The Schnapsen Log
Studies (solution)
Martin Tompa
Closing the stock, which Hans considers first, is unlikely to succeed: Peter is likely to hold ♠J in his hand, in which case Hans can only reach 60 trick points via his ♠A and marriage. With the stock left open, the obvious play is to declare the marriage before it’s too late. Let’s pursue that line of play.
If Peter holds the ♠T, he cannot afford to duck Hans’s lead from the marriage, because cashing the ♠A would bring Hans to at least 67 trick points. Instead, Peter is likely to win the trick with ♠T, after which the top two trumps will give him plenty of trick points to win the deal. So, while declaring the marriage limits Hans’s loss to 1 game point, it is also likely to give up the chance to win the deal.
What can Hans do instead to fend off the possibility of Peter’s big trumps? He can start a forcing defense by postponing the marriage and leading ♥A for Peter to trump! If ♠T happens to be the last face-down card in the stock, Peter can defeat this play by discarding ♠J and then claiming the remaining tricks. But in all other cases, Peter cannot afford to duck ♥A. If, for instance, Peter discards ♦K, Hans would have 42 trick points, and then cashing ♠A and finally declaring the postponed marriage would hand Hans 2 game points.
So Peter must trump ♥A, obtaining the lead in this position:
Peter: (53 points)
♠ TJ
♥ —
♣ T
♦ TKHans: (27 points)
♠ AKQ
♥ —
♣ KJ
♦ —
Notice how quickly Peter went from absolute trump control to this tenuous trump situation. He cannot force Hans back by leading ♦K, because cashing ♠A and declaring the marriage would bring Hans to 68 trick points. Peter’s best lead from this position is ♠J in an attempt to break up Hans’s marriage. Being experienced players, this is exactly how their play has proceeded, so let’s rejoin them at this point in the deal.
Hans says, “Ah, the ♠J. A good lead, Peter! I can’t win the trick with ♠A, because your ♠T would become the master spade and would give you enough trick points. You compel me to break up my marriage, but I do it gladly! Observe,” Hans continues, as he takes the trick with ♠K and lays his hand face-up on the table.
Peter: (53 points)
♠ T
♥ —
♣ T
♦ TKHans: (33 points)
♠ AQ
♥ —
♣ KJ
♦ —
“Just as you couldn’t afford to force me, I also can’t afford to force you with ♠Q, because that would give you 66 trick points exactly. But, from my inferior trump position, I can in fact pull trumps by leading my lowly ♣J, which gives you only 65 points. After that, all the remaining tricks are mine.”
“Very nicely played, Hans,” Peter says with a congratulatory smile. “Forcing me at trick 5 with the ♥A was a clever move! I have to admit it never occurred to me that you were already holding the spade marriage at that point. When I trumped, I was certain I would draw one of the marriage partners from the stock.”
“Interesting, isn’t it, that it’s better for me to delay the marriage than to declare it immediately?” says Hans. “Leading the ♥A at trick 5 guarantees 66 trick points for me unless the ♠T is still in the stock. So the expected number of game points I win with that play is ⅚(+1) + ⅙(−1) = 2/3.”
© 2013 Martin Tompa. All rights reserved.
