Equal-level Conversion?

Are you one of those people who fills out the overcalls point range on the convention card with something like 8 to 16? My answer to that question is a very British "Rubbish!" How can anyone seriously suggest that overcalls are about high card points? Especially the people designing convention cards!

To me, the difference between overcalling and doubling then bidding a suit is all about the suit quality and the shape of the rest of the hand. There are some really excellent offensively oriented hands that might do it with only 15 to 16 high card points. And others with 18 or 19 that are really only good enough for a simple overcall. Here's a hand from the other day where we were the only pair to reach game: ♠AKQJ72 ♥QT5 ♦A5 ♣64. All were vulnerable and my RHO, the dealer, opened 1♦. I regard this hand as somewhere in the vicinity of the tipping point between starting with 1♠ and double. But the quality of the spade suit tipped the balance in favor of double. The next player passed and, naturally, partner bid 2♣. After RHO passed, I bid 2♠. My partner, Alexander, who recognized this for what it was, had few qualms about bidding 3NT which he made with an overtrick. His hand was: ♠6 ♥K9 ♦QJ63 ♣J98732.

The only complication that we have to worry about is due to the concept of "equal-level conversion." Like some other bridge conventions or rules, such as "negative free bids" or "restricted choice," equal level conversion is about as badly named as anything could be. I've previously mentioned this subject briefly in Gosh, what a hand! The problem is that not everyone knows how to distinguish an equal-level-conversion from a good, one-suited hand. How can we be certain what's going on?

For the last several years, I've been thinking along the lines suggested by Robson and Segal in their book on competitive bidding (see that other blog entry for a reference). They talk about bidding above two-of-opener's-suit. But last evening at the bridge club [this was actually six months ago as I am now writing], I realized that there is one and only one determining factor which separates an "equal-level" conversion from a GOSH (good one-suited hand). Did you skip over the third suit after partner's response?

You pick up, in fourth seat, red on white,♠4 ♥AJ976 ♦AKT943 ♣A. LHO opens 1♠ partner passes and RHO raises to 2♠. How are you going to treat this monster? My friend Peter chose to bid 3♠, resulting eventually in the top spot of 5♥, but he was at another table. I'm really not sure what's best here, although I think I like 3♠, as it cannot possibly be passed by partner. At this vulnerability, double can't be too dangerous because partner will never pass the double for penalties. What about 2NT? Although it seems unlikely that this could be to play, it might be misinterpreted and then when partner chooses clubs and you rebid diamonds, partner might wonder if it was supposed to be natural all along.

So let's say for the sake of argument that you double and partner bids, as expected, 3♣. You are going to bid a red suit but which one you bid makes all the difference. When you double and partner selects one of the three unbid suits and you correct to the next cheapest (in this case 3♦), you are showing a two suited hand (note that the next cheapest might not be at the same level as the cheapest if for example hearts was their suit). This just shows a two-suited takeout and would be described, potentially erroneously, as an equal-level conversion.

But if instead you bid the fourth suit, bypassing the next-cheapest, then you are showing a GOSH (good one-suited hand).

Here's another hand from the same session to illustrate the principle of the (non) equal-level conversion. You hold ♠A432 ♥98 ♦AJ4 ♣QJT2 and with favorable vulnerability you decide to double the 1♦ call on your right. Personally, I like to have a little more ammo for this kind of off-shape double but the vulnerability is in your favor. If partner makes the expected 1♥ call, you will bid 1♠ showing the black suits. Here, you have converted at equal level, but partner may have to raise the level if he likes clubs more than spades. In practice, your LHO is the one with the balance of power (not partner) and he (LHO) redoubles. Partner bids 2♣ denying four cards in either major and they end up in a heart game, making five.

Occasionally, there will still be some ambiguity. If, going back to the first hand, my spades and hearts were switched, and the auction proceeded as before 1♦ X p 2♣ p ? 2♥ could still be showing a major two-suiter. If partner chooses spades and you bid 3♥, partner should get the message. But what if he likes the majors equally and passes 2♥? You might miss a game when you have a really outstanding hand (better than this one). In such a case you might have to make a jump bid of 3♥ over 2♣, but I think that would be rare.

And don't forget that you do need some extras (say 13 hcp?) if you have an off-shape double that will require conversion as you will often end up a level higher than you'd really like. Even then, you're likely to suffer the occasional 800.

Clearly, you have to be confident that partner won't misinterpret your rebid after a takeout double. As long as you have that assurance you can be much more frisky in your off-shape takeout doubles.

Nashua, NH

I don't often use this space to tell you about good results that happened at the table. Typically, I am more interested in some point of theory or maybe some problem hand that arose. But it's nice to be able to write about good results, especially when I can give most of the credit to my partner.

Last week I got to play with my wife and favorite bridge partner, Kim—for a change—in one of the big pairs events at the Nashua, NH, summer regional. We got a few gifts in the first session, resulting in a 63% game. One of my favorite hands, and an excellent example of the efficacy of the cooperative double, is the following:

[deal rotated]

What is particularly impressive here is that most of the evidence suggested passing my double. Yet, knowing that I was a passed hand, it must have appeared very likely that 2♠ would make (it would) and so Kim sensibly bid 3♥. At the point of the 2♠ bid, we were destined for either 5 or 10.5 matchpoints (out of 25), depending on our defense. When they didn’t double 3♥, we had improved to average. When one defensive trick was mislaid, we moved up to 17.5 mps, but then they dropped another, allowing Kim to actually make her contract. That put us all the way up to 23.5.

We were about half-way through the afternoon session, struggling a bit and getting insufficient gifts, when this hand came up. As you can see there's not much to the auction—but all day we had been defending a lot and doing it quite well, this being perhaps our best effort. We were lucky that declarer went astray a little—but we did everything we could to help him along.

Kim chose the ♠8 for her opening lead which helped create the illusion that she started with AJ98. I quickly decided to duck the first high spade so I could smoothly follow low (2). Now, it must have seemed "obvious" how the spades were dividing. Declarer has no very good option at this point, the suit he wants to develop first (spades) being playable only from the other side of the table. Obviously hearts is the suit to attack, but which one? I think running the 9 stands out, but on this layout it turns out just as wrong as leading low to the king and ace, which is what declarer actually did.

Kim had noticed my ♠2 (we play upside-down carding) and so she continued with the ♠9. After some thought, declarer backed his earlier hunch and played the king which I captured with my ace. It was still far from obvious how we were setting this contract, but I chose to lead ♣2. I knew this would persuade Kim to return a club if she won the trick (we play attitude leads in the middle of the hand) but I didn't mind that too much as I did have the 9 sitting over the T8 and quite possibly the thirteenth club. But even more so, I didn't particularly want her to continue spades just yet or to switch to another suit.

Some of the plays seem a bit odd, I know. It's possible that I have the exact sequence of spots wrong—my recollection is that my hand took four tricks including the last trick with a diamond—but I couldn't make that work so I must have misremembered. But the final outcome is correct—we ended up setting the contract by two tricks. No other N/S pair managed eight tricks on defense. Our result was a shared top (23/24) because two other pairs managed to set contracts of 2NT and 3NT, each by two tricks.

This board helped us to a 55% session which was just enough to give us a creditable fourth place. Not too bad for a 27-table event with average masterpoints of almost 3500.

Using double to find out about fit (part 2)

This follow-up of the earlier Using double to find out about fit is prompted by some comments by Jeff Lehman on my last DSIP-related blog The final problem. [I apologize in advance for the inordinate length of this article, but I simply don't have the time to make it shorter—but at least I have included quite a few hand diagrams.]

Jeff maintains that in a competitive auction, after we have found a fit, we should use double to penalize the opponents, bid with an offensive hand, and pass otherwise [I hope I have this right]. And I would guess that at least 95% of active bridge players would agree with him. I recognize that I am in the minority.

So, I'd like to explain why I think my style is better. But, first, I'd better summarize it. When we find a fit at the two-level, we usually don't know whether it's a single eight-card fit, a nine-card-plus fit or some kind of double fit. I say "usually" because pairs playing Bergen raises and perhaps some other conventions actually do know. But, I am talking about the normal situation where the auction has gone, say, 1♥ (p) 2♥ or perhaps 1♦ (p) 1♥ (p) 2♥, although for simplicity I will only discuss the first of these auctions. Let's say that the last bid is immediately overcalled by 2♠. Or perhaps there is a double, taken out to 2♠. How should we proceed?

I recommend what amounts to a pass-double inversion, just like some expert pairs play at higher levels when they're in a forcing pass situation. Here, we're not in a force, of course, but I should say that we will do something probably 75% of the time or more. Pass says either "I have neither extra strength nor extra distribution" or "I have a hand which would like to defend a doubled contract if you have extra strength." Double says "I'm relatively short in their suit [usually a doubleton], and I have extra strength but no clear bid." Much of the time, therefore, we will bid on, sometimes we will "nail" the opponents and sometimes we will meekly pass and let them have the contract.

The first thing we notice is that we no longer have a good way to invite game. All of our Kokish game tries, help-suit game tries and their like are essentially out the window. We can show a second suit, bid 2NT or we can bid 3♥ (higher bids will commit our side to game anyway). But those bids can also be used simply to compete with an offensively-oriented hand. Which style makes most sense? I believe that the scoring table favors an approach which goes: declare before game before slam. I don't have the space to justify this idea here but I do talk about it some more in Two golden rules of bidding. But very briefly: if they have intervened with 2♠, and can make it while you can take ten tricks not-vulnerable in hearts, you will earn 7 imps just by bidding on to 3♥ and only a further 4 imps by actually bidding game. If you think you might be able to make game but have no good way to find out partner's opinion, just bid it. If you're right you'll gain 11 imps, if you're wrong then at least you break even over letting them play even if they do double.

Here, I'm going to make an assumption that may shock you. Once we have established that our side has approximately half the deck (that's to say the high cards) or more, we do not need much in the way of extras to compete. It's a question of pigs at the trough—if you don't get in there you will starve. The most important issue we're faced with therefore is: declare or defend? (DoD). In other words, we are now trying to determine the absolute par contract whereas, before the intervention, we were only concerned with determining our (directional) par contract, which frequently is not the same thing. At pairs, quite a few matchpoints may be riding on whether we reach par or not. At teams, there is no difference between +100 and +110 for instance. But at matchpoints, getting it right could easily swing 25% of a board. Trying for game or trying for a big penalty are also possibilities of course, but they have to take a back seat to the main issue. So, we look at the possible tools we have available and, if there are two possible uses, we choose the meaning that most helps us to decide the DoD question. If we have sufficient tools still available to help us try for game, for example, then we use them for that purpose.

What tools do we have after the auction described above: 1♥ (p) 2♥ (2♠) ? Pass, double, 2NT, 3 of a minor, 3♥ (as mentioned above). By general agreement, pass and three of our suit (3♥ here) are non-forward going. Since defending 2♠ may be the par contract, we have to include pass in our arsenal for both players in a pair.

We are therefore left with double, 2NT, 3♦ and 3♣. I hope we all agree without any further explanation that 2NT, 3♦ and 3♣  are not logical contracts. One of these bids can be used as a game try and the other two can be used as you prefer for a different kind of game try, or simply a competitive bid. Personally, I think that the lowest of the available bids should be the game try (as it leaves the most room for partner to respond with some useful information) and the higher bids should be used to further describe your hand when you have good distribution. If RHO had bid 2NT, that would obviously remove one option... and so on until a 3♦ intervention leaves us no room for a game try at all. Let me put it on record that I do not like the "maximal double" here as an artificial game try.

Trying to penalize the opponents at this low-level is generally not going to work out profitably. If we can set their contract by two tricks doubled, that will be a very nice +300. But, wait a moment, if there are 16 total tricks available (most deals have at least this many total tricks) that means we could have made ten tricks in hearts for +420. Hence doubling for penalties won't be very profitable at equal or unfavorable vulnerability. Only at favorable vulnerability will it work out well, and even then it's only at matchpoints that the result will be a triumph. So, if we rule out wanting to penalize the opponents with a direct double, it frees up that call to show extra values and relative shortness in the enemy suit. Something like a short-suit game try. If partner has an extra trump, he will take the double out automatically. Likewise if he too is short in the enemy suit. All suit bids can be used to show extra distribution, and might even help us find that magic double fit that produces game even on minimum hands.

Thus, double is the most flexible DoD invitation. It has the advantage that if partner does decide to defend—and assuming he's right and that we don't choke during the defense—we get the greatest possible consolation for our "equity" (the score we were hoping to achieve with our two-of-a-major contract). But you mustn't abuse double here or you will end up with lots of -470s and -670s. See my various other posts in this series (DSIP). Generally, you will have a balanced hand with two cards in the opponent's suit. In this context, that means 5422, 5332, or possibly 5431 shape—not 5521 or anything like that. That's what the other suit bids are for. However, you might double your singleton (or void) suit if you've already shown two suits. And, if partner has a biddable suit in response to your double (or extra length in a suit he's already shown), he should take the double out.

So, does that mean that our opponents can enter into our auctions with impunity, safe in the knowledge that they can never be caught speeding? Not at all. Often they will escape relatively unscathed when we bid on to a successful contract or we let them play undoubled when we have nothing extra. But when the trap does close, they will find that the player with the most high-card points has the short holding in trumps. His partner will have the longer holding and these conditions are perfectly suited to extracting the largest possible penalty.

Sometimes, even when we do "catch them speeding," they can wriggle out into a better contract. So, give up on waiting for juicy doubles of low-level intervention after we've found a fit—it's better to use double as an essentially constructive tool and get the occasional penalty as a bonus.

Here's a typical layout from a recent instant tournament on BBO. At the table, all were vulnerable and West made a poor decision to reopen with double. Perhaps he should have considered the board number first. All looked good at first when East bid 2♠ and N/S passed, but things went rapidly downhill thereafter, resulting in -300, a very poor matchpoint score.

Declarer could have played it a bit better and saved a trick. Perhaps North should have redoubled over the first double to show a balanced hand with maximum points. South might then feel able to double the contract for a gain of 800 to N/S. But that's being a little greedy. N/S took no risk of anything bad happening and ended up with better than an 80% board.

Now let's look at some other variations and see how they might play out using the ideas described above. We leave the E/W hands to distribute themselves as they see fit and bid as before.

In the first example on the left, South is the one with extra strength, a balanced hand and a doubleton spade: hence double. The final contract is 2♠X for +100 (assuming an unchanged E/W layout). This loses an IMP to the par contract of +140 for 3♥.

In the second variation (right) neither North nor South can bid on over 2♠ and the opponents "escape". Nevertheless, they go down two for +200 to N/S. Surprisingly, again assuming E/W remain the same, N/S can actually make 4♥ on this layout. But is it reasonable to expect anyone to bid it? +200 is therefore likely to win at least average if not better.

And, in fairness, here's a hand that appears to deflate my arguments. It's from long ago (2006) on OKbridge (I found this using Stephen Pickett's wonderful program BridgeBrowser) where the players were all good. East/West were playing "standard" and the 500 they reaped was worth 7.35 IMPs.

Playing my recommended system, the result would almost surely be only 200 (no double) for only 0.75 IMPs. This is exactly what happened at another good table but this time, the defenders did even better and extracted 300 for 3.27 IMPs. In any case, I dare say the actions would be the same at matchpoints and there the difference is much smaller: 49/51 matchpoints for 500, 48 for 300, and 41 for 200. That's still an 80% board! In other words, you will get a very good matchpoint result on this hand without having to double.

And here's a hand which many players got seriously wrong (from the same source)—again all good players at the table shown.

Par on this board is +100 for N/S for 2♠X-1. The only reasonable way to get that result is for N/S to be playing according to my system and have South double with his extras and spade shortness. North will have no reason to take it out and par will be achieved. In practice many Easts took fewer than their allotted seven tricks and at those tables 2♠X would have done very nicely for N/S. Note that although this N/S did get a fine 300, it was only because West made a dreadful bid in my opinion. They were almost surely going to escape for -50 until then.

Now for a board where N/S use double to win the declaration:

Note that in almost every real-life playing of this hand, after the first six calls, South made a very undisciplined raise to 3♥. He has no shape and could have been summarily punished an a bad day. The safe way to show your extras is with a double as shown here. North, with four hearts and a doubleton spade will take it out to 3♥ and all will be well. If E/W bid on they will be -200 or, even worse, if N/S decide to take the push to 4♥ on their 21 hcp they will be extraordinarily lucky, given their lack of useful shape, and score game.

The final problem

No, this isn't my final blog. I hope not anyway. But I would like to wrap up some loose ends on the subject of doubles. Devotees of Sherlock Holmes will of course recognize the title as that of one of the adventures.

First, I want to stress something about doubles which I haven't really emphasized before. Cooperative doubles are always a last resort. This comes from the definition that you have no other possible bid yet you have too much strength to pass.

I have mentioned previously the "three strikes you're out" rule which comes into play whenever our side makes a total of three doubles (see Three strikes - you're out). But there are other flavors of the three strikes rule. 

For example, suppose that I open 1♠, partner raises to 2♠ (with or without competition) and then later,  one of us bids 3♠. Each partner has clearly limited his hand, there's no doubt about our best strain, and nobody is prepared to bid game. By bridge logic, if the opponents continue on to the four level, a double by one of us must be for penalties.

For some time, I've been trying to determine if there is a simple trigger that applies to these situations. Essentially, these are the criteria:

• each partner has limited his hand by making a non-forcing bid;
• we have found a fit or we have settled into a quasi-fit.

Let me try some examples:

1. ♠KJ4 ♥75 ♦KQT962 ♣AQ opposite ♠QT86 ♥KQJ63 ♦J ♣J63: 1♦ (p) 1♥ (p); 2♦ (p) p (2♠); p (p) X: in this case, opener has bid and rebid diamonds -- responder was content to sit there in a quasi-fit -- until the opponents decided to balance. We know we cannot find a fit at a safe level and weren't thrilled about having to make eight tricks in diamonds. Opponent's 2♠ call is music to our ears: Double!
2. ♠KJ942 ♥75 ♦KQ62 ♣A7 opposite ♠QT86 ♥KQ62 ♦J3 ♣J63: 1♠ (2♣) 2♠ (3♣); p (p) 3♠ (p) p (4♣) X: here, we have found a limited fit in spades (three spade bids altogether), neither player has made any attempt to bid game (thus each is limited in strength). Double!

But is it necessary for both partners to have limited their hands? What if the one partner who has limited his hand, with a pass or a non-forcing bid, doubles? Is that always for penalty?

The case where one of us passes is covered in The dead auction rule. But I'm not sure that covers all of the cases. Doesn't it also apply when one of us makes a non-forcing bid and then doubles?

More situations:

1. ♠KJ942 ♥75 ♦K2 ♣AJ67 opposite ♠QT6 ♥KQ63 ♦JT43 ♣82: 1♠ (p) 2♠ (3♣); p (p) X: here, we have found a limited fit in spades (just two spade bids this time), but opener is still unlimited while responder has limited his hand. Is it possible that responder can have a hand that is a penalty double of 3♣? It's relatively unlikely so that I have always defined this situation as being a cooperative double. How good are your spades, clubs? For many pairs, double is always penalty once we've found a fit.
2. ♠KJ942 ♥72 ♦AKJ2 ♣72 opposite ♠QT6 ♥JT65 ♦T3 ♣AJ83: 1♠ (p) 2♠ (x); p (3♣) X: here, we have found a limited fit in spades (just two spade bids this time), opener and responder are limited. Now, is it possible that responder can have a hand that is a penalty double of 3♣? Absolutely, he's sitting over the club bidder and he has a maximum balanced raise.

The conclusion, for me at least, is that as soon as both partners have limited their hands, then penalty doubles go into effect. But should penalty doubles only be in the direct seat? No, I think that's unworkable. We need to have both partners using the same meaning for double, otherwise it's possible that the fish can wriggle out of the net.

And now for a real hand, this one taken from the World Wide Pairs (hands rotated).

The bidding by the opponents is a little "forward" as the Abbot might say, yet this is the kind of thing that happens in club games. It's obviously important to be on the same wavelength as to the meaning of my final double. Given that my first double was essentially a bid of spades, our side had bid spades three times. Add to that the fact that I had passed over 2♠ showing no interest in going further, then it was clear that my final double was for business. [Editor's note: I have edited the bidding a little to suit my story better, although the first four bids are real, as is the final contract.]

Our result (+500 when we managed to get an extra trick on defense) was a local top and worth 99% worldwide. Note that 4♠ cannot be made legitimately, although there were quite a few making game (420) our way so we needed that extra trick. 

So, my question to my readers is this: is it a workable scheme to turn penalty doubles on whenever both partners are limited? Is it sufficiently obvious? I'm sure that it's correct to do it this way, but is it going to be usable in practice?