The Schnapsen Log

High Stakes (solution)

Martin Tompa

With my ♦AQ opposite Jozsef’s ♦TJ, I saw a possible opportunity for a throw-in. So I closed the stock and led my only trump, ♥Q. If neither of those diamonds was still in the stock, Jozsef would be thrown in with a position something like this:

Jozsef: (28 points)
♠ —
♥ TK
♣ —
♦ TJ

Me: (46 points)
♠ —
♥ —
♣ TQ
♦ AQ

Jozsef could now run his trumps, but I could discard my queens, or alternatively discard both my clubs. Eventually he would be forced to open up the diamond suit and I would capture his ♦T for enough points.

However, if either diamond was still in the stock, the throw-in would fail. Jozsef would be on lead from a position something like this:

Jozsef: (28 points)
♠ —
♥ TK
♣ A
♦ T

Me: (46 points)
♠ —
♥ —
♣ TQ
♦ AQ

Now he would have three tricks to run, and would accumulate 69 trick points before I could win another trick.

Since there were 5 possible cards remaining in the stock (not ♥K, which I knew was in Jozsef’s hand) of which the 2 diamonds would thwart my throw-in, there was a 2/5 probability that the throw-in would fail. Therefore,the expected number of game points I would gain was ⅗(+2) + ⅖(−2) = 2/5.

Could I have done better than winning 2/5 game point by leaving the stock open? I don’t think so. Suppose I lead ♥Q without closing the stock, trying for the same throw-in. Jozsef is unlikely to duck my ♥Q lead because he would see that, if he did so, I could likely cash my ♦A for enough trick points. If he instead wins this trick and the next with ♥AT, that puts us in this position:

Jozsef: (40 points)
♠ —
♥ K
♣ A
♦ TJ

Me: (46 points)
♠ —
♥ —
♣ TQ
♦ AQ

Is Jozsef endplayed in this position, forced to open up the diamond suit? No! For if he plays one more trump, what can I discard? Certainly not ♣Q, because then his ♣A catches my ♣T for 68 trick points. So I must discard ♦Q, leaving us here:

Jozsef: (47 points)
♠ —
♥ —
♣ A
♦ TJ

Me: (46 points)
♠ —
♥ —
♣ TQ
♦ A

Now Jozsef can lead ♦J, after which he will take the remaining tricks and 1 game point. It is a squeeze without the count, for his ♥K squeezes me out of my endplay threat, and after squeezing me he lets me in with ♦A before winning.

Is there something else I can lead at trick 5 without closing the stock? The only other plausible lead is ♣Q. Do you see what Jozsef must do on this lead? He is skilled enough to win this trick not with ♣A, but rather with ♥A, a ducking ruff play! That leaves him on lead from this position:

Jozsef: (28 points)
♠ —
♥ TK
♣ A
♦ TJ

Me: (46 points)
♠ —
♥ QJ
♣ T
♦ AQ

The beauty of the ducking ruff is that he saves his ♣A to catch my ♣T, and then runs his trumps for 68 trick points.

So it seems that closing the stock and throwing Jozsef in for 2/5 game point is my best play.

Kisses from your
Adolf

© 2013 Martin Tompa. All rights reserved.

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