The Schnapsen Log

Losing Tempo (solution)

Martin Tompa

It’s not often easy to find your way to winning the last trick when so many cards remain. But trick 5 is the point where you have to start thinking about it, in deals where the trick point score is so low. Make the wrong lead here, and you’ve given up the last trick and the whole deal.

Let’s start with a quiz. Look at the position again, and see if you can identify the suit where Peter might lose a tempo, as he did in the previous deal. I’ve given the position again here for your convenience. Try to choose the suit before you read more of my analysis.

Unseen cards:
♠ A
♥ AK
♣ TK
♦ K

Your cards:
♠ —
♥ Q
♣ AQJ
♦ A

Trump: ♠J
Stock: 1 face-down card
Trick points: Peter 18, You 26
On lead: You

If you picked the heart suit, you’re right. You can recognize it because it’s the suit where Peter has more cards than you do, and he might force you to trump. (Yes, I know you don’t have any trumps yet, but you might draw one from the stock. This is part of looking ahead.) The previous deal suggests that you leave the hearts alone and let Peter open up that suit.

Let’s see what happens if you ignore that advice and lead ♥Q from this position. Peter will likely win the trick with ♥A, because that prevents you from reaching 33 trick points immediately, and it’s his last chance to win a heart trick. You will draw ♠J from the stock, and this will be the position, with Peter on lead:

Peter: (32 points)
♠ A
♥ K
♣ TK
♦ K

You: (26 points)
♠ J
♥ —
♣ AQJ
♦ A

Peter continues the pattern of leading losers with ♥K, forcing you to trump. You continue the pattern at the next trick by leading ♣J. This puts Peter back on lead in this position:

Peter: (44 points)
♠ A
♥ —
♣ K
♦ K

You: (32 points)
♠ —
♥ —
♣ AQ
♦ A

When Peter now leads his loser ♦K, you are the one who loses a tempo at the next trick. You’ve run out of losers to lead. All you can do is cash ♣A (bringing you to only 62 points) and then give Peter the last trick. One game point to Peter.

So leave the heart suit alone. Let’s go back to trick 5 and find an alternative to leading ♥Q. You could consider leading one of your aces, but there are two different ways for you to realize that this isn’t a good idea:

1. You want to retain your aces as winners to regain the lead in the struggle for the last trick.

2. Assuming Peter already holds ♠A (which he does with probability 5/6), leading an ace is too expensive a sacrifice. When he trumps, he will have 40 trick points, and time to set up ♣T and ♥A as winners, which will bring him to 66 with the ♣J and ♥Q you contribute.

This leaves ♣J as the card to lead at trick 5. Once you’d recognized hearts as a suit to leave alone, you might have gone right to ♣J as the next possibility, since your general goal is to lead losers in the last trick battle.

Let’s see what happens if Peter wins your ♣J lead with ♣T. He will be on lead from this position:

Peter: (30 points)
♠ A
♥ AK
♣ K
♦ K

You: (26 points)
♠ J
♥ Q
♣ AQ
♦ A

Peter may well recognize that he doesn’t want to lose a tempo by playing hearts, and he doesn’t want to touch clubs because that’s a suit where you may lose a tempo. So he will do one of two things:

(1) Peter can lead his loser ♦K. You can then cash ♣A and force him to trump ♣Q. He is left with only ♥AK and must lose a tempo and the last trick to your ♠J. Notice that you want to be the first player to lose a tempo (as you were in clubs), not the last (as Peter was in hearts).

(2) The other thing Peter could do from the diagrammed position is pull your trump before leading his loser ♦K. This will leave you on lead in this position:

Peter: (43 points)
♠ —
♥ AK
♣ K
♦ —

You: (41 points)
♠ —
♥ Q
♣ AQ
♦ —

With the trumps gone, the danger of any tempo endplay vanishes, so you need no longer worry about opening up the hearts. From this position you can exit with ♥Q and you are guaranteed to win the last trick with a club. One game point for you.

Today’s last-trick morals, then, are (1) avoid opening up the suit where you might be able to execute a tempo endplay (this is the suit where your opponent has more cards than you), and (2) save your winners and lead your losers.

You might hope that we are done with today’s analysis, but not quite yet. We haven’t considered the possibility that Peter ducks your ♣J lead at trick 5. His only sensible discard is his loser ♦K (assuming he holds this card, ♥K if not), bringing you to 32 trick points. Now the outcome depends on what card remains face-down for you to draw when you win this trick.

If it is ♣K or ♥K, cashing ♣A and declaring the marriage will give you more than 66 trick points and 2 game points. If it is ♠A, cashing your three aces (♠A first, of course) will give you plenty of trick points and 2 game points. The other 3 possible cards you could draw, ♥A, ♣T, and ♦K, all result in you losing 1 game point. Of these, let’s pursue just ♥A, since that looks the most promising for you. You would be on lead from this position:

Peter: (18 points)
♠ AJ
♥ K
♣ TK
♦ —

You: (32 points)
♠ —
♥ AQ
♣ AQ
♦ A

Whatever you do, the only tricks you will win are ♥A and ♣A for a total of 62 trick points. You cannot maneuver to win the last trick, because Peter will just lead a losing king whenever he is on lead.

We’re ready to compute the expected number of game points you will win if Peter ducks your ♣J at trick 5. You will gain 2 game points if you draw any of three possible cards (♣K, ♥K, ♠A), and lose 1 game point if you draw any of the other three (♥A, ♣T, ♦K). This means the expected number of game points you will win is ½(+2) + ½(−1) = 1/2. So, in expectation, Peter is better off ducking ♣J at trick 5 than winning it. But even in this case, your expected gain is positive, so ♣J is still the best lead for you.

This was a complicated analysis, involving both tempo and expectation, which are advanced topics. If you made it through the analysis, congratulations! And you don’t need to worry about being able to do this full analysis at the Schnapsen table under game pressure. It’s sufficient if you recognize that this is a last-trick battle, if you recognize your opponent’s long suit as one to avoid, and if you lead your losers.

© 2012 Martin Tompa. All rights reserved.

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