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The Schnapsen Log

June 27, 2022

Two Last-Trick Problems (solution 1)

Martin Tompa

Concealed cards:
KJ
AT
♣ A
T

Your cards:

QJ
♣ KQ
Q

Trump: ♣J
Stock: Open, 1 face-down card
Game points: Tibor 1, You 1
Trick points: Tibor 13, You 42
Lead: K

Even if you hadn’t been told that this was a puzzle having to do with winning the last trick, it seems as though ducking the lead of K is a good idea. If you were instead to trump it, then, unless you draw one of the missing aces from the stock, you won’t take another trick. For example, if you trump with ♣K and draw T from the stock, you would be on lead from this position:

Tibor: (13 points)
J
AT
♣ AJ

You: (50 points)

QJ
♣ Q
TQ

It’s settled, then, you want to duck the K lead. But what small card will you discard? Suppose you decide to discard Q. This will be the new position, with Tibor on lead:

Tibor: (20 points)
J
AT
♣ A
T

You: (42 points)

QJ
♣ KQJ

Tibor must prevent you from retaining the trump marriage, so he cashes ♣A and forces you with J, putting you on lead from this position:

Tibor: (33 points)

AT
♣ —
T

You: (48 points)

QJ
♣ Q

It’s not hard to see how this will play out. You lead a losing heart, Tibor leads a losing diamond, you lead a losing heart. You end up with only 61 trick points and Tibor wins the last trick and the game.

Let’s go back to trick 5 and discard J on the K lead instead. This will be the new position, with Tibor on lead:

Tibor: (19 points)
J
AT
♣ A
T

You: (42 points)

Q
♣ KQJ
Q

Tibor again is compelled to cash ♣A and lead J, putting you on lead from this position:

Tibor: (32 points)

AT
♣ —
T

You: (48 points)

Q
♣ Q
Q

Now you have a tempo endplay at your disposal. You lead your losing Q, and Tibor is compelled to use up his heart winner without the benefit of gaining the lead with it. You win the last trick with your remaining trump.

Let’s go back to the original position at the top of this page and understand how you could see J immediately as the right discard, without the necessity of going through all these plays in your head. If you discard Q, you are leaving yourself with two heart losers and Tibor with two heart entries. If instead you discard J, you are leaving Tibor with only one diamond entry. Yes, he still has a heart winner, but it won’t be an entry, because he has more hearts in his hand than you do. That means he will be compelled to play hearts before you are. This is the essence of the tempo endplay.

© 2022 Martin Tompa. All rights reserved.


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About the Author

Martin Tompa

Martin Tompa (tompa@psellos.com)

I am a Professor of Computer Science & Engineering at the University of Washington, where I teach discrete mathematics, probability and statistics, design and analysis of algorithms, and other related courses. I have always loved playing games. Games are great tools for learning to think logically and are a wonderful component of happy family or social life.

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June
Two Last-Trick Problems, Jun 27
May
More Extremes of Luck, May 21
April
Grasping at Straws, Apr 4
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A New Scheme for Remembering Cards, Mar 23
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As Luck Would Have It, Sep 9
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