Tuesday, September 15, 2009

Bermuda Bowl Analysis

I have done some analysis on the performance of each pair in the Bermuda Bowl final.

The method is based on assigning each pair an IMP score on each board reflecting the result they deserve to get relative to an error-free world class pair. In most cases I did this independently of the actual result so a minus would be assigned for missing a good game regardless of whether the game made in practice.

There is also a luck score for each board which is not assigned directly and is just the difference between the accumulated 'deserved' IMPs and the actual IMPs that changed hands. The total of this over the 128 boards was only 6 IMPs (in favour of the USA) so luck had very little effect overall though there were big numbers on individual hands.

Here is an example of the methodology. On board 2, Lauria/Versace were -200 in 4C and Nickell/Katz were -100 in 3NT. Based on the N/S cards I judged that 4C will normally make and 3NT will be down one. However, on the actual lie 4C is down one (though it can make double dummy) and 3NT is down two. Accordingly I penalized Lauria/Versace 3 IMPs for an unnecessary extra undertrick, Nickell/Katz 6 IMPS as they 'deserved' -100 against +130, and Fantoni/Nunes 3 IMPs for letting Nickell/Katz get out for -100 instead of -200. Since the USA gained 3 IMPs and the deserved IMPS totalled zero, this counted as 3 IMPs in the luck column for the USA. The luck here is in the fact that an unusually bad lie converted a possible partscore swing against the USA into just a question of undertricks.

The totals were:
PairNum BoardsAvg. IMPs per board
Meckstroth/Rodwell128-1.15
Hamman/Zia80-1.59
Nickell/Katz48-2.10
Lauria/Versace96-1.50
Fantoni/Nunes80-1.21
Sementa/Dubion80-1.95

As you can see, Meckstroth/Rodwell did slightly better than Fantoni/Nunes, while Lauria/Versace did slightly better than Hamman/Zia. Nickell/Katz and Sementa/Dubion were easily the weakest pairs on their respective teams.

It appears that the choice of lineups accounts for almost the entire winning margin. The US played their best pair for every board and their weakest pair for the minimium number. If Italy had done the same, by my reckoning they would have closed the gap from 36 IMPs to 7 IMPs - less than the carryover.

The calculations are in this Excel spreadsheet. I am certainly open to any of this being disputed as there may be excellent reasons for the bids and plays chosen that I am unaware of.

The play records are located here.

The Case for the Weak NT: Summary

So far we have seen:

Both the weak and strong notrump carry negative inferences that are useful after opening one of a suit. However, because the weak notrump includes all of the weakest playing strength opening hands, it has the effect of increasing the lower limit of your other one level openings. This is a big plus.

The strong notrump leads to awkward rebid problems on unbalanced hands in the 15-17 range. This is less of a problem with the weak notrump as the suit opened can be rebid with a minimum opening and 1NT is available with a better hand.

Missing a 4-4 major fit is a possible disadvantage for the weak notrump, but this happens much less often than is commonly believed and need not always lead to a bad result even when it does occur.

The side that opens 1NT is much better placed in the subsequent auction. A weak notrump means this advantage is enjoyed more often. A weak notrump opening also means the opponents need to consider whether they have a game or can extract a penalty, in addition to just locating their best partscore. All of this in the very limited space available to them when you have started with 1NT.

Finally, a computer analysis of the likelihood of being doubled for a penalty after opening 1NT shows you can expect a 10 IMP loss once every 800 hands, under assumptions very favourable to the opponents. Under more realistic assumptions, the loss is probably miniscule or non-existent.

I would like to conclude by pointing out that the weak notrump works just as well with a five card major system and 2/1 game force as it does with Acol or similar systems. Do try it!

The Case for the Weak NT: Going for a Number

Nobody likes to get doubled and concede a big penalty. There will be times when this happens and you get a bad result that could only have been avoided by not playing a weak notrump in the first place. The question is how often this happens and whether the cost outweighs the benefits described in the previous three sections. I've done some computer analysis on this, using the following assumptions:

- Your weak 1NT opening is in first position at any vulnerability.
- An unpassed opponent will double your 1NT if and only if he has 15 or more HCP.
- A passed opponent will double your 1NT if he has a decent single suited hand (DONT).
- If RHO has a double, LHO never bids in front of him.
- When 1NT is doubled you will always run to a suit contract.
- You always end up in two of your best fit. With good runout methods you can usually achieve this.
- After you run, opponents always make the optimum double dummy decision, i.e. doubling you if and only if the penalty they can get exceeds what they could score in their own best contract.
- The scoring is IMPS and the theoretical par contract is achieved at the other table

These assumptions are very favourable to the opponents of the weak notrump bidder. In reality, there are all kinds of things that may go wrong for them:

- They may double and you make.
- They may get an inadequate penalty.
- You may have the balance of power and redouble, either making (1560 is not unheard of) or penalizing them.
- They may choose to bid or pass instead of doubling when a penalty is possible.
- Even if your doubled contract is theoretically optimum for them they may drop a trick on defence. In low level contracts, defence is harder than declarer play and opening leads are harder still.
- Similarly, even if the penalty is theoretically optimal because their game or slam fails double dummy, it might make in practice.

The results of the computer simulation are as follows, for each position of the weak notrump opener:

1st seat: 1NT opened on 8.08% of hands. An average loss of 0.22 IMPS per hand each time 1NT is opened.
2nd seat: 1NT opened on 3.65% of hands. An average loss of 0.18 IMPS per hand each time 1NT is opened.
3rd seat: 1NT opened on 1.47% of hands. An average loss of 0.45 IMPS per hand each time 1NT is opened.

Put another way, this averages out to one 10 IMP loss once every 640 hands. If you don't play the weak notrump in third seat, it's a 10 IMP loss once every 800 hands.

Remember this assumes the opponents make perfect decisions every time. They certainly won't in practice, and you'll break even or gain for all the reasons listed above. Actually, after adding back in the times you get +180 or they have some other kind of accident, you may well end up showing a profit even on the hands where doubling is an option for them. This is added, of course, to the gains in all the situations discussed under the other headings.

Friday, September 11, 2009

The Case for the Weak NT: Advantages of opening 1NT generally

The limited strength and distribution of a 1NT opening allows auctions that are less revealing to opponents compared to opening one of a minor. The contracts reached after a 1NT opening are therefore more likely to make. You'd rather bid 1NT-3NT than 1D-1S-1NT-3NT because you have a better chance of a favourable opening lead and the subsequent defence will be more difficult as well.

The weak notrump occurs more often so it gains the most from this.

When the hand belongs to the opponents, it is more difficult and dangerous for them to enter the auction when you open 1NT, compared to opening one of a minor:
  • They have to start bidding at the two level
  • They have the additional objective of trying to get a penalty, not just bidding to their own best contract
  • If they pass with a decent hand, there may well be no second opportunity
  • Whether your partner passes or bids, there is still no safety for them as your side can have almost game values and no fit
  • The limited shape and strength of the 1NT opener makes it easier for you to judge when to double them
  • The 1NT opener has not shown a suit so takeout doubles and cue bids are not available for them
  • Auctions over opponents 1NT are generally not discussed and understood as well as auctions over their suit opening.
Over a strong notrump, finding your best partscore is the overriding objective and methods can be tailored just to do that. Defences such as DONT, Meckwell and Lionel are all designed to do this but you'll find it hard to extract a penalty or bid constructively towards game if you try using these against a weak notrump.

There's no real solution to this - bidding accurately over an opponent's weak notrump is just extremely difficult. Here are a couple of examples:

xx xx KQxx
KQJ10xxor KQJ10xxopposite xx
Qxx AQx Kxx
xx xx Axxx

If West has the first hand, 1NT could well make if he passes and 3H is too high if he bids and partner invites. On the second hand, E/W have a game in hearts. After a 1C opening, both hands are easy to bid depending on whether your jump overcalls are weak or intermediate. Starting a level higher after a 1NT opening, there isn't enough space to do everything.

AQxx Kxxxx xx
xopposite Qxxxor QJxxx
KJxxx Qx xx
Qxx Kx Kxxx

Let's say E/W have a bid showing spades and another suit. West will be reluctant to bid over 1NT, especially vulnerable, in case East has the second hand and he concedes a significant penalty against a part score. Of course, if East has the first hand he will miss an easy game. There is no such problem after a minor suit opening.

AQxx Kxx xxx
KJxopposite Qxxxor xxxx
AQJx xx xx
xx QJxx QJxx

If West doubles, his partner with the second hand will have no choice but to pass and concede something like 380 (or 960 if they redouble). Obviously if he passes and partner has the first hand, E/W will miss either a game or a sizeable penalty. If West doubles a 1C opening for takeout opposite the second hand, E/W will get no higher than 1H or 1S, probably down one undoubled.

Thursday, September 10, 2009

The Case for the Weak NT: Playing the wrong partscore

After a 1NT opening there is always a risk of a missing a 4-4 major fit on a partscore hand. The weak notrump occurs with greater frequency which makes this more likely and also the extra strength of the strong notrump means that 1NT will still often make when a better spot is available. To actually lose IMPs this way, though, several things have to happen:
  1. 1NT has to go down while 2 of a major is making
  2. The opponents must remain silent over 1NT. If they bid, you can make a takeout double and still find your 4-4 fit.
  3. The opponents must not be able to successfully outbid you. It is risky to enter the auction over 1NT, while balancing when opponents bid and raise at the two level is relatively safe. So you might never be able to play 2 of a major anyway.
About 13% of hands qualify for a weak notrump opening. On about 10% of these, responder will pass when you have a 4-4 major fit. Moderately aggressive opponents will only let you play in 1NT on about 20% of such hands. Overall, this is about one in every 770 hands, not including those where they can successfully bid over your two of a major but would pass 1NT, or where the 1NT contract does as well as, or better than, two of the major.

You can also alleviate the problem by responder using Stayman on weaker hands with 4-4 in the majors. As long as partner doesn't open 1NT with 2254 or 2263 shapes you'll play a 4-3 at worst which may still be better than 1NT. It's better to have two decent suits for this as three trumps opposite four small ones doesn't usually play well. You also need to agree that after 1NT-2C-2D-2H opener must correct to 2S holding three spades and two hearts.

There is also a corresponding situation where a 1NT opening makes it easier to locate an eight card major fit. This is where opener is balanced and responder has a five card major. After a 1NT opener, responder will transfer and pass. After a 1C/D opening and responder bids his major, opener may raise with three cards or bid 1NT. If he bids 1NT responder will pass and the eight card fit will be lost. If he raises, you'll play a 4-3 fit some of the time and the range of opener's raise is uncomfortably stretched if it may include a weak balanced hand with three card support. Playing a 5-2 when responder transfers and passes is less likely to be wrong than missing a 5-3. The extra frequency of the weak notrump is therefore a benefit on these hands. Furthermore, when 1NT is not opened, a three card raise on a balanced hand is not a stretch as opener will have 15+ HCP.

Finally, after opening one of a minor with 12-14 balanced it is not clear what is supposed to happen with a 4-4 fit when responder does not introduce the suit immediately, e.g. opener has four spades and the auction starts 1C-1H. If opener bypasses 1S and rebids 1NT, you lose spades when responder is too weak to act so are in the same position as a weak notrump opener except your two extra bids have helped the defence. If opener bids 1S instead of 1NT you risk playing 1NT from the wrong side or not at all when that is the best contract.

To summarise, opening 1NT may risk missing a 4-4 major fit on a partscore hand and the weak notrump does make this more likely. However this is much less frequent and less serious than is commonly believed, and in any case such hands will not usually end quietly in two of a major after a minor suit opening. There are other situations where a 1NT opening makes it easier to correctly find a major suit part score.

Tuesday, September 8, 2009

The Case for the Weak NT: Offshape 1NT openings and rebids

Playing a weak notrump, there is less need to open 1NT with imperfect shape. For example:

x
AJxx
Kxx
AKJxx

Playing a weak notrump you open 1C and rebid 1NT if partner responds 1S. However, playing a strong notrump you have a real problem. The hand is not good enough to reverse but too good to rebid 2C. I suspect most experts would open 1NT if the singleton spade was an ace or king, otherwise open 1C and either 'upgrade' to a reverse or 'downgrade' to a 2C rebid. This is unsatisfactory as there is a significant gap between the upper limit of a simple rebid of the suit opened and the lower limit of a reverse. I suppose you could also try a 3C rebid on a five card suit but that is a significant misdescription.

Opening 1NT leaves you poorly placed if partner is weak with five spades (he'll transfer and pass) or when he has four hearts, e.g.

xxx
KQxx
xxx
Qxx

Or a balanced hand with no spade stop:

xxx
Kxx
AQxx
Qxx

And the worst case is good club support:

Axx
KQx
Ax
xxxxx

It would be a pity to bid 1NT-3NT when 7C is possible. Even if you only open 1NT when the singleton is an honour, a hand with the king of spades instead of the king of diamonds would do equally well in 7C. If the hands didn't fit well 6C would still often be a good contract.

After opening 1C and hearing 1NT from partner, the 1NT rebid is not ideal either but you do avoid the worst of the problems with an offshape 1NT, exemplified by the example hands above. The reverse problem does not apply with an offshape 12-14. Without the king of diamonds you would be too weak for a 15-17 1NT rebid but there is no problem as you can open 1C and rebid 2C if partner bids 1S.

There are some players who are happy to open 1NT offshape and believe they gain by doing so. If you are one of them, then you won't regard it as a disadvantage that the strong notrump forces you to do so. However, the idea that you gain by opening 1NT as often as possible is also yet another argument in favour of the weak notrump.

Saturday, September 5, 2009

The Case for the Weak NT: Inferences when 1NT is not opened

Balanced hands in the 12-14 range have the least playing strength of all opening hands. Therefore, the weak notrump effectively increases the minimum strength of opening bids of one club and one diamond so these have a narrower range. Conversely, the strong notrump removes intermediate range hands from the one of a minor openings. Consider the following hand:

Qxx
AKxx
xx
AKxx

LHO makes a preemptive jump to 3S over your opening bid. Partner passes. There is no problem if you opened a strong notrump as you've shown extra strength already so have no reason to bid more. It's more difficult if you opened 1C playing a weak notrump. Suppose you pass 3S. Consider three possible hands for partner:

x Jx xx
Qxx Qxx Qxxx
Axxxx AJxxx Axxx
Qxxx Qxx Qxx

The first hand gives some play for 4H or 5C though I think partner might double, rather than pass. The hand with shortness needs to take the lead in these situations. It would be nice to have a fourth heart but a 4-3 fit could be ok. Even playing a strong notrump, there are plenty of hands where you want to be in the auction but it will be hard for opener to act after a pass.

The second hand is probably close to a maximum pass. You might make 3NT but it needs some luck. Likewise the third hand is marginal for 4H and partner would double if stronger.

Examples like this suggest to me that it's acceptable to pass an average strong notrump in this situation. Also bear in mind that partner can make a negative double a bit more freely playing a weak notrump as he knows you won't have a weak balanced hand. And none of the above would be straightforward if the opening bid was a 15-17 1NT instead of 1C.

Playing a weak notrump, the inferences after a 1C/D opening occur in situations such as the following:

AQJxx K10xx K10xx
xxxopposite Axxor Ax
xx AQxx AQxxx
Qxx xx xx

In each case, the bidding starts 1D-1S-2S. Opposite the first hand, you cannot make game and are in danger at the three level. With the second, game is close to 50% and worth bidding at IMPs. Removing hands such as the first one by opening them with 1NT means opener's playing strength falls with a narrower range and decisions about whether to bid game are therefore more accurate. What tends to happen playing a strong notrump is that opener will stretch to bid 3S on hands not much stronger than the second, which may well lead to a hopeless contract opposite a minimum responder.

The exclusion of strong notrump hands from an opening bid of one of a minor does not carry any such useful inference as opener may still have an unbalanced hand of equivalent playing strength.

The Case for the Weak Notrump

This is the introduction to a series of posts analysing the merits of a strong (15-17) notrump vs a weak (12-14) notrump. The name of this post might suggest the analysis will not be particularly objective, but the evidence is strong enough that it's hard to avoid any other conclusion.

I will assume the rest of the system is five card majors and a 2/1 game force structure, though there won't be much difference if not. The arguments for or against the weak notrump fall roughly into five categories:I'll post on each of these over the next few days plus a summary at the end.