Percentages

You "win" another competitive auction and await dummy with some trepidation. Dummy comes down and it seems there are guesses in every suit. How to proceed? To be successful, you have to familiarize yourself with the basic percentages. That doesn't mean you need to have every play covered to the last decimal but you should know the odds for finesses and for common suit splits. This information is needed constantly and is far more important than any bridge convention. Here's an example from a recent STAC game.

The auction begins:

RHO You LHO Partner
2D:(1) Pass 2H: X
Pass 3C: 3H: 4C:
Pass Pass Pass
1) Flannery showing 4 spades, 5 hearts and 11-15 points

The opening lead is the HT and dummy appears:


S: K8xx
H: x
D: AK7x
C: K9xx
S: Tx
H: xx
D: J98x
C: AQJ8x

Partner had their bidding shoes on but we are in a reasonable spot. The success of the contract will likely hinge on the diamond suit. We have one thing in our favor, the bidding has been very informative. One of the huge disadvantages of bids like Flannery and Mini-Roman is that if you wind up defending against a good declarer, you might as well turn your cards face up. The normal percentage play in the diamond suit is to cash the AK and hope for a singleton or doubleton queen. We are in no hurry, let's see what we can find out in the meantime.

The first few tricks are noteworthy:

H:T, x, K, x
C:T, J, x, x
C:8, x, x, x

Trumps are 2-2. No reason not to pull trumps and chance a silly ruff. We need to keep our options in diamonds, but we have plenty of entries in each hand. Note the play in clubs to maintain 2 entries to either hand in that suit. Not likely to be factor on this hand but it's useful to practice the technique. Still no rush to play diamonds, let's see if the spade ace is onside:

S:x, x, K, A
S:Q, T, x, J
S:x, C:x, J, x

No luck there, it's time to play diamonds. We have learned something, however, the normal percentage play in diamonds is NOT going to work. Remember the play, RHO has been show to have 14 high card points: the S:AQ and H:AKJ. We have not seen all the hearts but the first trick tells us everything. RHO does not have room for the D:Q. RHO has 4 D:, 5H:, and 2C: so can only have 2D:. Thus we know the Queen will not drop from either side. Need we give up? No. Since we know LHO has the Queen, we should try and sneak the Jack by him:

D:J, Q, K, x

That didn't work. Now is the time to play the percentages. We can hope the ten is doubleton or we can take a second finesse against the ten (a variation of a standard double finesse). Finessing is a 2-1 favorite here since we know that LHO has 2 diamonds left and RHO only one. (In real life it's probably even better due to other subtle inferences). We shall return to hand by ruffing a spade.

S:8, 9,C:Q, H:x
D:9, 7, x, 5

Success! The rest is easy and we're writing +130 in our scorecard for a nice result.

The previous hand focused on the play in a particular suit. This next hand focuses on the deal as a whole in terms of how to approach the hand. After a routine auction to 3N against silent opponents LHO leads the S:J. This is what we see:
S: Kx
H: xx
D: AKxxxx
C: Jxx
S: Ax
H: Axxxx
D: xx
C: AQT9

The form of scoring is a factor in these decisions, for this exercise our goal is just to make the contract.

Plan the play before calling a card from dummy at trick 1; you may regret your choice otherwise. The first choice is which hand to win the first trick with.
One plan is to win the trick in dummy and take the club finesse, if it works, we're home. If it doesn't though, we're going to be down barring a defensive collapse. That's a 50% success rate; pretty good for most of my contracts but let's see if we can do better.

Another option is to win the first trick in hand and play a low diamond from both hands. That will succeed if the diamonds break 3-2 (roughly a 2/3 chance). Additionally we will succeed if the C:K is onside no more than twice guarded. Better than the first plan but is it the best one?

Frequently the best line involves combining our chances. That is the case here. We can succeed when either the club finesse works OR diamonds break (roughly 5/6 chance) regardless of how many clubs RHO has. The key is to determine whether diamonds are breaking before losing the lead. The first trick must be won in hand (you'll see why soon).

S:J, x, 9, A
D:x, x, A, x
D:K, x, x, ?

Does LHO follow to the diamond? If so, we can give up a diamond, certain that they will break and assure at least 9 tricks. The S:K is our entry. If LHO (or RHO ) discards on the 2nd round, we know they are not breaking and can try the club finesse. We can even handle a 4-2 club split by saving the spade entry in dummy. That gives us a slight edge over the 2nd line, a small one, but they add up quickly over the long haul. A little foresight, a little care, and a little math maximized the chances for success.

Here is a percentage play in different form:
S: xxx
H: AKJ9
D: QJxx
C: Kx
S: AQTx
H: xxx
D: A
C: AT87x

We're in 3N (again) and we get a low spade lead. There are no immediate dangers so it looks right to play on our longest suit --- clubs. If clubs are 3-3, we will take 4 tricks in the suit. Our spots may not look significant, but they are a big factor in the play. We have a decision to make after 2 tricks:

S:x, x, J, Q
C:x, 9, K, x

The 9 is a big card and changes the way we should play the suit. If the 9 is an honest card, there are only a few club holdings that LHO can have: 9, J9, Q9, QJ9. If the 9 had not appeared, we'd have led low to the T as the best play on the 2nd round. With case 1, that will be OK, but will lose in case 2 and 3 (RHO will still have the guarded J or Q). Anything will work with case 3. A 5-1 split is unlikely (about 15%), so the odds favor catering to cases 2 and 3. The correct play on the 2nd round is the ACE. If an honor falls, the T8 remain as equals to the outstanding honor and we will take 4 tricks.

It's possible that LHO has tricked us and made a great play from 9x and talked us out of our winning play. Sometimes you just have to tip your hat to the opponents when they make such a play.

Familiarize yourself with the common suit splits; and then put that information to use. There is no need to be a math whiz, simple fractions are sufficient in almost all cases. Keep in mind that percentages do change based on information gained during the auction and play (consider the first hand). Just knowing the basic odds, however, will improve your game.

Suit break calculators, as they are known, are found all over the web. The Richard Pavlicek site (accessible from Bridge Links) contains a thorough presentation on the subject with calculators and quizzes to test your knowledge.