Life So Short, the Craft So Long to Learn

The Schnapsen Log

May 31, 2012

On the Brink of Defeat (solution)

Martin Tompa

Does Itell already hold all the missing trumps TKQ? If he does, he plans to trump the next trick with T and send you home with the royal marriage. This suggests that you should lead A. You will have to get lucky and draw T, ♣A, or ♣K from the stock. That gives you a 3/5 probability of winning this deal, since you know K isn’t in the stock, and a 2/5 probability of going home and sulking.

Do you remember my advice that, if you aren’t on lead at the last trick before the stock is exhausted, you should first consider ducking, because there are fewer cases to consider? I have analogous advice when you are on lead at the last trick before the stock is exhausted: the first thing you should consider is closing the stock. Not only do you freeze your opponent’s trick points, you also simplify the possibilities you have to consider: you are looking at all your final cards, and you know your opponent has to follow suit.

What happens if you close the stock in the situation you face right now against Itell? It seems crazy, as you have only one sure trick, A. But wait, what if you were to throw Itell in with a trump? Would he eventually have to open up the club suit and set up your ♣T as the winning trick? There are two things you need to work out: can you maneuver so that Itell is on lead with nothing but clubs in his hand, and will he have reached 66 trick points before you get a chance to win ♣T?

The first question is easy: since Itell has only clubs and trumps in his hand, once he cashes his trumps he will have to lead clubs. What about the second question, his accumulated trick points? If you lead K or Q, there is a clear danger that he will trump with T and declare the marriage, so that’s no good. But if you first cash A and then force him to trump, that’s guaranteed to break up his precious royal marriage. So far, so good. How many trick points can he accumulate before giving you ♣T? A will bring you to 60. Then you will throw Itell in with either of your nonclub cards. He can win at most two heart tricks with TK, to which you will contribute K and Q, bringing him to 48 points and this position, in which he is on lead:

Itell: (48 points)

♣ AK

You: (60 points)

♣ TQ

Itell may then cash ♣A for a total of 62 trick points, but that will be his last trick before yielding to your ♣T. Will you be able to resist gloating when he realizes you have endplayed him? I hope so, because you still have many more game points to win before your war with him is over.

Notice that we did this whole analysis without worrying about which card remains in the stock. In fact, my implicit assumption in the analysis is that what’s in the stock is the worst possibility for you, ♣J, and even then the throw-in works like a well-tuned machine. If one of the trumps or ♣A is in the stock, that only makes things better for you, as those are cards we assumed Itell could use to win tricks. The analysis of closing the stock will not always be this clean: in the general case, some of the possibilities for the last stock card will lead to a win for you and some will lead to a loss. In those cases, you will have to compute your expected number of game points, as we’ve discussed in a previous column, and compare that to what happens if you don’t close the stock.

© 2012 Martin Tompa. All rights reserved.


blog comments powered by Disqus

About the Author

Martin Tompa

Martin Tompa (

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.


Getting Started

Links for Schnapsen and Sixty-Six

Links in German

Links in Hungarian

Recent Columns

Sidestep a Few Landmines, Sep 2
Two Last-Trick Problems, Jun 27
More Extremes of Luck, May 21
Grasping at Straws, Apr 4
A New Scheme for Remembering Cards, Mar 23
As Luck Would Have It, Sep 9