Stiff Kings

One of the more enjoyable moments at a bridge table is when you can catch a stiff King behind the Ace when you could've taken a finesse. It's not always easy to figure out the position of the King. But when you know for certain that it's wrong sided, cashing the Ace may be your only chance.

Here's one from a team match this weekend:
♠ Kxx
♥ A8x
♦ AKQx
♣ T9x

♠ Jx
♥ QJT9xx
♦ 87xx
♣ x

The auction went (RHO starting, all Vulnerable):
1♠ - pass - pass - Dbl
2♠ - 3♥ - pass - 3NT
pass - 4♦ - pass - 4♥
pass - pass - pass

LHO started ♠9 to RHO's Queen. RHO switched to ♣A followed by ♣K. I didn't see any reason to discard ♠J, so I ruffed.

Now we need to find ♥K... From the auction you may point in RHO's direction, but LHO hasn't shown a single point and can easily have the King. Are there any other clues?

Yes! For one, RHO tries to cash some tricks as soon as possible, without taking his ♠A, so RHO might try to avoid an endplay. However, there's an even better argument for placing ♥K in RHO's hand.

If he would not have ♥K, he would probably choose another line of defense. After ♣A he can count 3 tricks and the only chance for defeating the contract is when partner would be able to get a trump promotion (from the auction he knows ♦s are 4-4 so I can't discard any losers on a 4th ♦). So he'd switch back to ♠A and a ♠. This means RHO must have ♥K and has given up on the trump promotion. Obviously, if he would play ♠A and another ♠, and I'd ruff high, it would reveal the position of the ♥K immediately, which is why he avoided this scenario by playing ♣s.

It was a nice try of him, but it still revealed the position. I don't see any immediate way to hide the ♥K, perhaps playing a ♦, suggesting a singleton, may work better. But I'd still be able to make the same reasoning and play my ♥A anyway.

Bluffing

Here's a hand from this weekend's competition:

Dealer: West Vul: None Scoring: imps	♠ Q8 ♥ AK7xx ♦ J ♣ KQT9x
♠ KJT9xxx ♥ QT ♦ QTx ♣ 7		♠ Ax ♥ 8 ♦ xxx ♣ AJ8xxxx
	♠ xx ♥ J9xxx ♦ AK9xxx ♣ -

An easy one you might think, and you'd be right ofcourse. However it surprised me that my RHO chose the wrong line of play and went down in a lay down contract.

Here's what happened: the auction is over quite fast, and some may disagree with North's bid. However, it worked ok.
3♠ - 4♣! - 4♠ - 5♥
all pass
4♣ showed a good 2-suiter with ♥ and ♣, aka "leaping Michael's". Technically the hand is a bit too weak for this (too many losers).

I was sitting West and lead ♠J. Partner took his Ace, thought for 5 seconds and returned a ♠ to my King. I figured that partner would have cashed ♦A before returning ♠ if he had it, and same goes for ♣A. So the only chance seemed to be a ♥ trick. Obviously we can only make a ♥ trick when we play in triple void and partner has ♥J or declarer ruffs high to avoid a trump promotion of singleton ♥Q. So I played ♠2, making sure declarer would know that my partner didn't have any ♠s left, and to face him with a problem.

Now declarer took 5 minutes to make a wrong choice. He ruffed with the Ace, played ♥K and was quite surprised to see the Queen in my hand!

I thought this was a wrong move, but my view was already biased, so I polled about what others would do. None went for ♥A. So I guess my analyse was right. What South should've thought about is "how does West know it's safe to play in a triple void?". If you can answer that question, then you'll know that West has ♥Q with a high probability.

Law of Symmetry: fact or fiction?

Basically the Law of Symmetry states that a singleton or void is usually not alone in a bridge hand. It claims that the frequencies of bad splits are increased. So, for example, when you have 9 trumps and a singleton somewhere, the law suggests you play for a 3-1 split since the probabilities have increased.

You probably wonder if this is true, or if it’s just rubbish and superstition. From now on, never forget this: it’s pure rubish! And there’s mathematical proof. Here it is:
- suppose you give North and South a 4333 distribution, give North 4 ♦s, South 4 ♣s.
- from the NS perspective, you have pretty normal chances of splits in all suits.
- now you put 2 ♥s from the North hand to the South hand, creating a singleton. Put a ♠ and a ♦ from South to North.
- North now has a 4-1-5-3 and South has a 2-5-2-4.

Has anything changed to the existence of singletons? Yes.
Has anything changed to the probabilities from EW hands? No! They still own the exact same cards together, so the frequencies haven’t changed.
You can start with whatever hands you like, and the frequencies won’t change for opponent’s splits in the suits whenever you exchange some cards between North and South.

You might have the impression that when you have a freak distribution, you usually get bad splits. However, the reason why has nothing to do with the shortness you own. It’s about your long suits, the number of cards you control in another suit! For example, if you have a 10 card fit, it’s obvious someone will have a singleton. That however doesn’t change the frequency of 2-1 or 3-0 splits in the suit, no matter if you have a 5-5, 6-4, 7-3, 8-2, 9-1 or 10-0 fit.
To back this up: the more cards you have together with your partner in a suit, the more chance you get for opponents to have a singleton or void:
- 5 card fit: 7-1 or 8-0 split = 3,1%
- 6 card fit: 6-1 or 7-0 split = 7,3%
- 7 card fit: 5-1 or 6-0 split = 16,0%
- 8 card fit: 4-1 or 5-0 split = 32,17%
- 9 card fit: 3-1 or 4-0 split = 59,3%
- 10+ card fit: 100%
If you have monster fits, you have more chance to have some shortness yourself. And opponents have more chance to have some shortness as well. However, having a singleton or void doesn’t imply you have a monster fit with partner! So the law has no ground at all.

A final conclusion: a singleton or void in your or partner’s hand doesn’t increase the chance of a singleton or void in opponents’ hands. It’s your long suits that do the trick. But the absolute frequency of splits in a suit doesn’t change. So there’s no reason to choose a different line of play because of "the Law of Symmetry".

Dangerous Doubles

Here's a hand from a while ago. I held:
♠ AK842
♥ 9875
♦ 5
♣ AK6

Partner North starts the auction (we're at unfavorable):
1♦ - pass - 1♠ - pass
2♣ - pass - 2♥! - Dbl
pass - pass - ???
(!) 4th suit GF

Now what? Partner doesn't have anything useful to mention over our 4th suit forcing (the Double gives us more possibilities), so partner will either have Ax or xx, perhaps even xxx imo. So I decided to pass, since it was unlikely we could get a game score ourselves, but we can probably manage 8 tricks in a 4-2 fit on hcp-power.

The full hand was:

Dealer: North Vul: EW Scoring: imps	♠ JT ♥ K4 ♦ AQJT6 ♣ J873
♠ Q963 ♥ AJT62 ♦ K ♣ 542		♠ 75 ♥ Q3 ♦ 987432 ♣ QT9
	♠ AK842 ♥ 9875 ♦ 5 ♣ AK5

According to GIB a small ♥ lead defeats the contract by 1 trick, all other leads let the contract make. Opponents made a mistake in their defense and I made 2♥D+1 for +570.
As the cards lay, 3NT is laydown, but I didn't expect ♥K in partner's hand. The Ace was possible, because partner may want to rightside the contract when I have Qxx.

Doubling on such low level is dangerous, especially if you don't see an immediate way to defeat the contract. With the West hand, you can hardly see 6 tricks coming in (♦K wrongsided, too many ♠s, and no great trump holding), so it's probably safer to pass and trust on partner's lead skills to defeat the contract. You might even get another chance at 3-level.