Tuesday, September 15, 2009

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.

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