Monday, April 1, 2013

Ravens, Romans, Humanity and Bridge

A man had in his attic a raven that he wanted to get rid of. One day he went armed with a broom. The raven saw him coming, guessed his intentions and flew to a nearby tree. When the man left with his broom, the crow went back home.

The man did not give up. He went the next day with a friend, both armed with a broom: the raven fled on his tree. After ten minutes, one of the two men went downstairs while the other remained at his post. Convinced of misleading the raven, he waited and waited and waited. Exhausted, he finally left, and the crow returned home again.

Two days later, the man tried again, but this time with two accomplices. Same result: the raven waited patiently until everyone was back down and returned to the attic. With three accomplices, same result. The raven, smart, just counted the people going up and waited for the same number to come back down. However, when the man went up with 4 people, making a total of five, the raven was unable to count them and the proprietor finally succeeded in his evil plans.

You wonder of course if I am taking you for a ride? Not at all. Crows, like humans, are able to tally a certain number of elements without needing to count.

What is the largest number of elements immediately grasped by the human mind, without the need to count? Precisely 4. That is probably why European cities are so pleasing to the eye and their environment seems so ... natural. The buildings of Paris, Hamburg, Munich, Vienna, Rome, etc., generally have 4 floors plus a mezzanine.

The prehistoric hunters used notches to count preys, but beyond 4, they found that the calculation became confused. So they invented this little trick to make 4 vertical bars and one horizontal across to create groups of 5 easy to count. Just like the 4 fingers and thumb.

In Indo-European (language family at the origin of languages spoken today in Europe and Asia), the first 4 numbers are declinable, that is to say they end the same way as the word they are linked to. After that, they are indeclinable.

In Imperial Rome, they gave a name only to the first 4 children, the fifth being called simply the fifth (Quintilian), the seventh (Septimus) or the eighth (Octavius). Same for the months of the year. The Roman calendar had only 10 months, and only the first 4 bore a name: March, April, May, June, names of Roman gods. From the 5th month, they said simply 5th month (quintiles), 6th month (Sextilis). That is why we have September (7th), October (8th), November (9th) and December (the 10th).

You will tell me that there is no 5th month, since it is called July, and that the 6th is called August. I'll answer that July was named "quintiles’’ (the 5th) until Marc-Anthony decided to rename it Julius in honor of Julius Caesar, born in July and reformer of the calendar in 45 BC. "Sextilis" (the 6th) became August when Augustus, Emperor also, decided to give his name to posterity.

Our universe has 4 elements: air, land, water and fire. There are the 4 cardinal points, the 4 seasons, the 4 corners of the world.

And then we have:

Open to the four winds
On all fours
Four-leaf clover
Four-letter word (oops)
Four-minute mile
Four-wheel drive

And last:

Will you make up a four for bridge?

4, a magic number?

The hand has 4 fingers ... and an opposable thumb (which allows us to hold the cards).

At bridge, there are 4 players, 4 colors. When we collect trumps, we don’t really need to count: the eye sees when everybody follows. When playing in a 4-4 fit, you pick the trumps as follows: 1st round, 4 trumps, 2nd round, 4 trumps, 3rd round, 3, and we are left with 2. 4432, most common distribution at bridge.

When playing in a 4-4 fit, those two even numbers will produce 5 tricks.

The geometric figure symbolizing the man is the square, 4 corners (as in the famous drawing of Leonardo da Vinci), while the image of the divine is the circle (perfection). In the drawing of Leonardo, the square is in the circle: man enters the divine.

At bridge, sometimes the mistakes of others (imperfect) give you the chance to be perfect.

You play 3NT. The lead is the heart 7, apparently top of nothing, since the rule of 11 tells you there are 4 cards higher than the 7, and you have all 4 higher than the 7. Only Q9 are missing, so East probably has Queen fourth.

  1. You play small in dummy, East plays the 9 and you win the Jack (not the 10, always hide your cards as declarer).
  2. You play a club to the queen, which holds.
  3. Next you play a small spade. East plays small, you play the Jack.
  4. West wins the Ace and, without thinking, plays back a heart.
Up to this point, West hadn’t made a mistake (well, maybe he should have ducked the spade Jack). He didn’t give you anything with the lead.

But, at the 4th trick, he had to think, take his time and do what we always have to do at bridge: count. This heart return, less than divine (!), gives you the opportunity for 11 tricks, if you know how to take advantage.

At duplicate, you need to take advantage of such mistakes, because the top generally resides in card play, not in bidding. West demonstrated here he did not enter the circle of the divine. Worse, he made absolutely no effort to enter the divine. He did not think for a second, he did not count declarer’s tricks. Bridge allows humans to enter the circle of the divine, but only if they are willing to make the effort.

Access to the divine is not and never will be by chance. In this, bridge enables us to equal the gods.

You win the heart return with the King in dummy, come back to your hand with the King of clubs and… count.

East probably has 4 hearts to the Queen and also 4 spades to the Queen, West not having lead a spade. He preferred to lead the 7 from 7xx in hearts than lead a spade from Axx. If East has 4432, with or without the Ace of diamonds, he is dead. If he has the Ace, he will be squeezed. If he doesn’t have it, he will be end played with the heart Queen at trick 11 and will be forced to give you 2 spade tricks.

East therefore has probably 4432, and you have 4423. The hands were then probably these:

And we are now here:

It is now time to cash the Ace of hearts (West follows, confirming your analysis), discarding a diamond from dummy. You then play a club to dummy and follow the discards (and signs of discomfort) from East.

On the club to the Ace, he discards a diamond. On the following club, another diamond. On the last club, unable to bear the pressure, he throws his Queen of diamonds.

4 cards remain. Here is the situation created by West’s return at trick 4.

That is the end you foresaw at trick 4.

You play a spade to your 10, winning. Then the 10 of hearts to East’s Queen. He must play back a spade, inverted stepping stone, to the last 2 tricks, +660, top.

At bridge, if you want access the divine, we must agree to split hairs in 4.

And some day, at trick 4, you will be able to foresee the play 4 tricks from the end.

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