## Problem no. 42, 2012

### The problem

Recently I browsed through Eric Jannersten's book Find the Mistakes. Pretty soon I realized that the plays Jannerstens calls Bad plays often don't deserve to be called that, or that the plays he calls Good plays don't mean declarer played optimally. A telling example is the one with number 24.

South dealer, North-South vulnerable

 8 4 A K 7 3 K Q 9 7 4 2 6 K 10 7 6 A J 3 J 9 6 5 8 2 10 3 J 6 5 Q 9 5 K 10 8 4 3 Q 9 5 2 Q 10 4 A 8 A J 7 2

 South West North East 1 pass 1 pass 1 pass 2 pass 2NT pass 3NT pass pass pass

West led the five of hearts. In the "bad play", declarer won the opening lead with the ten of hearts. He played diamonds from the top and emerged with eleven tricks. But he is crtiziced for playing like that by Jannersten. In describing how South should have played, the layout is changed to this one:

 8 4 A K 7 3 K Q 9 7 4 2 6 K 10 7 6 A J 3 J 9 6 5 8 2 10 J 6 5 3 Q 9 5 3 K 10 8 4 Q 9 5 2 Q 10 4 A 8 A J 7 2

When South after the ten of hearts cashed ace and king of diamonds, West threw a heart; and on the queen of diamonds, West pitched a club. When East gained the lead with the jack of diamonds, he alertly shifted to the jack of spades, covered with the queen and the king. West played the spade six to East's ace, and then the three of spades gave West two more spade tricks. 3 notrump was thus defeated.

"South erred at trick one", Jannersten writes. "He shouldn't be greedy but go up with dummy's ace. Then he plays a low diamond towards his hand. If East follows, South just covers East's card. Then he does what he can to stop East from gaining the lead. Here, West wins the trick with his singleton ten, but South's spade stopper is secured. Should West lead a low spade to East's ace, South then covers the jack of spades and has the nine left to stop the suit with."

It is correct, as Jannersten writes, that the contract is secured if the declarer loses a diamond trick to West, but not if East gains the lead. Still, I disagree with Eric Jannersten. I prefer to call the latter plan "bad" and the former "good". But why?

### Solution

Most books teaching IMPs strategy states the most important thing is to ensure the contract. If you miss an overtrick or another, it's a cheap insurance compared to going down in a makeable game or slam.
This doesn't always hold true, since if the layout you cater to is rare, you will lose more IMPs in the long run if you play for safety compared to those not bothering about the unlikely layout. Simple mathematics.
In this case, Jannersten's line leads to just made (or an overtrick if ace-king of spades are in the same hand), if you choose his "good play", while those choosing the "bad play" will make two overtricks. If East has J-10 or J-10-x in diamonds, you cannot but make the contract, so we don't count those cases. In the remaining 3-2 splits playing "well" lose 2 IMPs. It is roughly half of the deals, so protecting against West's honor singleton in diamonds will cost 100 IMPs over 100 deals.
And even if West had jack or ten singleton of diamonds, 3 notrump still makes unless the the opponents can win four spade tricks. That is possible only if West has precisely four spades and East-West can win four spade tricks. The chance for a singleton honor in diamonds with West is 2.8%, and if we to that add that he also needs to have precisely four spades (headed by at least the king or the ace), we are down to, say, 2% (probably less than that). In those few percentages we win 12 IMPs per deal for playing safe.
To conclude: Jannersten's recommended plan wins 24 IMPs in those deals where a safety play was neded, but it loses 100 IMPs when it wasn't. So, on average, a player not playing for safety will win 0.76 IMPs per deal.

[ The competition | Back ]