Counting Systems at Auction Bridge

With Special Reference to a New Method of Estimating the Value of a Hand

R. F. FOSTER

MORE than four years ago, in this magazine (August issue, 1917), the card-playing world was given the first outline of a system for getting at the average playing value of any hand of thirteen cards, by assigning a certain value to each of the high-card combinations which the hand contained. By adding these together, the total number of tricks the player might expect to win in play was easily arrived at.

The object of the suggested system was to see, by counting, if the hand would justify a bid. If the hand was good for four tricks, with a named suit for trumps, or at notrump, the bid was sound. The process was as simple as adding up nickels and dimes to see if one had enough to justify the statement that one had a dollar.

In the early days of auction the value of a hand and the bidding on that value was largely guess work, the most popular system being to count up the losers and call the rest winners. The no-trumper was about the only logical call in the game.

The earliest counting systems were used in connection with the game of bridge; but as that game was not a bidding game, and there was no contract to make any given number of tricks, and no such thing as indicating where the bidder's strength lay for defence against an adverse bid, or for assistance in case the partner had a better call, the system was useless in the many varied situations that arise at auction.

THE first of these systems, introduced, I believe, by C. S. Street in his teaching, was to count the number of cards in the suit proposed for the trump, add the honours above the ten, and the outside aces and kings. If the total was eight or better, it was a safe declaration.

Then we got the Robertson rule, which is still used by those who know nothing of bidding beyond the first call, as dealer. In this system, the cards were counted as individuals, the modern idea of combinations being unknown. Aces were reckoned at 7 each, kings at 5, queens 3, jacks 2, and tens 1. This gave 18 for each suit, and if the hand was 3 above this, or 21, it was good enough for a bid. This was based on the original bridge idea of having to hold a queen above the average hand for a no-trumper.

J. W. F. Gillies, of London, in his latest book, "Calling at Auction", brings the Robertson rule up to date for free bids by deducting one for unguarded honours, and adding for their combination. Q J x x, for instance, is worth 5; but Q J x, only 4, and Q J alone, 3. Instead of demanding 21 for a free bid, Gillies thinks 14 quite enough. He advises a heart call with five to the Q J 10; the A Q and two small clubs; two small cards in spades and diamonds. This counts 5 in hearts and 10 in clubs; one over his standard. This would be looked upon as pretty forward bidding in America, the hearts having no defensive strength.

A recent return to the old system of counting the losers depends on subtraction instead of addition. The rule is this: Consider the thirteen cards in the hand as good for 13 tricks. Then, taking each suit separately, deduct one for every time you can follow suit to an ace, king, or queen that you do not hold. Here are two examples:

PROBLEM XXVIII

The following rather interesting ending has been sent to us by Ernest Bergholt, card editor of The Field, as an excellent example of the work of a composer so far unknown in this country, H. A. Adamson.

This gives us 9 tricks as the playing value of the first example, with hearts or clubs as trumps; 8 tricks as the value of the second example, with spades as trumps, or at notrumps.

A variation of the Robertson rule which had a number of followers at one time was to call aces worth 4, kings 3, queens 2, and jacks 1; tens nothing. Robert L. Beecher, who was a member of the Knickerbocker Whist Club some three years ago, had a system based on this count of which he thought so well that he challenged the champion four of the club to play their system against it in a set match.

His idea was to bid no trump on any hand that counted 11 or better, regardless of the distribution; but if. there were six or more cards in hearts or spades, or five with four honours, to bid two. There were no original or free bids of one in suit.

Dr. Thurston G. Lusk, secretary of the Knickerbocker Whist Club, after the failure of the Beecher system, adopted the same count, but varied its value according to the player's position at the table, and adopted it to suit calls, as well as no-trumpers. With 11 values, he advises the dealer to bid, but does not restrict him to no-trumps. Dr. Lusk requires 12 values for the second hand to bid, if the dealer passes; 14 for the third hand, after two passes; and 16 for a fourth hand free bid. This is contrary to modem experience, so far as the second bidder is concerned, it being now admitted that he can bid with a weaker hand than in any other position at the table, having at least one weak adversary, and a partner who has yet to speak.

Later in this article we give an outline of the best trick-estimating system thus far published, that of W. C. Whitehead.

NO previous system allows for the unequal distribution of values; nor for the increased value of high cards when held in combination with other high cards, such as ace and king of the same suit. They are also open to the objection that as soon as certain individual high cards are shown in the play, the count of the hand is disclosed up to that point, and the negative inferences as to other cards are open to the opponents. Here is an interesting and instructive example from the match between the Beecher system and the Knickerbocker team: Z deals and passes, having only 9 values. When A and Y pass, B calls the diamonds. It is not a good fourth hand no-trumper with a singleton spade. Z opened with the ace and a small spade, B trumping the second round and leading a high trump, which Z won with the ace. Another spade was trumped by B and the queen of trumps dropped the jack from Z's hand.

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Continued, from page 67

Now, at the fifth trick, B can count Z for having held 9 values. Had he also held a queen, he would have had a bid. He cannot have any jacks, as they are all in dummy. Therefore both the missing queens, in hearts and clubs, are with Y, and it is a simple matter to finesse against them with absolute certainty, winning five by cards and the game.

The fundamental principle in modern bidding, which was first explained in this magazine four years ago, rests upon the fact that the high cards, which are usually counted on for sure tricks, will produce twice that number of tricks for the partners that get the contract. That is, given equal cards, the declarer will win twice as many tricks with them as his opponents will win with their high cards. This fact was first pointed out sixteen years ago in Foster's Complete Bridge, published in 1905, and examples of it were given, among them one deal in which all the four hands were exactly alike, yet the declarer won eight or nine tricks out of the thirteen. In Milton Work's Red Cross duplicate deals, with perfect bidding and play, the declarer's side wins 246 tricks with their 126 aces and kings, while their adversaries, playing against the declaration, win exactly 66 tricks with 66 aces and kings.

Starting with this as a basis, and working out the values for every combination of high cards, for free bids, in attack, or for assisting bids or doubling, Wilbur C. Whitehead has now given us in his latest work, Auction Bridge Standards, the most thorough and complete counting system possible to imagine, and shows its application not only to every position at the table, but to every circumstance of the bidding.

The Whitehead system is based on "quick" or sure tricks, and parts of such tricks, the fractions being used to allow for the presence of cards that are not as good as aces. We have been given permission to publish the scale.

High Cards Values

A K Q and others...2 1/2

A K J... 2 1/2

A K; A Q J; or K Q J... 2

A Q 10; A J 10; or K Q 10... 1 1/2

A Q and others... 1 1/4

A; or K Q, and others... 1

K J 10 and others.... 3/4

K; or Q J and others... 1/2

Q and at least two small.... 1/4

J 10 and others.... 0

When counting up a hand for defence, its quick-trick value stands; but when Counting it for attack, this quick-trick value is doubled. Here is an example: Z, deals and bids no-trump. He counts 3 quick tricks as equal to 6 if he plays the hand. The singleton king is not reckoned. Dummy has 2½ quick tricks, or 5 in attack. Add these to the 6 held bythe declarer and we get 11 as the value of the combined hands. As played, they got 11 tricks.

If we count the opponents' hands, we find B's worth nothing, for either attack or defence. A's hand is worth 2J4 quick tricks in defence, and he took two.

So many requests have come to hand for a statement of the best way to play the hand that appeared in the June number, in which the declarer was set for three tricks, instead of going game, that the following brief outline is given.

The final declaration is two no-trumps by Z, with A to lead a small heart. Dummy, Y, should have put on the queen, and led the ace and then a small diamond. B puts on the king and returns the heart. This Z wins with the ace, and makes his three diamonds, on which A discards three clubs; B a heart and a spade; dummy two spades.

When Z leads a small club, the king wins and a spade is returned. B puts on the ace and leads another heart. After A has made the two heart tricks, Y and Z make the rest, three odd and game.

Answer to the August Problem

HTHE cards in Problem 17 were as follows:

Hearts are trumps and Z leads. Y and Z want five tricks.

Z opens with a spade, which A trumps, Y playing the spade queen. A leads the king of clubs, which Z wins with the ace, and leads the jack of diamonds. A covers with the queen and Y trumps. When Y leads the small spade, B discards a club. Z wins the spade, A discarding the five of diamonds.

When Z leads the jack of clubs, A wins with the queen, and Y makes two clubs, or Z makes two diamonds, according to A's lead. To avoid this ending, A may refuse to cover the jack of diamonds. In that case, the jack holds, Y shedding a club. Z follows with the nine of diamonds, which Y trumps, and leads a spade. Z makes the diamond king, losing a club at the end.