Problem

The Auction:

West opens the auction with 1♣, North overcalls 1♦, East responds with 1♥ and you respond 1♠. West jumps to 3♥ showing 4-card support in hearts and North goes to 3♠. East bids 4♥ and you must decide whether to go to on. What are you going to bid?

Solution

As North opened the bidding, he should have opening values (or close) while you have eight points. It certainly is not enough for a game, so if you are going to make a sacrifice and bid 4♠, you must calculate the respective cost of (potential) undertricks.

Both sides are vulnerable so if the opponents make 4♥, they will score 620 points. If you go down by two tricks – then depending if you are doubled or not – the result will be minus 200 (undoubled) or minus 500 (doubled).

It is certainly worth a try, so you declare 4♠. East doubles.

West attacks with the ♥A winning the first trick. You can see at once that your estimate was right, you are going down by two.

West leads a small club, you duck, East takes the second trick with the ♣J and leads the ♣Q, which you take with the ♣A. You lead the ♣9 from dummy and ruff; next you lead the ♠K, East takes the trick with the ♠A and leads the ♠7. This probably means the trump split is 4-1 and East has the rest of trumps. You play the ♠8 from hand; West plays the ♦9 and ♠9 lands you in dummy.

You must be careful now as East has two more trumps, also the opponents have far more winners than you, so you must make sure you will win tricks with all the rest of your winners. You have only three tricks thus far and it is important to get tricks with all of the winners – ♦A, ♥K and your three remaining trumps. Otherwise you will go down more than two and the sacrifice will become a disaster.

You take the next trick with the ♦A, then lead the dummy’s ♣7, ruff and take a trick with the ♥K. Now you can lead the ♥7 from your hand and ruff.

No choice left but to lead the diamonds from dummy, East ruffs and leads the ♥Q, you ruff and lead the remaining diamond – West plays the ♦K and East his remaining trump.

A sacrifice is successful only when you are sure the opponents are going to make the contract and your loss in penalty points will be less than the possible gain of opponents.

The opponent’s game points will be 400 or 420 (not vulnerable) and 600 or 620 if vulnerable.

It is good to remember how much going down will cost you.

If you are doubled and go down by 2, then the result is minus 300 points for you (not vulnerable).

If you are doubled and go down by 2, then the result is minus 500 points (vulnerable).

If you are doubled and go down by 3, then the result is minus 500 points for you (not vulnerable).

If you are doubled and go down by 3, then the result is minus 800 points (vulnerable).

So a sacrifice is certainly worth the risk, especially if the vulnerability is favorable and you can be sure not to go down by more than two or maximum three tricks.

Par Contract Analysis

The par contract on this deal is 4♥ by East/West.