The Schnapsen Log

Closing In (solution)

Martin Tompa

The first thing one should think about, when following to the last trick before the stock is exhausted, is ducking the trick. Normally, there is an obvious discard if you decide to duck, but my hand was filled with so many losers that there is something to be said for discarding a spade, a heart or a diamond! Which one should I choose?

The way to decide is to imagine the position after each of those discards. That is the beauty of considering the duck, that you know exactly what card you will draw from the stock (♣J) and know exactly what the position will be. So let’s consider the position after each of the three possible discards.

If I discard ♠J, this will be the position after we both draw from the stock, with Tibor on lead:

Tibor: (26 points)
♠ T
♥ TK
♣ —
♦ AJ

Hans: (43 points)
♠ —
♥ QJ
♣ KJ
♦ Q

Neither of us can get to 66 trick points, so the contest comes down to winning the last trick. I have only two entries to my hand, the two trumps, and Tibor also has two entries, his two hearts. (Tibor’s ♦A is not an entry, because I should never lead a diamond, since it is a suit in which Tibor has the greater length.) Since Tibor is on lead, he is bound to win the last trick, as long as he forces me to use up a trump each time he is on lead. He leads ♠T for me to trump, I lead a heart, he cashes ♦A and then forces me to trump ♦J, and I lead my last heart, giving Tibor the last trick.

It is not hard to see that discarding my ♦Q at trick 5 is even worse, if that is possible. The position is the same, except I retain ♠J instead of ♦Q:

Tibor: (27 points)
♠ T
♥ TK
♣ —
♦ AJ

Hans: (43 points)
♠ J
♥ QJ
♣ KJ
♦ —

In this position, Tibor has three entries to his hand and I have only two, so Tibor is certain to win the last trick, as long as he always forces me with a diamond when he has the lead.

We didn’t even have to consider discarding ♦Q, once we had looked at the position after discarding ♠J. It is clear that, after ducking trick 5, I am always going to have two entries and Tibor will be on lead. So, if I am to have a chance of winning the last trick, I must make a discard that removes one of Tibor’s two heart entries, namely a heart discard. Here is the position after discarding ♥J on trick 5:

Tibor: (26 points)
♠ T
♥ TK
♣ —
♦ AJ

Hans: (43 points)
♠ J
♥ Q
♣ KJ
♦ Q

This at least looks promising for me. I never will want to lead either hearts or diamonds, since Tibor has the greater length in both of those suits. If I can manage that, then Tibor’s only entry is ♠T, whereas I still have my two trump entries, so I should be able to win the last trick.

Before we verify that, though, we should check that Tibor still cannot reach 66 trick points from this position. The reason for concern about this is that, by discarding ♥J at trick 5, I will have allowed Tibor to cash three big cards (♠T, ♥T, ♦A) instead of only two as in the other situations above. Tibor’s 26 points, plus 31 from his own hand, plus 8 from my hand, comes to a total of 65, fortunately 1 point shy of winning.

So let’s just make sure now that I can win the last trick from this position. Tibor is on lead and surely won’t lead his only entry, ♠T. The best he can do is cash one of his other high winners and continue in that suit to force me to use up a trump. Those two red suits are equivalent, so let’s assume he cashes ♦A and continues with ♦J. I will then be on lead from this position:

Tibor: (40 points)
♠ T
♥ TK
♣ —
♦ —

Hans: (49 points)
♠ J
♥ Q
♣ J
♦ —

I will now lead ♠J to knock out Tibor’s entry. This position is what Peter and I used to call a tempo endplay because, after Tibor regains the lead, he is forced to “lose a tempo” by cashing his winning ♥T, allowing me to win the final trick with my last trump. This is the beauty of avoiding leading suits in which I have fewer cards than my opponent does: eventually he is forced to lead them and lose a tempo.

For completeness, I suppose we should consider whether I can win more than 1 game point by trumping trick 5 instead of ducking. There is the slight chance I might draw ♥K from the stock for the marriage and enough trick points to score 2 game points. Other than that, whatever I draw from the stock will provide me at most one more trick, not enough to reach 66 trick points, and Tibor will easily win 1 game point. Discarding ♥J is my best play.

With additional kisses,
your Hans.

© 2014 Martin Tompa. All rights reserved.

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