The Schnapsen Log

Race to the End (solution)

Martin Tompa

The focus of your attention, instead of Katharina’s hat, should be your ♣TQ opposite her ♣AK. If you play passively here, you are going to end up being endplayed in this suit, forced to open up the clubs yourself. For instance, if you lead ♦J, Katharina is likely to discard ♠K if she has it, or ♣J if she doesn’t. There isn’t much you can draw from the stock at this point that will allow you to win this game. For instance, even if you draw ♥K, which seems like a very lucky draw, you will be on lead from this position:

Katharina: (21 points)
♠ —
♥ J
♣ AKJ
♦ T

You: (31 points)
♠ A
♥ AK
♣ TQ
♦ —

Despite your good hand and trick point advantage, you cannot win from here. If you cash ♥AK and ♠A, you will collect ♥J and ♣KJ from Katharina, giving you only 65 trick points and leaving you with two losing clubs. If instead you try to force Katharina with ♠A, she will throw you in with ♦T and you will be left with those same losing clubs. If instead you try to win the last trick by starting out with a losing club, you will lose the race: Katharina wins the club, forces you with ♦T, wins the next club, forces you again with ♣J, and wins the last trick with ♥J.

Let’s go back to the beginning. Instead of leading the passive ♦J, what happens if you lead ♠A? Katharina will likely trump with ♥K, giving her the lead from this position:

Katharina: (36 points)
♠ K
♥ —
♣ AKJ
♦ T

You: (25 points)
♠ —
♥ AJ
♣ TQ
♦ J

Now Katharina has a nice elimination play at her disposal, which I have no doubt she will find: she cashes ♦T to remove your only safe exit card and then throws you in by leading ♠K.

So even leading ♠A is too passive to avoid trouble in clubs. What’s gone wrong is that we didn’t consider what should have come first when on lead at the last trick before the stock is exhausted: closing the stock. If you do this, you have your own elimination play available. Cash ♥A and ♠A, in that order, to remove Katharina’s safe exits. Then throw her in with ♦T. This will leave her with nothing but clubs in her hand, so she will be forced to concede ♣T as a winner. That trick will bring you to 67 trick points. Only by seizing control and closing the stock will you win the race and be the one to execute the club endplay. Your reward will be 2 game points.

Can anything go wrong with this plan? Yes. If Katharina is very lucky, the face-down card in the stock when you close it will be ♦T, you won’t be able to throw her in when you lead ♦J, and you will be stuck with those losing clubs. With probability 1/6, you will lose 2 game points. Therefore, the expected number of game points you will gain by closing the stock is ⅚(+2) + ⅙(−2) = 4/3, which is much better than losing a game point if you leave the stock open. Actually, this calculation would only make sense if Katharina weren’t so close to winning the game. Since Katharina is only 1 game point away from winning the game, what makes sense is to say that you will lose the game with probability 1/6, but with probability 5/6 you will go on with the game point score tied at 1 each.

© 2012 Martin Tompa. All rights reserved.

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