Protecting Equity

The concept of protecting your equity applies to any form of bridge scoring and at any bidding level but it is especially pertinent for part-scores at matchpoints.  The idea is that if you think you were going to make your contract and the opponents bid on, you have to double them in order to protect your equity.

In the double-or-pass decision, only their vulnerability is relevant.  In most situations, where our part score would score more than 100, doubling has much more to gain if they are vulnerable. Otherwise, doubling only makes good sense if we expect to set them two or if we were planning to get 90 (in 1NT or 2-of-a-minor).  Doubling to protect our equity in the latter case would be extremely rare.

Let's give an example.  Only they are vulnerable and both sides have found a fit.  We have bid 3H, expecting to make (+140) and the opponents counter with 3S.  We basically have two choices: bid on, hoping that we can actually make 4H (or be down only 1 while they can make 3S) or double them, hoping that they can't make 3S.  There is of course the option of passing, which is appropriate if we are vulnerable and/or we think that they have the balance of power.  If we pass and they are down 1 only, our +100 will not score well against those making +140, which is why we would want to double to protect our equity.

Let's say we encounter this board in the last round of a 13 round duplicate.  So far, the board has been passed out once and 3S their way has made twice and gone down one undoubled twice.  3H our way has made four times and gone down once.  One pair our way went down in 3NT doubled and another pair actually made 4H.  Assuming that our defense is going to be accurate, we expect to score +100 as is, earning a 6 (on a 12 top) for an average score.  In other words, if we do nothing, we will get an average board.

We might make 4H (for 11.5) but at the risk of going down (only 2.5 if they double) [gain:5.5 or lose 3.5], but let's say our hand is fairly balanced in light of the auction so we are not seriously considering 4H.  If partner still has a bid, he might bid 4H regardless of what we do, but let's suppose that whatever we do will be final.  Let's say that we decide to double to protect our equity.  If we're right, we will earn an 11 (gain 5).  If we're wrong, we will get an absolute bottom (lose 6).  On the other hand, if we had allowed them to make 3S undoubled, that would have scored only 1 matchpoint so, in fact, our double actually has a rather good reward/risk ratio: 5 to 1. 

Note how important it is that they are vulnerable.  I was reminded of this by my partner Steve yesterday in the morning STAC game.  On board 16, I elected to double 3S.  On paper, this wasn't a terrible decision, because I rated to gain 4.5 mps on a 15 top (there were 9 pairs in 3S the other way) and, assuming that we weren't setting it, we probably were only getting something like 6 mps anyway.  But now the reward/risk ratio is actually only 3/4 (nothing like the 5/1 we had above).  This is primarily because they weren't vulnerable!  So, our hypothetical gain was only from beating the 9 defenders of 3S (who we would otherwise have tied).  Because of the opponents' lack of vulnerability, the hoped for +100 wouldn't have restored our equity which in this case was +110 for 3C.  Assuming that there were a few pairs our way making 110 or 130, we'd have gained a whole point against each of these if the opponents were vulnerable, meaning that our R/R ratio would at least be greater than 1.

As it happens, of course, we couldn't defeat 3S (actually we let them score an overtrick) and 4C would have been down 2 vulnerable, possibly doubled.  Despite our 21 hcp, they can take 9 tricks in spade while we can take 8 tricks in clubs.  The commonest number of total tricks (17) but on this occasion biased in favor of the other direction.  Allowing them to make 10 tricks would only have earned us 3 matchpoints so in a way we only lost those 3.  But maybe our defense would have been more passive if we weren't trying to set the contract, in which case we'd have scored 7.