The Schnapsen Log
Avoid the Ducking Ruff (duck ♥T)
Martin Tompa
“We know that Claudius will win 1 game point if you take his ♥T lead with the ♥A,” Uncle Hans continues. “The question we have to answer is whether he does worse if you duck this lead. In other words, what is your best play on his lead of ♥T?
“If you duck, say with ♥Q, that brings Claudius to 51 trick points to your 0, with Claudius still on lead. Now we have to consider the possible cards Claudius could draw from the stock. Any trick in addition to his ♠A will give him enough points.
“If Claudius draws ♠K, that gives him the royal marriage and 3 game points. If he draws ♥A, he can cash his two aces for 3 game points. The most interesting draw for him is ♦A, which puts him on lead in this position.” Hans rearrages the cards on the table.
You: (0 points)
♠ TKJ
♥ AK
♣ —
♦ —Claudius: (51 points)
♠ AQ
♥ —
♣ —
♦ ATQ
Hans continues with his usual enthusiasm. “Even though you have more trumps than Claudius, he has the important advantage of being on lead. Bridge players would say that Claudius has a ‘tempo’, meaning he can knock out one of your trumps before you get your chance. His next lead of ♦Q is both a forcing defense and a counterforce play. You can trump, but then you are stuck. You cannot force him back with a heart, because he would get his extra trick by trumping with ♠Q and then win by cashing ♠A. Whether you trumped his ♦Q with ♠T or ♠J, your next trump lead would allow him to capture your ♠K with his ♠A, giving him 66 trick points and 2 game points.
“The other cards he could draw from the stock are ♠J, ♥Q, or ♥K. With any of these draws, he cannot force you to trump, but he can throw you in instead. Suppose, for instance, that he draws ♥K.” Hans again rearranges the cards.
You: (0 points)
♠ TKJ
♥ A
♣ —
♦ AClaudius: (51 points)
♠ AQ
♥ K
♣ —
♦ TQ
“From this position, Claudius can throw you in with either ♥K or ♦Q. You can cash your two aces and collect 29 trick points, but then you have to lead a trump, and whichever one you choose will allow Claudius to capture your ♠K with his ♠A for 66 trick points and 2 game points.”
Hans concludes. “All right, then, it’s time to analyze Claudius’s expected game points. He wins 3 game points if he draws either ♠K or ♥A, and wins 2 game points otherwise. That means his expected gain is ⅓(+3) + ⅔(+2) = 7/3 game points. So how does your duck of his ♥T lead compare to you winning it with ♥A?”
“I’m much better off winning the trick, just as I originally thought,” you reply haughtily. “I only give up 1 game point by winning it instead of giving up 2⅓ game points on average by ducking. So I should win it.”
© 2012 Martin Tompa. All rights reserved.
