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Contemporary Development With Functional Programming

The Schnapsen Log

August 14, 2019

Compelling Opponent (solution)

Martin Tompa

Concealed cards:
Q
AQ
♣ K
AK

Your cards:
J

♣ A
TQJ

Trump: ♣J
Stock: 1 face-down card
Game points: Tibor 2, You 1
Trick points: Tibor 13, You 41
On lead: You

If the first thing you considered is closing the stock, congratulations. That is indeed what you should first consider when on lead to the last trick before the stock is exhausted. If you close the stock, your goal is to win a trick with T, and the way to do that is with an elimination play: you cash ♣A and exit by leading J, hoping that Tibor will be compelled eventually to lead K. If you found this play, well done.

The problem is that many things can go wrong with this elimination play. The most obvious is that K is the last face-down card in the stock, and you won’t take another trick after you exit with J. The next most obvious thing that could go wrong is that Q might be the last card in the stock, so you won’t be able to exit with J and you will be the one compelled to open up the diamond suit.

Do you see anything else that might go wrong? It’s more subtle, but your elimination play will also fail if ♣K is still in the stock. When you lead ♣A, Tibor will quickly jettison his K, and you won’t take another trick.

This wasn’t such a good plan after all. There are three possible cards that can be left in the stock, any of which will be your downfall. With 3 out of 6 concealed cards bad for you, your probability of losing the game with this elimination play is 1/2. This could turn out to be your best bet, but now is the time to rethink closing the stock.

If you were to leave the stock open, is there something you can lead that will allow you eventually to win a trick with T? If you lead J, Tibor may again jettison K, particularly if one of those useless queens or A is the last face-down card in the stock. If you lead J, Tibor may discard Q and you draw Q from the stock. Or he may discard Q and you draw either Q or A from the stock. In any of these cases, Tibor will have his own elimination play and you will be compelled to open up the diamond suit. See if you can work out these elimination plays.

That leaves only one possibility for you: lead the counterintuitive T. This actually shouldn’t be so counterintuitive: with your ♣A in reserve, Tibor is compelled to win this trick and you will draw the helpful ♣J from the stock.

Suppose Tibor wins your T lead with A. This will be the resulting position:

Tibor: (34 points)
Q
AQ
♣ K
K

You: (41 points)
J

♣ AJ
QJ

Tibor’s best play is to force you to trump by leading Q. You then lead J, putting Tibor on lead again from this position:

Tibor: (40 points)
Q
A
♣ K

You: (46 points)
J

♣ A
Q

At this point, Tibor is endplayed. He would like to force you to trump again, but the only lead that could do this is A, and that would give you 68 trick points. He can cash his Q, but after that his only lead is ♣K, which does you the service of pulling trumps, and you take the last trick with your established diamond.

Do you recognize this endplay? It’s a counterforce, which we haven’t seen in quite a while.

Tibor has another possibility at trick 5, which is to win your T lead with ♣K instead of with A. This turns out to be no better for him. He would be on lead from this position:

Tibor: (27 points)
Q
AQ
♣ —
AK

You: (41 points)
J

♣ AJ
QJ

He can again force you with Q, but you then lead any of your losers, and eventually he will be compelled to lead A.

To summarize, the play that is a guaranteed win for you is to leave the stock open and lead T. If you found this play, well done you!

© 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.

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September
The Horns of a Dilemma, Sep 4
August
Compelling Opponent, Aug 14
June
Imperfect Information, Jun 24
December
Singleton Tens, Dec 1
November
Complete Information, Nov 28
September
Gamble, Sep 30

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