The Schnapsen Log

By the Process of Elimination (solution)

Martin Tompa

If you lead a club or heart and Emmi wins the trick, her two aces, your singleton ♣T, and her club marriage will give her plenty of trick points to win the deal and 2 game points. It seems unlikely Emmi wouldn’t win the trick on one of these leads, unless you lead ♣T and you are lucky enough that ♣A is the last card face-down in the stock. So let’s move on to leading one of your aces.

If you lead ♦A, this will leave Emmi with the only remaining trump, ♦J, and will leave you with very few winners. The only card you can draw from the stock that will give you a win of the deal is again ♣A. This would be the position after Emmi discards ♣J on your ♦A:

Emmi: (19 points)
♠ —
♥ AK
♣ KQ
♦ J

You: (40 points)
♠ A
♥ QJ
♣ AT
♦ —

From here you can cash your clubs and reach 68 trick points. But any draw other than ♣A gives Emmi 1 game point, so leading ♦A is no more probable to win the deal than leading ♣T.

By the process of elimination, we are left with leading ♠A. This lead does seem better than the others, since it doesn’t give up the lead with that club marriage outstanding, nor does it give up trump control. Let’s go through the possible cards you could draw from the stock if you lead ♠A.

Assuming for the moment that Emmi already holds ♣J and discards it on your ♠A, you will have 40 trick points. Cashing ♦A would pull Emmi’s trump and brings you to 53 trick points. This means that, if you drew ♣A, ♥A, or ♥K (for the marriage), you could easily accumulate enough trick points to win 2 game points.

That leaves the 3 small clubs to consider as possible cards you might draw from the stock. Drawing ♣K is similar to (and somewhat simpler than) drawing ♣Q, so consider your position after drawing ♣Q:

Emmi: (19 points)
♠ —
♥ AK
♣ AK
♦ J

You: (40 points)
♠ —
♥ QJ
♣ TQ
♦ A

This position, with you on lead, is a good exercise for you to continue. When you think you see how to win from this position, you are welcome to read my analysis.

The only other draw from the stock that we need to consider is ♣J. In this case, Emmi will discard ♥K on your ♠A, resulting in this position:

Emmi: (19 points)
♠ —
♥ A
♣ AKQ
♦ J

You: (42 points)
♠ —
♥ QJ
♣ TJ
♦ A

This position, with you on lead, is a bit more interesting to analyze than the previous one. When you think you see how to win from this position, you are welcome to read my analysis.

If you succeeded in winning from these remaining positions, all that is left is to analyze the expected number of game points you will gain by leading ♠A at trick 5. If you draw any of 3 cards (♣A, ♥A, ♥K) from the stock, you will gain 2 game points. If you draw any of the remaining 3 cards (♣K, ♣Q, ♣J), you will gain 1 game point. Therefore, your expected gain from leading ♠A is ½(+2) + ½(+1) = 3/2. This is by far your best play at trick 5.

© 2013 Martin Tompa. All rights reserved.

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