Chapter 13

Balancing Over a 15-17 Notrump

Play a system such as DONT, Brozel, or Woolsey, that allows you to show most two-suiters.  Do not play a system where double shows count.

A computer study of many deals shows you should think Always Balance.  Vulnerability and length of the longest two suits are important.  Having a singleton (or void) is a plus, but is not a necessity. 

With nine cards in two suits and a bid that shows two suits, always balance.  You expect to make over 50% of your bids.  Making is not sensitive to balancer's point count.  How well you do depends on vulnerability — Both vulnerable you would do better passing if partner would lead your suit.

To bid or not to bid on less distributional hands can be a matter of personal preference.  Possibilities: 

• Treat the long suit in a 5-3-3-2 pattern as a six-card suit.  If you bid, you will make less than 40% of your contracts.  You are betting the set will be less than the partscore.  If no one is vulnerable then bid, otherwise pass.  The quality of the five-card suit does not matter. 
• 4-4-3-2 and 4-4-4-1 patterns.  Bidding depends on vulnerability and point count.  One plus is an overcall that shows two specific suits.  A second plus is +110 in a major rather than +90 in a minor.  If do you bid with a 4-4-4-1 pattern, show the higher two suits.  In DONT, 2 shows spades and hearts.  In Woolsey 2 shows spades and hearts.  In Brozel 2 and 2 shows that suit and hearts, and 2 shows spades and hearts.
  • You are not vulnerable - Always balance DONT is best.
  • We are vulnerable - Have count or pass. 

If you choose Always Balance (I do), then second seat simply bids to the best spot.  Second seat does not bid to the Marty Bergen limit, and second seat does not attempt to reach game.  Long ago the rule for raising a friend's three-level preempts was game in hand plus trump support, and that should be rule here.  If you can count nine tricks, you can invite, and with ten you may bid game.  If you want a minimum suit count for advancer's bid, choose five or six.  If advancer has many points, then fourth seat is simply bidding his hand.  Defensive points should be between 15 and 25, and 20 is a much better guess than 25.

Against weaker notrumps, I choose Always Balance.  The above applies.  An experiment several years ago showed that the chances for game for either side after a 10-12 notrump was 30%, which means your chance is about 15%.

Balancing over a 15-17 Notrump

	Vulnerability
Pattern	None	N-S	E-W	Both	Comment
6 + cards	Always Balance				Double dummy numbers say no when both are vulnerable.  Partner will not lead your suit.  Balance.
5-5-x-x					If everyone else is passing, you should play DONT, otherwise Woolsey.  With both vulnerable, numbers say bid.
5-4-x-x					With both vulnerable, always balance = 43%.  Count is starting to matter.  You make over half the time, so balance.
4-4-x-x	Always Balance		Have values		Count matters.
5-3-3-2					Balancer treats a 5-3-3-2 pattern as a one-suiter.  Results are similar for any five-card suit, or a three-of-the-top-four suit.

We could have anticipated that results depend on the four vulnerability conditions, and that the most unfavorable vulnerability is Both.  Assume: 

• We or They play 1NT.
• There is no defenders or declarers advantage. 
• The deal produces four to nine tricks. 
• No doubles. 

• No one vulnerable.  We want to play 1NT.
• We are vulnerable.  With 7-9 tricks, We want to declare.
• They are vulnerable.  With 4-6 tricks, We want to play 1NT.
• Both vulnerable.  They should play 1NT. 

Here is one of the four charts Larry Cohen might make to show this.

Chart for 13 trumps - They are Vulnerable

We play the hand in 1NT		They play the hand in 1NT
Our # of Tricks	Our Score	Their # of Tricks	Our Score
9	+150	4	+300
8	+120	5	+200
7	+90	6	+100
6	-50	7	-90
5	-100	8	-120
4	-150	9	-150

A bidding program (the Senorita) and the Gib double-dummy solver are used for simulations.  There are three types of auctions to consider in a simulation:

1. A North-South auction without competition.  This bidding accurately represents real world bidding.
2. An East-West auction without competition.  DONT and Woolsey follow Cohen and Robinson rules to find a strain quite accurately.  There are cases where overcaller proposes one or two suits, and advancer wants a different suit, and I continue to fine tune these auctions.  If West overcalls, the bidding continues to find the systemic East-West strain.  Several defensive bidding systems are used.  If West and North pass and East bids, then East-West bid to their strain.  If West passes and North bids, then East-West stay out.  (Some defenses use business doubles.  I do not know the follow-ups.  The requirement for a double is set high to avoid most doubles.) 
3. Real world auction where both sides bid.  North-South's may:
   • Ignore the interference, and work intelligently toward their contract. 
   • Launch 3NT. 
   • Let East-West describe their hands, and then reenter the bidding. 
   • Be disturbed by an overcall. 

Competitive auctions are less likely when fourth seat balances, and so that is the problem treated here.  The final contract is most likely the offensive contract or the defensive contract, and not something else.  The motivation should be your best score, and not disturbing the opponents.  Usually you are satisfied with finding your best suit as low as possible, and not worried about further competition, or bidding to game.

Let us get this out of the way now.  One should argue that a computer simulation does not represent the real world, and therefore the results need to be interpreted.

• Gib starts with a defender's advantage, as it finds the best lead.  In the play of the hand, Gib may have a declarer's advantage, as it knows what finesses to take and which way to take two-way finesses.  Guessing finesses is important in the play of balanced hands.  Total trick analyses assume defender's and declarer's advantages wash.  Folklore is being created to the effect that declarer's advantage dominates at notrump.
• If you bid, they might improve the contract.  We have seen them bring the minors into play.
• They might double.
• One could argue that we defend better.  Therefore, a balance may exchange a good board for a top or bottom. 
• Responder could set a trap.  Traps went out with the dodo bird. 

I think these factors favor bidding with distributional hands.  You have to guess at what declarer's advantage is at 1NT when fourth seat has various patterns.  I am sure it increases as fourth seat goes from a 4-4 pattern to a long suit.

In the simulations, the opener is South and the balancer is East.  I did the problems using several defensive systems.  It suffices to show DONT results.  Unmarked DONT should be read as "East Has Values DONT".  The results for different hand patterns are:

One-on-One Matchpoints (%) vs Vulnerability and Hand Pattern

Pattern	Strategy	None	N-S	E-W	Both	Make%	Deals	Comments
6 + cards	AB DONT	79	57	62	49	67	2256	E-W make 2/3 of the time.  Most of the matchpoint scores are above 50%.  East has "values" over 2/3 of the time.
	DONT	74	54	56	48	67	1637
5-5-x-x	AB DONT	91	73	75	58	71	2304	With ten cards in two suits, matchpoints and makes are higher.
	DONT	88	70	67	52	76	1654
5-4-x-x	AB DONT	73	61	55	43	51	2208	Matchpoints and makes are decreasing.  Only half the East hands have "values".
	DONT	65	56	52	48	54	1193
4-4-x-x	AB DONT	64	53	42	29	37	2592	Even lower matchpoints when you bid with 4-4.  Makes are related to points.  Only 20% of the East hands have "values".
	DONT	55	50	49	50	45	487
5-3-3-2	AB 5-3 DONT	65	55	37	23	35	1008	A fictional system.  Makes are below 40%.  Points matter.  Do not bid vulnerable on air.
	5-3 DONT	55	49	47	46	38	393

These are numbers for balancing over a 15-17 notrump.  I would expect similar results for other notrump ranges.

Whether or not you make with a 6 + card suit seems unrelated to point count.  If West has the points, East wins trump tricks to take successful finesses through South.  If East has points, the average points per deal is probably higher, but the finesses won't work.

These experiments suggested an optimized DONT, an optimized Brozel, and an optimized Woolsey.  The optimization corresponds to that suggested in the first table in this chapter, and is not intended to produce the best simulation score.

The table below has the results of a 2304-deal pair game where one East-West pair passes, and the other pairs play 4-4 DONT, 4-5 DONT, Woolsey, Brozel, Hamilton, and Always Balance and optimized versions of everything but Hamilton.  Each match is also scored at IMPs, and IMP results agree with matchpoint results.  This table will be rebuilt with minor changes to the optimized systems. 

East-West Pass-out Matchpoints (Percent) vs Vulnerability

Rank	System	None	N-S	E-W	Both	Average
1	Opt DONT	58.08	51.36	51.86	50.31	52.90
2	Opt Brozel	55.00	51.76	51.90	49.61	52.07
3	Opt Woolsey	53.59	51.45	52.14	49.61	51.70
4	AB 4-5 DONT	51.60	51.32	52.06	50.41	51.35
5	AB Wool	53.59	51.45	52.14	47.60	51.20
6	AB Brozel	54.90	51.65	51.81	45.21	50.89
7	AB 4-4 DONT	58.08	51.35	49.05	40.90	49.84
8	5-3 DONT	47.14	49.57	49.25	51.94	49.48
9	4-5 DONT	47.14	49.48	49.25	51.85	49.43
10	Brozel	47.78	49.21	48.99	51.64	49.40
11	4-4 DONT	47.88	48.43	49.41	51.48	49.30
12	Woolsey	46.71	48.29	48.91	51.66	48.89
13	Hamilton	46.66	48.38	48.51	51.83	48.85
14	E-W Pass	31.84	46.29	44.72	55.96	44.70
	Deals	576	576	576	576	2304

To be precise, second seat plays 4-4 DONT, and fourth seat plays the indicated system.  Pairs are ranked according to their score averaged over the four vulnerabilities.  Pass is the big loser with no one vulnerable or one of the pairs vulnerable.  Pass  is best with both vulnerable, because Gib finds the double-dummy defense.  I still favor one of the optimized systems with both vulnerable.

• E-W pass.  They play 1NT.
• AB = Always Balance.  Balance with an acceptable distribution for the bidding system.  4-3-3-3 and 5-3-3-2 patterns are not bid (except in 5-3 DONT.) 
• 4-4 DONT = Bid with any 4-4 pattern.
• 4-5 DONT = Bid with any 5-4 pattern.  Pass 4-4.
• 5-3 DONT = Treat five-card suit as six-card suit in 5-3-3-2 hand.
• Woolsey = Washington D.C.  Standard notrump defense.  2 = hearts and minor (5-4).  2 = spades and minor (5-4).
• Brozel doubles with a one-suiter, bids 2 , 2 to show that suit and hearts (4-4), bids 2 to show hearts and spades (4-4), and 2 for spades and a minor (4-5 or 5-4).
• Hamilton is called Cappelletti in the East.  Double = penalty!  The minimum for a double was set high to exclude (almost) all doubles.  2 and 2 = that major and minor (5-4 or 4-5).
• Opt = Optimized.

If you compare the pair-game, not vulnerable Opt DONT with E-W pass, you find 58.08% and 31.84%.  These numbers are watered by many other pairs doing the same thing on the boards.  In a not vulnerable, one-on-one comparison, the numbers are 75% for Opt DONT and 25% for E-W pass.

The requirements for a second seat overcall are light.  Second seat has, in the longest suit, 12 suit points not vulnerable and 15 suit points vulnerable.  The first hand in the next section is four points light for a not vulnerable overcall.

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