? As often as not, whatever strategy he decides on, like those in war, business, or lovemaking, fails because it cannot take into account the throw of the dice.

The dice throws can confound one in another way. There is a convention in the game that if one throws "doubles" (the same number coming up on both dice) one moves that number twice. If one rolls the dice so that two "threes" appear, he must move counters a total of four "three" moves, not two. But again judgement intervenes, for he may move one counter twelve spaces, two counters six spaces each, or four counters three spaces each. (But he may not move three counters four spaces each.)

So another element of unpredictability is operating.

Are you getting a sense of loss of control? You plan and scheme and manipulate, with a growing sense of security and, yes, let us admit it, greed and power. And then, with one throw of the dice, even if it is only one die landing on the wrong face, perhaps a one instead of a six, all the plans are dashed. You declare bankruptcy. There is not even any insurance money to start you up again.

Then there comes a second point in the game when one knows whether the strategy has worked. (Remember that that first point is when convention yields to strategy.) I called it the "critical throw." It represents the climax of the game, and starts the third and final stage of the game. After that, the winner has probably been determined, and all that remains is for the mechanical working out of the counters coming home to their inner courts.

These three distinct stages I call the introduction (where conventional moves are most common), the battleground (where strategy is worked out and judgement dominates), and, after that critical throw, the denouément (where the inevitable consequences of the previous moves play out).


I remember a horrible incident I learned about when I was still in elementary school. A neighbor, richer than my family, sent her daughter off to a girls' boarding school, a "good" school where the girls were shepherded and guarded and watched, so I suppose that the parents felt secure.

One night, as the girls were eating dinner in their dining hall, a powerful thunderstorm broke above the school. All at once, a bolt of lightening struck the brick chimney at the far end of the hall. The bricks were torn from their mortar and hurled down upon the girls below. My neighbor's daughter was buried beneath the debris, killed on the spot.

There it was:

the introduction: the parents, wanting a good education at a good school for the daughter, sent her to boarding school, and she was in the dining hall at mealtime -- all conventions.

the battleground: the storm, what to do to protect the occupants, the strategy, not to disturb the girls but to trust to the protection of the building.

the denouément: the thunderbolt, the loose bricks, the death of the girl.

It was a bad throw of the dice. Whatever my neighbor's strategy, that thunderbolt cancelled all plans. Perhaps it restored some kind of cosmic balance.

But what do we know of that curious method of decision-making: the throw of the dice? Why do certain combinations come up and others not? Is all governed by abstruse mathematical operations we only dimly perceive? Or is there some other erratic, chaotic element operating, something called karma, fate, nemesis, god?



1 comment:

Hadass Eviatar said...

Interesting (although I'll admit I skipped over the deeper details of backgammon). I like the thoughts about balance and imbalance. BTW 15 is not prime, merely odd, which is what I think you meant (it is not divisible by 2, but it is by 3 and by 5).

You might want to look up Seth Godin's blog: http://sethgodin.typepad.com/seths_blog/. You will like the way he thinks, I believe.

Happy Sukkot and love, Hadass.