A Special Method for Illustrating Bridge Auctions: the Torring Chart

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Title

A Special Method for Illustrating Bridge Auctions: the Torring Chart


Gavin Wilson


August 18th, 2016

Abstract

Is there a way of combining the typical account of the bidding sequence as used in bridge textbooks, newspaper columns and magazines, with the hand record which indicates the best scores available in each denomination in double-dummy play?


Claygate Bridge Club; Gavin.Wilson@org2b.com

Keywords

  • Contract Bridge, Duplicate Pairs, Scoring, Graphical Methods

Introduction

Where bridge clubs have the benefit of computer-dealt hands, players receive a 'hand record' at the end of each session, which shows them not only the layout of each board but also the maximum number of tricks available in each suit (and no-trumps), and with each of the four players as declarer, were the board to be played double-dummy i.e. in full knowledge of the contents of each hand. However these hand records, sometimes nicknamed 'answer sheets', do not show the best auction to reach these contracts; nor do they show the actual auction witnessed by each player.

Newspaper bridge columns, on the other hand, typically display both the board layout and the actual auction, without formally describing the maximum number of tricks that should have been made in each denomination. Column space is, no doubt, a consideration. This paper describes an endeavour to include both the actual auction and the information contained in the answer sheet in a single diagram, which the author calls a 'Torring Chart'.

Furthermore the inclusion of the maximum number of tricks available in each suit shows the risks the players run with each bid, and a clear visual explanation of why the optimum contract is indeed so, in that any further bidding by either side will damage their score.

Background

Here is a typical hand record:

Torring Bridge Club — 7th August 2016 — Hand #14
♠ J 8 7
4 3
K Q 6 4 2
♣ 10 9 5
♠ 6 5 4
J 9 8 6
A 10 8 5
♣ Q 2
Dealer: East
Vulnerable: None
♠ K 10 3
A K Q 10 7 2
J 7 3
♣ 7
♠ A Q 9 2
5
9
♣ A K J 8 6 4 3

Optimum Result: N•S 5♣ 400


N
S
E
W

NT
6
6
4
2
9
9
3
3
5
5
8
8
7
7
6
5
11
11
2
2

The bridge journalist might supply a description of the auction thus:


N
E
S
W

-
1
2♣1
2
3♣2
33
3♠4
4
5♣5
End

1. Playing weak jump overcalls.
2. Supporting partner's overcall on a total-trumps basis, hoping partner has six clubs.
3. A hand containing only 13 HCP, but six hearts and six losers.
4. By showing a second suit to partner at the 3-level, South seeks out a double-fit in the black suits, in which case slam might be possible.
5. Game, not slam, is the limit of the opportunity.


The Torring Chart

It would be better if the auction and the answer sheet answers could be combined into a single diagram:

Torring Chart
Hand #14 of 7th August 2016 at Torring Bridge Club
Dealer: East
None Vulnerable
500 N•S
Ⓔ Ⓦ
400 N•S
Ⓝ Ⓢ
N
300 N•S
W
150 N•S
S
N
140 N•S
Ⓝ Ⓢ
N
100 N•S
E
70 N•S
Ⓝ Ⓢ
BID ↣
1♣
1
1
1♠
1NT
2♣
2
2
2♠
2NT
3♣
3
3
3♠
3NT
4♣
4
4
4♠
4NT
5♣
5
5
5♠
5NT
Max Trix in Suit
7
8
9
11
110 E•W
E
Ⓔ Ⓦ
W
Pass
E
S
W

What Does All This Mean?

As you may gather, the horizontal axis of this chart shows the bids available in any bridge auction. The vertical axis shows the value of each bid if it were to be the agreed contract and the hand were played perfectly by both sides — doubled if the contract is going off. Scores above the horizontal bid axis are positive for N•S; scores below the horizontal bid axis are positive for E•W. Here is an explanation of what each of the boxes on the chart means:

N
means a bid by North. (Only the sides of the box pointing N•S are shown.)
7
means that the maximum number of tricks which can be made in this suit is 7, by N•S.
Ⓔ Ⓦ
means that this is the optimum contract for the board, and it is declared by either East or West.
Ⓝ Ⓢ
marks the cheapest opposition bid — in this case, by North or South — which, if doubled and then declared by the opposition, would result in a worst score for the opposition than the optimal contract, which in this case belongs to E•W.
W
means a bid by West. (Only the sides of the box pointing E•W are shown.)
8
means that the maximum number of tricks which can be made in this suit is 8, by E•W.
means that the best score in this suit can only be achieved by South as declarer.
S
❌ W
means that South has made this bid, which West has now doubled..

What Does This Give Us?

What this gives us is a graph showing the progress of the auction, as given by the pink squares on the Torring chart:

  • On the first round of bidding, the contract is flipping above and below the zero-score line, as each player's bid brings the contract back into positive territory for their side.
  • But after North's 3♣ bid, the auction stays in positive territory for N•S.
  • East's next bid of 3 reduces N•S's potential score, but it is still positive for N•S.
  • When North then bids 3♠, the marker on the chart also shows that this is the best contract available for either side in spades.
  • When West then bids 4, this actually improves the score for N•S, because it will go off two with best play, giving 300 to N•S. To an all-seeing player, 4 is therefore a bad bid. (But wouldn't the all-seeing player would bid straight to 5♣ with his opening bid?)
  • North's 5♣ bid brings the board to its optimal contract, conferring 400 on N•S.
  • The chart illustrates that this is the optimal contract, because N•S have no higher contract which makes, and the cheapest overcall which E•W can now make is 5, which goes down three, giving N•S 500 points after the presumed double. (The Torring Chart always assumes that contracts going off with best play are doubled.)

The Torring Chart is a useful educational device for showing bridge students the value of each bid, particularly in a competitive auction, in terms of its impact on the likely score.

Limitations of the Torring Chart

The Torring Chart takes a little time for the unaccustomed to understand, but keen students quickly become familiar with, and appreciate the approach.

The chart is big. It is bigger than the sum of the two tables displaying the auction and the optimal number of tricks in each suit.

No doubt the graphics can be improved, but the above is a satisfactory start. Setting up the chart can be time-consuming, even with the help of a computer. What is needed is a computer program to do the work of laying out the Torring Chart for the hand, and plotting all the auction points.