Deep Finesse Is Never Wrong (Well Hardly Ever).
But What Does It Mean?

by David Jackson

For those of us who watch major tournaments on BBO, such as these World Championships in Brazil, we hear frequently that, according to Deep Finesse (DF), declarer could have made, or the defenders could have beaten the contract. Seeing all four hands, it is often clear what the declarer or the defenders could have done differently. But even then there are many hands where it is extremely difficult to figure out how the hand could have been made or defeated, although DF says that it is so. However, DF is never wrong unless you believe that one mistake in the last five years makes that statement untrue. The sheer power and accuracy of DF’s analyses forces us to consider what sequence of plays will guarantee the outcome that DF says can be achieved.

To say declarer ‘could’ have made or the defenders ‘could’ have defeated the contract is very different than saying it ‘should’ have made or it ‘should’ have been defeated. DF is both a double dummy defender and a double dummy player, for instance it always makes the ‘best’ lead and subsequent continuations for the defenders, always knows if honours are dropping or which suits are breaking and plenty more incredible stuff too. Perhaps you think you would like to play and defend like that, but if you did you would very quickly be up before the ethics committee for taking outlandish anti-percentage plays which turn out to be successful. A conviction and life-time ban would speedily follow. DF is a poor role model for us to try and emulate. We should aim to bid contracts that on sensible play and/or normal defence have a good chance of success. This means avoiding many contracts that are ‘makeable’ - DF will make them but you would never make them and also bidding many contracts that are ‘not makeable’ - well DF won’t let you make them but no defenders in their right mind would find the sequence of plays to beat you. We should be interested in the probability that a contract will make when declarer and defenders play normally rather than whether it is makeable when DF is playing and defending.

Let us look at two examples

Hand (a)

	♠ A 2 ♥ A Q 10 2 ♦ 6 5 4 ♣ A 10 5 4
	♠ 6 5 ♥ 6 5 4 ♦ A Q 10 2 ♣ K J 4 3

Two balanced hands with a total of 24 points plus three tens. Not quite enough points for game and certainly an old-fashioned analysis tells us that this is a poor 3NT after a spade lead. You can’t afford to lose the lead and the contract is not much better than three successful finesses. Perhaps there is a 14-15% chance of success.

What has DF to say about this 3NT contract? Well nothing at all at this stage since DF needs to know all four hands before it can tell you whether a contract is makeable or not. I was able to use DF’s undoubted analytic abilities in this example by employing another program, Dealmaster Pro, to construct 2000 deals with these specific E/W cards but with the N/S cards chosen randomly from the remaining 26 cards. The DF analyzer is part of the Dealmaster Pro software and it is a simple matter to analyse 2000 hands. 3NT was a ‘makeable’ contract on 1080 occasions - that is 54% of the time. Not really surprising since DF knows which way to finesse in clubs and if a king-jack combination in one of the red suits is onside or alternatively both red kings are onside, then DF will know which option to take.

So by going down this route of simulating a large number of possible hands that the defenders can hold, then DF can make an extremely accurate statement about a 3NT contract or any other contract, without knowing what the defenders cards are in a particular hand. DF tells us that 3NT will be a ‘makeable’ contract 54% of the time. That 54% sounds good but I think you would much prefer not to be in this 3NT if you had the choice.

Similarly, suppose the outcome of a contract depends on a two-way finesse for a queen. You or I might consider this a 50/50 proposition but DF will make the contract 100% of the time. It is pointless to construct thousands of possible hands that the defenders might hold DF will always succeed.

Consider:

Hand (b)

	♠ A 2 ♥ A 10 5 ♦ A J 5 4 ♣ A 10 9 2
	♠ 6 5 ♥ K J 6 ♦ K 10 9 2 ♣ K J 4 3

Even in game there is no guarantee of success, but what about 6NT or 6♣/♦? After a spade lead you really just need to find the three missing queens. In reality, 6NT is probably not much better than 15-16% whereas 6♣/6♦ might be around 25%. However, these contracts are not much problem to DF. 6NT is ‘makeable’ 100% of the time. 6♣/♦ is not quite so good as, for example, a 5-0 break in either minor may mean the contract will fail but for DF the slam is still makeable about 93% of the time.

Because DF tells us that 6NT is always makeable and that 6♣/♦ is makeable well more than 90% of the time with these cards, do we want to be in any of these slams? Of course not.

In these examples the percentage of times that the contract is ‘makeable’ exaggerates substantially the probability that the contract will make by normal play. This is so because the best defence (the double dummy defence) is easy to find but it is not easy to duplicate DF’s double dummy play. The reverse can also be true. If the double dummy defence is really difficult to find but declarer’s play is trivial (so DF’s double dummy declarer play is no advantage) then the percentage of ‘makeable’ contracts can vastly underestimate the probability that a particular contract will succeed.

For the problem solvers: In the second example the reality of making 6NT was about 15% (three two-way guesses) against DF’s 100% makeable. Perhaps someone can come up with an example where the reality is considerably less than 15% but DF says the contract is always makeable (regardless of how the opponent’s cards are located).