Tuesday, April 17, 2012

Penalty Doubles (part 2)

Last time we talked about the five types of penalty double:
  • Lead-directing;
  • Equity-preserving;
  • Penalty-increasing;
  • Psyche-exposing;
  • Tactical.
In particular, we discussed lead-directing doubles in general terms. I mainly want to talk about equity-preserving doubles now so let's get the other three types out of the way quickly.

We'll start with the least common type of double: the tactical double. There are probably many different types of tactical double such as doubling cuebids to sow doubt in the minds of the opponents as to the placement of key honors. But surely the best-named toy here is the Stripe-tailed Ape double whereby, as the opponents bid on their way to a slam you think they might make, you deliberately offer them the option of playing a lower-level contract doubled. When they expose your ploy by redoubling, you have to run like the proverbial ape. Several things can go wrong of course. You'd better have a good suit to run to when they redouble because you are likely to be doubled. Or, the slam might not be making because of some holding in partner's hand, and instead of going, say, +100, you are now -990. Or what happened to me several years ago at a club game playing against an expert pair. I doubled 4♠ and didn't get redoubled. The hand made 6♠ and so I was -1190. But it was a Pyrrhic victory – nobody else actually bid the slam so I got the same bottom as I would have had my opponents bid the slam (-1430). And, who knows, maybe they weren't going to.

In the early days of bridge, when psyching was very common and there were no take-out doubles, the primary reason for the double was, I would argue, to expose pyschic bids. Without the double, the opponents could just bid your suits and make it impossible to find your games or slams. Psyches are relatively uncommon these days. But because we've traded most of our penalty doubles for other kinds of double, a psyche can be hard to expose and consequently quite effective.

Hand-in-hand with that use of double, came the penalty-increase usage. Overbidding was common and double was necessary to keep everyone reasonably honest. The idea is of course that if the opponents have bid a contract (usually a game or slam) that we are pretty sure is going down at least two tricks, we should double, providing of course that our double doesn't tell declarer how to play the hand successfully. Opportunities for this kind of double don't come up all that often. The standard of bidding these days is sufficiently good that, in a non-competitive auction, if a pair bids a game, they will have a play for it unless there are very bad breaks which could not be anticipated. We need to have well-placed cards, especially trumps in a suit which, preferably, declarer has bid more or less on his own, and some sure tricks like aces. The reason for all the caution is simple arithmetic. It's madness to try to increase a penalty by 100 if there's a chance that they might still make (or, worse, make because of the double). Assuming the more favorable case where our double makes no difference to the play, we risk 170 points (for a major suit game) to gain 100. If they redouble, then we are risking 340 to gain 100. For a slam, the odds are even worse. But if the double tips declarer off to the winning line in a game contract, we are now risking 890 points for the sake of 100.

Note that there's another more subtle reason why the double might not pay off. If the trump stack and the outside high cards are all in your own hand, you are quite likely subject to repeated endplays. It's much better if the trump stack is sitting over declarer and the high cards of the partnership are in the other hand. In my partnerships where we play a two-way double scheme, most of our best penalties come from partner passing a cooperative double for penalties – precisely because now the partnership assets are likely to be split. In general, in a non-competitive auction, if the opponents get too high, it is generally going to be good for us with no need to gild the lily.

Now, we come to the equity-preserving double. Essentially, the opponents have sacrificed (deliberately or accidentally) over your contract that you were expecting to make. At the game level, the equity-preserving double is probably at least as common at IMP scoring as at matchpoints. At levels below game, it is much more common at matchpoints. Let's take an obvious example. Red on white, you pick up a balanced 15 count and open 1. Partner makes a limit raise of 3 and you bid the fourth heart. One of the opponents then bids 4♠ and you double. You were very optimistic that you were making 4 but both you and partner have balanced hands (he would likely have splintered with a singleton). You therefore double and hope to earn 800 which would more than make up your "equity." At IMPs, you would likely gain 4 imps and at matchpoints you will probably get close to a top. On the other hand, if you can only take 6 tricks (quite likely), you will lose 3 imps at teams (not a tragedy) but will likely be well below average at MPs. But you did what you could to preserve your equity by making the penalty double. You haven't suggested a stack of trumps or that suits will be splitting or lying badly. You are just doing what you must – "take the money."

Playing matchpoints, you have to be much more aware of possibilities for an equity-preserving double. Let's say you and your partner have bid to 3, a contract which you feel fairly confident of making as you have the balance of power and an eight-card fit. Your vulnerable opponents now bid 3♠. If your hands are sufficiently balanced that you don't expect much play in 4, you double. Assuming that you get them down 1, you will earn 200 which will more than make up your "equity," the 140 you could have scored on your own. On a 12 top, you can probably expect to earn 10 for +200, 6 for +140 and only 2 for +100. If it turns out that they (and you) can make 140 all along, you were probably getting only a few matchpoints for -140 so if you slip and they score up 530, you could say that the double (combined with bad defense) only lost a few matchpoints.

Note that the equity double doesn't work so well if the opponents are non-vulnerable. You would have to beat them two to make up your equity and if you're sufficiently strong for that, there's a reasonable chance of successfully making 420 or 620 in game. That's because the most common number of total tricks in these competitive deals is 17. If you can beat them two in a nine-trick contract, you might well be able to make your own ten-trick contract. Every hand is different, obviously, and each situation has to be evaluated on its own merits. But if they are vulnerable, you only need to double and collect a one-trick set for a result which will at least beat all other part scores.

Equity-preservation can also result from passing a two-way (or cooperative) double.

The main point is that your double in these situations is not intended merely to increase your penalty. At matchpoints, for example, when your opponents have overbid in a non-competitive auction, you will be getting a good board anyway. Doubling is unlikely to give you more than one or two matchpoints extra and there is a risk that you might lose what would otherwise be an average board if they do in fact make the hand. This is especially true when the opponents overbid to four or five of a minor. Even if they make, many of your virtual teammates might manage to make 3NT, possibly with an overtrick. If they don't make, a plus score should be good for you – you weren't in the auction to begin with.

Now, to the quiz in part one. Your hand was: ♠83 QJ98 62 ♣J9754, red against white. The auction proceeded, starting with partner: 1–2–p–2NT; 3–4–4–p; p–5–p–5NT; p–6♠–p–p; X–p–p–p. What did you lead? If you led a club, you are the hero! A double in such circumstances never asks for a trump so that's out. Partner has freely bid two suits and the opponents seem to be unimpressed. Double can't help distinguish between partner's two suits (without the double, my rule is always to lead the second-mentioned suit because that is generally the suit for which partner went furthest out on a limb). So, in keeping with the rule mentioned in part one, partner doesn't want you to lead either of his suits. Partner ruffs the club and cashes one diamond for +100. At the other table, it went p–2♣–p–2; X–2♠–p–2NT; p–4♠–p–5♠; p–6♠–p–p; X–p–p–p. Opening leader, apparently not familiar with the central concept of part one of this blog, led a diamond for -1210.

1 comment:

  1. In the interests of full disclosure, I took a little journalistic license in the quiz setting. I was the partner and, for several reasons including my doubts that a diamond was cashing, declined to make a lead-directing double. So, we gained 5 imps on the deal, not the 16 that should have been forthcoming. Regrettably, not finding that double cost my team 3.45 masterpoints!