NONILLION-TO-ONE BRIDGE MYSTERY
The actual odds against the British winning the world bridge championship from the U.S. were about 5 to 6. The theoretical odds against two identical hands occurring during the same evening's play were exactly 1,287,473,706,371,731,028,141,698,599,999 to 1.
Both happened in New York last week. England's crack team, already champions of Europe, defeated the top team of the American Contract Bridge League in eight sessions by a stunning 5,420 points. The identical hands came in the third session, within two hours of each other, from different decks, one green and one brown, the cards appearing exactly the same in all the positions around the table.
Although the "nonillion-to-one hand" (it actually was mediocre) did not affect the outcome of the match, the mystery almost obscured the tournament itself for the succeeding days. The British were playing brilliantly (see next page), but many onlookers were too busy asking very British but unbridgish questions to notice. Whodunit? Howdunit? Was there hanky-panky in the locked room? (Tournaments are played in both an open and a closed room.) Could it have been pure chance?
The actual circumstances were not very revealing. The third session began, as all tournament sessions do, with the players "preparing" the 10-inchlong numbered, aluminum tournament boards (center of table, below). These are delivered to the scene with fresh decks already separated into 13-card hands which are inserted in the boards' neat slots. Each competing player takes one or more of the boards that will be used in the next six or eight hands and prepares it in advance. This means removing the cards from the slots, putting them together, shuffling them, dealing them out in four new hands of 13 cards each, and returning them to the slots. When these chores are done, the players take the lowest numbered board, draw out their hands and begin to play. You must understand that in this kind of bridge the players never shuffle, cut and deal at the table the way you do when you have a foursome in your own home.
A little after midnight on the night of the third session, the U.S.'s Alvin Roth, playing Board 75 (the 75th hand of the 224 that comprised the match), suddenly said: "Wait a minute—I've played this hand before!" A quick check showed that Board 64, played some two hours earlier and by now safely stacked away for official recording, showed exactly the same hand. There was consternation, several official huddles and, finally, a ruling that Board 75 be reshuffled, redealt and replayed in both the closed and open rooms.
The next day The New York Times quoted the odds against the appearance of identical hands as 158,000,000,000 to 1. IBM put some of its best mathematicians on the problem, and a day later they raised the ante and offered "the right answer": 1 out of 5.3645 times 10 to the 28th power.
Then Editor Alfred Sheinwold of the American Contract Bridge League's monthly Bulletin proved that IBM, not knowing about bridge arrangements, had forgotten to multiply by 24, which is the number of possibilities for four bridge hands to be arranged on a board (NESW, NSEW, NWES, etc.). Sheinwold's calculation of "the exact odds" was the 31-figure number cited earlier—one million plus a couple hundred octillions. Bridge expert Oswald Jacoby concurred in this theoretical estimate.
A QUINTILLION YEARS
The Sheinwold figure meant that if all the people on earth shuffled and dealt cards all day, every day, it would take them quintillion years to deal nonillion hands. But it had not been quintillion years since the last identical deal—only 10, as a matter of fact. In 1945 some Scottish bridge players reported receiving the same cards twice during the same evening.
Something wrong with the shuffling? Yes, said the New York Times, something was amiss in the shuffling. But what? SI had assigned me to cover the championship matches; now I decided to play bridge detective as well. Boards 64 and 75 certainly showed some evidence of eccentric card distribution. Each of the four hands had three similar honors—three Jacks, three Queens, three Kings, three Aces. And several suits went around the table regularly—2, 3, 4, 5, etc. Perhaps the clue to the identical hands was not in the open and closed rooms at all, but farther back, in the offices of the ACBL, which provides both cards and boards.
GENIAL JOHNNY GENISE
There, in a back room nine blocks away, I found a genial young stockroom-keeper named Johnny Genise, dividing up new decks into four hands and putting the hands into the four slots of duplicate or tournament boards. The new decks, the same brand used throughout the world championship, were made by the Whitman Publishing Company in Racine, Wis. Genise opened a new pack and showed me that they were not arranged like decks, sweeping through the suits, but were in the order shown in Column 1 of the chart.
How did Johnny put a new deck into the board? With a practiced thumb, he whipped off 13 cards at a time, and inserted each hand into the board as shown in Column 2. He dropped out the Jokers as he did so, and demonstrated how he slid the Ace of Spades deftly out of its original position and onto the bottom of the second hand. He did this, he said, because it is the practice in the U.S. to insert the north hand in the board with the cards facing up, usually with the Ace of Spades showing. To the player who later prepares the board for a tournament, this means that the hand needs to be shuffled and dealt. Did he always put the cards in the boards in the same way? "Sure," Johnny said, and quickly and automatically did it the same way again and again. What if a player, charged with getting particular boards ready for play, perhaps Boards 64 and 75, took them as they came from Johnny Genise and neither shuffled nor cut? Johnny didn't know.
An experiment seemed to be the answer. After some hours with the cards the writer tried the course of action shown in Columns 3 and 4 in the chart—and there, lying on the table, was the celebrated identical hand! Boards 64 and 75 had never been shuffled, and very likely never cut. Since there are 24 possibilities of piling the cards NESW as in Column 3 in the diagram, and there are 24 possibilities of inserting the hands ESWN in the board as in Column 4, the odds are 24 times 24, or a measly 575 to 1.
The cards could have been cut only if they happened to be cut somewhere in the deck where there was a multiple of four, counting from either end. Here the chances are 12 out of 51. This kind of cut, if it happened, would have produced the same hand, and it also would have raised the odds. But not to nonillions.
Tournament officials were inclined to accept this explanation of the "howdunit." Alvin Landy, executive manager of the ACBL, said: "I'll tell you one thing—in the future we'll make sure the new decks are well shuffled before being put into the boards." The surprised non-playing captain of the British team, Reginald Corwen, cried: "Shocking carelessness on the part of the players!"
But which players? Who really dun it?
The match records show that Boards 64 and 75 were both prepared in the closed room. Board 64 was prepared during the first half of the session; Board 75 during the second half. Who was in the locked room when both deeds were done? Well, Edgar Kaplan, for one, as one of the official referees. Who else? Well, only Adam Meredith of the British team—all other players either were shifted into or out of the room.
Mr. Meredith was asked: "What is the custom in English tournaments when a player receives a board to prepare in which one hand has the cards facing up?" Said Mr. Meredith: "Why, in England as in the U.S. and all over the bridge world, it means, of course, that the hand must be shuffled and cut."
Then Mr. Meredith added: "Our only trouble was that we didn't do that once—if you are referring to that freak hand."
The real trouble, of course, was that somebody didn't do it twice.
HOW THE TWO IDENTICAL HANDS WERE DEALT
Here is the way the celebrated hand (see photo on opposite page) was dealt twice in one evening, once with brown cards, once with green cards. The theoretical odds against identical hands like this are 1,287,473,706,371,731,028,141,698,599,999 to 1, but this diagram shows the actual odds are somewhat less. Try it yourself.
(1)
[Ace of Club]
[2 of Club]
[3 of Club]
[4 of Club]
[5 of Club]
[6 of Club]
[7 of Club]
[8 of Club]
[9 of Club]
[10 of Club]
[2 of Spade]
[3 of Spade]
[4 of Spade]
[5 of Spade]
[6 of Spade]
[7 of Spade]
[8 of Spade]
[9 of Spade]
[10 of Spade]
[Jack of Spade]
[Queen of Spade]
[King of Spade]
[Ace of Spade]
[Jack of Club]
[Queen of Club]
[King of Club]
Joker
Joker
[Jack of Diamond]
[Queen of Diamond]
[King of Diamond]
[Ace of Diamond]
[Jack of Heart]
[Queen of Heart]
[King of Heart]
[Ace of Heart]
[2 of Heart]
[3 of Heart]
[4 of Heart]
[5 of Heart]
[6 of Heart]
[7 of Heart]
[8 of Heart]
[9 of Heart]
[10 of Heart]
[2 of Diamond]
[3 of Diamond]
[4 of Diamond]
[5 of Diamond]
[6 of Diamond]
[7 of Diamond]
[8 of Diamond]
[9 of Diamond]
[10 of Diamond]
BOARD
75
E
Cards down
(2)
[Ace of Club]
[2 of Club]
[3 of Club]
[4 of Club]
[5 of Club]
[6 of Club]
[7 of Club]
[8 of Club]
[9 of Club]
[10 of Club]
[2 of Spade]
[3 of Spade]
[4 of Spade]
(3)
[Ace of Club]
[2 of Club]
[3 of Club]
[4 of Club]
[5 of Club]
[6 of Club]
[7 of Club]
[8 of Club]
[9 of Club]
[10 of Club]
[2 of Spade]
[3 of Spade]
[4 of Spade]
N
Cards up, [Ace of Spade] showing
(2)
[5 of Spade]
[6 of Spade]
[7 of Spade]
[8 of Spade]
[9 of Spade]
[10 of Spade]
[Jack of Spade]
[Queen of Spade]
[King of Spade]
[Jack of Club]
[Queen of Club]
[King of Club]
[Ace of Spade]
[Ace of Spade] put on bottom
(3)
[5 of Spade]
[6 of Spade]
[7 of Spade]
[8 of Spade]
[9 of Spade]
[10 of Spade]
[Jack of Spade]
[Queen of Spade]
[King of Spade]
[Jack of Club]
[Queen of Club]
[King of Club]
[Ace of Spade]
S
Cards down
(2)
[Jack of Diamond]
[Queen of Diamond]
[King of Diamond]
[Ace of Diamond]
[Jack of Heart]
[Queen of Heart]
[King of Heart]
[Ace of Heart]
[2 of Heart]
[3 of Heart]
[4 of Heart]
[5 of Heart]
[6 of Heart]
(3)
[Jack of Diamond]
[Queen of Diamond]
[King of Diamond]
[Ace of Diamond]
[Jack of Heart]
[Queen of Heart]
[King of Heart]
[Ace of Heart]
[2 of Heart]
[3 of Heart]
[4 of Heart]
[5 of Heart]
[6 of Heart]
W
Cards down
(1)
[7 of Heart]
[8 of Heart]
[9 of Heart]
[10 of Heart]
[2 of Diamond]
[3 of Diamond]
[4 of Diamond]
[5 of Diamond]
[6 of Diamond]
[7 of Diamond]
[8 of Diamond]
[9 of Diamond]
[10 of Diamond]
(3)
[7 of Heart]
[8 of Heart]
[9 of Heart]
[10 of Heart]
[2 of Diamond]
[3 of Diamond]
[4 of Diamond]
[5 of Diamond]
[6 of Diamond]
[7 of Diamond]
[8 of Diamond]
[9 of Diamond]
[10 of Diamond]
(4)
Player takes deck and deals out four hands in a line in front of him, then inserts them in board, and the hand is ready for play later.
BOARD
75
E 1
S 2
W 3
N 4
(1) Arrangement of new deck from Whitman Publishing Company.
(2) How Johnny Genise put new cards into the boards used in tournament.
(3) How player X removed the cards from board before the session and piled them into a deck.
(4) Player X did not shuffle but simply dealt cards into 4 hands and placed them in board ready for play later.
PHOTO
IN OPEN ROOM BRITAIN'S SCHAPIRO, REESE PLAY MATHE, ROSEN (FACING CAMERA)
PHOTO
ILLUSTRATION