Alisdair v The Rule of Seven

Ah, the rule of Seven. Such a useful little tool. Like any tool, it is only as useful as the one who wields it. For the uninitiated, the Rule of Seven is a rule-of-thumb for Declarer to use for handling a side suit with limited stoppers. Consider the following combinations:

(a) Axx opposite xxx
(b) Axxx opposite xxx
(c) Axx opposite xx

In each of the above scenarios, these are side suits, and as Declarer, they are immediately led at you.
The rule is thus:

Subtract the number of cards in your fit from 7. This gives you the number of times you need to duck.

Simple, right? For (a), the fit is 6, so 7-6 = 1. Duck ONCE and then win the Ace on the second round.
Using the same logic, you don't duck at all with (b), and you duck twice with (c).

Great. A rule that is as easy to remember as it is to use. So far, so good. But why does it work?
The mathematical logic is sound. Employing this rule helps you block the suit when the distribution is uneven. This means that when you win the trick, the only reason that both opponents can still hold a card in that suit is because the suit split as evenly as possible. This means that you can treat one hand as the "danger hand" and play to ensure that hand does not get in to cash tricks. (This is especially relevant Declaring NT contracts). It also means that you don't duck more than you need to.

Take, for example, option (a). The opponents's cards could be distributed 4-3, 5-2, 6-1 or 7-0. Obviously, when both opponents follow suit, they are at worst 6-1, and when you win the Ace on the second round and everyone follows, it is no worse than 5-2. You have now successfully cut the defence' communications in that suit. Unless the hand that started with 5 has another entry, they will never be able to cash their winners. If the split is 4-3, you have not cut communication, but they can only gather 2 further tricks from that suit.

Is this an Open and Shut case? This is Bridge; of course its not.
For example, consider the possibilities in (b). Not ducking still protects against a 5-1 split, but not against 4-2. This is the "exception" where you do not guarantee the suits splits as evenly as it possibly can. The reason the rule still applies is that 3-3 breaks are so unlikely anyway. It baffles me when I speak to players that still feel that a suit "SHOULD" split 3-3. No it shouldn't! You are entitled to that happening 35% of the time; no more. Alternatively, if you have 4 cards, you might promote a pip as as second trick so that's why the rule says not to duck.
HOWEVER, IF you took the view that: "I can afford to lose one trick that I don't need to lose, just to ensure that I don't lose three", you would reason that you need to duck once to protect against the 4-2 split.

The take away from this is two-fold:
1: Context matters
2: Sometimes the even split is the one you are worried about.

Consider this hand I played last night:

K84
1095
K1064
A32

AQJ
A72
Q82
KQ65

3NT by the bottom hand
Lead: 4 of hearts
Match Points
No opposition Bidding

Note the heart suit. The rule of Seven says I should duck once. I play the 5, the King appears, and I duck. The 6 is returned - I duck again. Why?

Well, I do not want to lose 3 heart tricks. I can see 3 spades, 1 heart, 3 clubs and 1 diamond trick. If the minors split 3-3 (which I have just pointed out I am NOT entitled to!), I can make 9, but I may need to lose the lead twice to set that up and that brings me down if they also get 3 hearts. I can afford TWO heart losers. I am giving the contract the best chance of making by ensuring that when I win the Ace of Hearts, the suit is blocked. Sure enough, when LHO returns a third heart, RHO pitches a spade. I have lost one more heart trick than necessary.
Some may be thinking that I am wrongly adopting a teams strategy here. The goal in Match Points is to make as many tricks as possible, so it is worth the risk just to ensure that I don't lose a trick un-necessarily. I disagree. Let's see why.

Now that I know I cannot afford LHO to gain the lead for any reason what so ever, I have to assume RHO has the Ace of diamonds. Otherwise, this contract has no play and it is irrelevant how many times I ducked. So, I cash King and Ace of Clubs, with both opponents following both times. I now play a small diamond from table, RHO follows, and I play the Queen. It wins! I'm now at 8 tricks; time to combine chances. I play a small diamond from hand - and the Jack appears from LHO. I cover with the King. RHO wins with the Ace, but this sets up my 10. I now know I am making this contract. In fact, as long as RHO does not have 5 spades, I am making an overtrick. Looks like I'm making the Match Points. RHO returns a spade - his best shot at defeating the contract. There's nothing he can do to stop me making 10 tricks, given his actual hand.

Why am I making ten instead of 9? The extra duck in hearts of course! Not only was it a prudent guard against the 4-3 break, it effectively rectified the Count for a minor suit squeeze. I win the spade with the Jack and cash my Queen of clubs. LHO discards, and now I know RHO started with 3=2=4=4 (4-4 in the minors). I play my Queen of Spades and overtake with the King, to ensure that on the last spade, I am winning in hand. Crucially, on the last spade, RHO has to discard. He squirms and pitches a diamond, and I now play my last diamond to the ten, and my 6 is now a winner. His alternative was to pitch his club, which would make my 6 a winner, on which I would pitch my 6 of diamonds before cashing the ten of diamonds.

Conclusion: The Rule of Seven is an OK rule, but using a tool properly involves knowing when to use it.