Psellos
Contemporary Development With Functional Programming

The Schnapsen Log

June 24, 2019

Imperfect Information (solution)

Martin Tompa

Here is the position after you win Tibor’s lead of ♣Q:

Concealed cards:
AKQ
TQ
♣ K
ATJ

Your cards:

AK
♣ T
Q

Trump: J
Stock: closed, 5 face-down cards
Game points: Tibor 5, You 5
Trick points: Tibor 38, You 14
On lead: You

Your hand is thankfully quite strong. Your ♣T is a guaranteed trick, since you know Tibor holds ♣K from the marriage, and you are additionally blessed with two good trumps. What hands do you fear Tibor holding?

If your plan is to draw a round of trumps by leading A, then the hand you fear Tibor holds is this one:

Tibor: (38 points)

TQ
♣ K
A

You: (14 points)

AK
♣ T
Q

In this situation, after you have cashed A, you cannot stop Tibor from winning T and A, bringing his total trick points to exactly 38+10+4+11+3 = 66. If indeed Tibor holds this feared hand, you can probably see what you need to do. Instead of leading A, you must coerce Tibor to open up the trump suit himself, which calls for an elimination play: cash ♣T and throw Tibor in by leading Q. You will then win both trump tricks and 3 game points.

But what hand do you fear Tibor holds if you attempt this elimination play? He could win your diamond lead and would then have only two cards left in his hand, while your remaining cards are AK. The hand you fear Tibor holds is this one:

Tibor: (38 points)
KQ

♣ K
A

You: (14 points)

AK
♣ T
Q

With a second marriage in reserve, you will have just handed him the victory. (He could, in fact, hold T instead of A and the result would be the same.) If he holds the spade marriage, then you do want to begin by cashing A in order to break up his marriage.

Are you now paralyzed into inaction? How can you decide which play to make?

What you must do in this situation is to put yourself in Tibor’s place and use inference to determine which of these feared hands he is more likely to hold. Holding which of the following hands would Tibor be most likely to have closed the stock?


TQ
♣ KQ
A

KQ

♣ KQ
A

KQ
T
♣ KQ

Keep in mind that Tibor cannot see certain key cards such as A, AK, and ♣AT. You cannot be sure which of these hands Tibor holds, but the hands with two marriages are very vulnerable. They each have only one possible entry card. With either of these hands, Tibor would know that there is a very good chance that he will not get to declare the second marriage. With either of these hands, wouldn’t he be more likely to leave the stock open and lose at most 1 game point than close the stock and probably lose 3?

The first hand shown, with a good trump holding and A, looks more like a closing hand. Tibor would feel there is a good chance that he will win both T and A, and either Q or ♣K in addition. With this inference, you should choose the elimination play.

© 2019 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.

Read about Winning Schnapsen, the very first and definitive book on the winning strategy for this fascinating game.

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