Psellos
Contemporary Development With Functional Programming

The Schnapsen Log

March 24, 2014

A Ragged Endplay (solution)

Martin Tompa

The first thing you should consider, when following to the last lead before the stock is exhausted, is ducking. If you do duck, probably the best discard is Q, in order to deny the Maestro the possibility to cash his T later. Here is the position after discarding Q and drawing the remaining cards from the stock, with the Maestro still on lead:

Maestro: (21 points)
TQ
TJ
♣ —
A

You: (40 points)
KJ

♣ Q
TK

From this position, the Maestro has a winning line of play: he pulls a round of trumps by playing A, then forces you to trump by leading J. That puts you on lead from this position:

Maestro: (36 points)
TQ
T
♣ —

You: (52 points)
KJ

♣ Q

The best you can do is cash ♣Q, on which the Maestro discards Q, bringing you to 58 trick points. After that, the Maestro takes the remaining tricks and wins the entire game.

Every other discard you could have made on the ♣A lead is similar. The Maestro pulls a trump, plays the winning T, forces you to trump J, and eventually wins the whole game. Thus, ducking is no good, and you may just as well trump his ♣A without further thinking. This is one of the advantages of considering ducking first.

For completeness, though, let’s go ahead and plan the rest of the play after you trump ♣A, because one of the cases is very interesting. After you trump with T, your trick point total is 61. If you draw any of T, T, or A from the stock, that’s another immediate trick and you win 2 game points and the whole game. If you draw Q, that makes a marriage and you again win 2 game points and the whole game. The only remaining card you can draw is the lowly J. That would leave you on lead from this position:

Maestro: (7 points)
TQ
T
♣ —
AK

You: (61 points)
KJ
QJ
♣ Q

With this handful of losers, your initial prospects look bad. However, that K turns out to be a guaranteed winner via a throw-in play: you simply lead any card other than a spade, sit back, and waits for the Maestro to lead Q, which he must do eventually. The Maestro can cash 4 winners first, but will only get to 52 trick points. Whenever he leads Q, you will get to 68 trick points and win 1 game point. What I particularly like about today’s position is that you endplay your opponent in order to win your lowly king.

So with probability 4/5, you will win the whole game. With probability 1/5, you will win 1 game point and go on to play one more deal that decides the game against the Maestro.

© 2014 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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