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The Pass, the Bash, and the Ugly
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Sorry for the reference to my favorite movie, but, DO-WEE-DO-WEE-DO, OOH-OOH-OO. Tom Allen recently posted a question about Passing or Bashing in Matchpoints. This got me wondering. What is the rationale behind a pass-or-bash philosophy? Is it sound?

There is one obvious argument for this approach - two notrump is never the right contract. If you can make a game, you should be in game. If you can't, then you should stop in 1NT. Climbing up to 2NT, inviting a game, and going down a trick, is one of the cardinal sins of bridge.

Notice, if you accept this philosophy, then pass-or-bash carries a number of subtle additional advantages. First off, you won't need any invitational 2NT calls. So you can free up 2NT for some other systemic function. For instance, you can gain some of the advantages of two-way Stayman, and play 1NT - 2 - 2X - 2NT as forcing, asking for more information. This would greatly help on slam hands and choice of game searches. Next, you make it much harder for the opponents to try a speculative penalty double. Finally, you give up less information when you get to game. This is particularly true if system forces you to invite through a 2 mechanism. Compare these auctions on defense:

W
N
E
S
1NT
P
2
P
2
P
2NT
P
3NT

or

W
N
E
S
1NT
P
3NT

Even the old-fashioned

W
N
E
S
1NT
P
2NT
P
3NT

tells the defenders that opener is not minimal, which eliminates some hands from the defenders' mental stew.

Finally, and this is a big plus for the Pass or Bash crew, when luck is out, sometimes there are only seven tricks. The Passers gain against the failing 2NT, while the Bashers lose, but only an extra undertrick. In these cases, they get 10-3 odds, not 10-6, for trying for the game bonus.

Of course, this approach has its price. For instance, I said that 2NT can never be the best contract. That isn't really true. If your choices are Pass or Bash, and you choose Pass, and fourth hand has some shape, they may well land in a making part-score (or aid the defense when fourth hand balances and you bid on). The auction

W
N
E
S
1NT
P
2NT
P
P
P

may well gain over

W
N
E
S
1NT
P
P
2

Then there is the obvious price - when you invite and partner rejects, game rates to be poor, and our expected IMP value playing 2NT will be much higher than 3NT bid by the Bashers.

The subtle gains are numerous, and are certainly worth some IMPs. How much does it cost when you lose an invite? Quantifying that is hard, but that is my goal here - to put IMP numbers on the three approaches to border-line hands, the Pass, the Bash, and the Ugly, out-of-vogue Invite.

Let's start this out in the completely hypothetical. We'll assume that you are vulnerable, at IMPs, the best possible scenario for Bashers, and you pick up a marginal hand, a hand where you judge game to be around 40% opposite a typical 1NT opener. That is beyond the break-even point for a vulnerable game, so our Bashers will Bash, not Pass. To calculate the odds, and costs, I need to make some shaky assumptions. These are:

  1. Partner will accept an Invite on exactly half the notrump hands.
  2. When the game fails, it will fail by either one or two tricks. Two-thirds of the failures result in a one-trick set. One-third of the time, seven tricks are the limit.
  3. Game chances are obviously better if partner would accept an Invite. I assume that game makes 50% of the time when partner would accept, but only 30% of the time when partner would decline.

Given those assumptions, the arithmetic is pretty easy. First off, let's look at Passing vs. Bashing. The Bashers gain 10 IMPs on the 40% of the hands where game makes. They lose 6 IMPs when there are only eight tricks available, and seven if they go off two, against the 90 at the other table. So, that is

10*.4 - 6*.4 - 7*.2 = .2

Bashers gains one-fifth of an IMP per board. That translates to around 13 IMPs in a 64-board knock-out.

Next up, Bashing against the Ugly Invites: Half the time, both pairs play 3NT, with a slight edge in information to the Bashers. When the Ugly's stop in 2NT, game is poor, and the Inviters gain substantially. Sure enough, those gains work out to .25 IMPs per board. 16 IMPs over a long match to the Ugly crew.

Not surprisingly, Ugly clobbers the Passers, reaching a 50-50 vulnerable game on half their hands. Ugly wins by a third of an IMP per board, up 21 IMPs in our long match.

Bashers defeat Passers +13 IMPs

Ugly Invite over Passers, +21 IMPs

Ugly upsets Bash, by 16 IMPs

Can these numbers be checked? I have noticed that top Precision players tend to Bash, and blast into 3NT with any balanced 9-count opposite a 14-16 opener. That seems a bit crazy to me, so I ran some simulations. Sure enough, using (admittedly flawed) double-dummy analysis, a balanced 9-count, with no five-card suit, will make a game opposite a 14-16 opener 38.2% of the time. Good enough to justify a try for the vulnerable game bonus.

According to the Encyclopedia, 42.4% of these openers will have only 14 points. So, I dealt out 424 14 point openers, and 576 15 or 16 point hands, against random balanced 9-counts. For Invites, I had opener accept with any 15 HCP, and reject with any 14 HCP. Here are the numbers:

Range Less than Seven Tricks Exactly Seven Eight Nine or More

14 59 115 165 85

15-16 24 74 181 297

IMP comparisons are pretty easy, with the higher contract losing 3 IMPs when there are fewer than seven tricks available.

Here are the numbers:

Passers Beat Bashers, .077 IMPs/Board, 5 IMPs in a 64-Board Match

Inviters Beat Passers, .69 IMPs/Board, by 44 IMPs in a long match

Inviters Beat Bashers, .662 IMPs/Board, by 42 IMPs a match

My conservative gut said I should invite on most 9 or 10 counts. What happens on 10-counts? Passing is clearly silly, and a huge loser. So the choice seems to be Bash or Invite. Here, the Bashers won out, defeating Ugly by .275 IMPs a hand, up 18 IMPs in a long match. Change the vulnerability, and Inviting with a 10-count worked out slightly better, up .091 IMPs a board, or 6 IMPs better in our match.

Since Passing was superior to Bashing with a nine count, vulnerable, then passing has to be the winner white. Inviting, not vulnerable, on a 9-count is still better than passing, but only by .066 IMPs a board, or around 4 IMPs in a long KO.

The notrump range turns out to make a huge difference. The closer the hands are in strength, the better they play - 12 opposite 12 is a much better 3NT than 8 opposite 16. When I turned my simulations to 15-17 notrumps, the scenario flipped. Balanced 8-counts should pass 1NT, even vulnerable. Inviting lost, by more than half an IMP a board, with twice that loss to Bashers. Balanced 9-counts do best bashing, clearly right vulnerable, and essentially a wash against inviting white.

What's it all mean? Who knows? Being able to invite is still numerically sound, even in IMPs. However, the gains from having an Invite go down as the notrump range rises. The target is narrower than I expected, and Bashing is superior to Inviting on balanced 10-counts opposite a 14+ notrump, at least when vulnerable. Eliminating Invites from your system will certainly gain on some other hands, and gains immediately from information concealment. There is a clear and quantifiable IMP cost. Is it worth the price?

Maybe the right approach is a compromise. I suspect that the auction

W
N
E
S
1NT
P
2
P
2
P
2NT

should not be invitational. Using this bid for other purposes makes sense. But, I think we still need ways to invite afterStayman, or directly. Will Pass-or-Bash systems be common fifty years from now? I doubt it, but ...

Some of these numbers are a bit bogus. Inviting loses out quite a lot when it leads to a minus score, which is the main rationale behind the Pass or Bash philosophy, but I tend to question those losses. As a simple example, suppose the auction starts out

W
N
E
S
1
P
2

and you are considering a game try. You lose big, according to the theory, if you end up in 3, and go set because of an unlucky lie of the cards - bad breaks or losing finesses. Of course, those bad breaks work in the opponents' favor, and it is extremely likely that they could make three of some suit. Minus 100 in three spades, when you might have been +110 seems pretty bad, but, in practice, -100 often beats par. Total Tricks tends to offer some protection when you Invite, and are rejected.

I, personally, play a wide-range weak notrump, and have to Invite frequently. I hate getting to 2NT down one, but it happens. Surprisingly enough, many of these disasters are covered by my team-mates, who got into the slower auction, and scored up +110 or +140.

This is a complex issue. I would love to hear from others who have studied this.

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