The Schnapsen Log

No Leeway (solution)

Martin Tompa

The Minister is in a desperate position. If the Deputy Mayor wins this trick and draws the last face-down card in the stock, the Minister is certain to lose the game, because cashing ♥T and ♦A and catching the Minister’s ♦T will give the Deputy Mayor more than enough trick points. On the other hand, the Minister is so far behind in trick points that winning this trick and drawing the last face-down card himself also cannot lead to a win. What can the Minister hope to draw from the stock that will enable him to reach 66 trick points? The Deputy Mayor will have ♠A and at least one of ♥T and ♦A when the stock is exhausted. Therefore, at best the Minister can cash ♣T and ♦A before the Deputy Mayor wins a trick and cashes another to reach 66.

Is the Minister’s position totally hopeless? No, because we have neglected the first thing he should consider when on lead with one card remaining face-down in the stock. The first thing to consider, even with so few trick points, is closing the stock. The Minister has one hope only, that the last card face-down in the stock is exactly the ♦A. If that is the case and he closes the stock, the Minister will be on lead from this position:

Deputy Mayor: (38 points)
♠ J
♥ T
♣ QJ
♦ K

Minister: (22 points)
♠ TQ
♥ K
♣ T
♦ T

The Minister has 4 tricks he can run, and at the end of that run he will have reached 66 trick points exactly. Closing the stock is a desperation play, and the Minister is desperate.

Notice that it is insufficient if the last face-down card in the stock is ♥T, even though this gives the Minister a much-needed trick. This would be the position:

Deputy Mayor: (38 points)
♠ J
♥ —
♣ QJ
♦ AK

Minister: (22 points)
♠ TQ
♥ K
♣ T
♦ T

The Minister again would have 4 tricks to run, but this time they bring his trick point total only to 60.

The Minister’s desperation play has probability 1/5 of success: he knows the Deputy Mayor is holding ♣Q, so there are 5 possibilities for the last face-down card in the stock, of which only 1 leads to success for the Minister. But 1/5 probability of success is better than the alternative: leaving the stock open and giving up all hope.

© 2013 Martin Tompa. All rights reserved.

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