The Schnapsen Log
An Endplay with Holes (solution)
Martin Tompa
You are on lead at the last trick before the stock is exhausted. What is the first thing to consider when in this position? Right, you should consider closing the stock. In the current deal, this has the extra advantage of gaining you 2 game points if you succeed, since Rudi is still under 33 trick points.
The situation in spades looks intriguing, doesn’t it? You would like to compel Rudi to open up that suit, so that you can win both spade tricks and hopefully capture his ♠T. This looks like it calls for an elimination play: eliminate your entries in the other suits, throw Rudi in, wait for him to lead spades, and hope that he holds the ♠T.
But how would you go about eliminating your entries? You have two potential entries outside of the spade suit, ♥K and ♣Q (if Rudi is holding ♣J). You cannot eliminate both of them. The more straightforward plan is to exit by leading ♥K, which seems to be the more likely entry back into your hand.
If the master trump ♥T is still in the stock, the situation is simple:
Rudi: (19 points)
♠ TQJ
♥ —
♣ KJ
♦ —You: (43 points)
♠ AK
♥ K
♣ Q
♦ Q
Your ♥K will win the trick, and you can then cash ♦Q and ♠A. These three cards will add 18 trick points, bringing your total to 61. Rudi must contribute at least 7 more from his hand and you will succeed.
So let’s continue on the assumption that Rudi is holding ♥T. When you exit with ♥K, he will be on lead from this position:
Concealed cards:
♠ TQJ
♥ —
♣ KJ
♦ —Your cards:
♠ AK
♥ —
♣ Q
♦ QTrick points: Rudi 33, You 43
Rudi cannot lead a spade because, as we have already seen, winning ♠K, ♠A, and ♦Q would give you enough trick points to win. His only chance, then, is to lead clubs. He can exit with ♣J, taking advantage of the entry card you could not eliminate and thus avoiding your endplay. But that brings your trick point total to 48, and cashing ♦Q and ♠A gives you enough trick points to win.
Rudi’s only other choice, then, is to cash ♣K and ♣J, assuming he holds both. You will discard your two queens on these, leaving Rudi still on lead from this position:
Concealed cards:
♠ TQJ
♥ —
♣ —
♦ —Your cards:
♠ AK
♥ —
♣ —
♦ —Trick points: Rudi 45, You 43
If he has the ♠T, your elimination play will have finally succeeded and your final trick point total will be at least 70. If you are unlucky enough that the last face-down card in the stock is that ♠T, then you will only reach 63 trick points.
Thus, you will succeed in all cases except the one in which ♠T is still in the stock. This means that your expected gain is ⅚(+2) + ⅙(−2) = 4/3 game points.
Can you do better leaving the stock open? It seems unlikely. Rudi can win any card you lead and, if he does so, can cross the 33-point threshold with his ♥T and ♣K.
© 2015 Martin Tompa. All rights reserved.
