The Schnapsen Log

A Bird in Hand (solution)

Martin Tompa

Because you have so few winners in your hand, it is tempting to trump Peter’s ♦A in order to cross the 33-point threshold and limit your loss to 1 game point. But you know the first order of business when following to the last trick before the stock is exhausted: you should consider what would happen if you duck. Let’s do that.

The obvious discard is ♦J, to deny Peter the opportunity of cashing his lucrative ♦T later. If you make this discard, Peter will be on lead from this position:

Peter: (40 points)
♠ Q
♥ T
♣ K
♦ TK

You: (21 points)
♠ T
♥ AJ
♣ QJ
♦ —

That ♥A in your hand makes the prospects look somewhat rosier, doesn’t it? It’s amazing how the ace of trumps can brighten up any hand.

You have 3 entries to your hand (♥AJ and ♠T) and Peter has only 2 (♥T and ♣K). Peter can accumulate 19 more trick points with those 2 winners, so will only reach 59. These facts mean you should be able to win the last trick and 1 game point. Your strategy to win the last trick, as usual, is to lead a loser every time you gain the lead.

Peter is going to lead his diamonds in a forcing defense designed to strip you of trump control, but you already know you have enough entries, so trump control needn’t worry you. He will start with ♦K, which you trump with ♥J. The loser for you to lead is a small club, say ♣J, won by Peter’s ♣K. His next diamond is ♦T, which robs you of your last trump and leaves you on lead in this position:

Peter: (46 points)
♠ Q
♥ T
♣ —
♦ —

You: (48 points)
♠ T
♥ —
♣ Q
♦ —

Now your last loser, ♣Q, forces Peter to trump, and your ♠T wins the last trick and the game point.

All right, then, ducking trick 5 turned into a success. We should still consider trumping Peter’s ♦A at trick 5, for the chance of winning 2 game points instead of 1. It’s not hard to see that the only draw from the stock that would give you a win is ♣K:

Peter: (27 points)
♠ Q
♥ AT
♣ —
♦ TK

You: (34 points)
♠ T
♥ —
♣ KQJ
♦ J

With this lucky draw, you can cash ♠T and declare the club marriage for 2 game points. The next best draw from the stock would be ♦T, leaving you on lead in this position:

Peter: (27 points)
♠ Q
♥ AT
♣ K
♦ K

You: (34 points)
♠ T
♥ —
♣ QJ
♦ TJ

The only tricks you are going to make are your two tens, which will carry your trick point total only to 61. What’s more, in this position it is Peter who has 3 entries (♥AT and ♣K) to your 2 (♠T and ♦T), so Peter will win the last trick.

I’m sure you can imagine that 1 good draw and 4 bad draws won’t work out well for you, but let’s do the calculation to make it precise. The expected number of game points you will gain by trumping Peter’s ♦A is ⅕(+2) + ⅘(−1) = −2/5. Since this is negative, you expect to lose 2/5 of a game point if you trump, rather than winning 1 game point if you duck. In this case, a bird in hand (Peter’s ♦A) is definitely not worth the game point in the bush.

© 2013 Martin Tompa. All rights reserved.

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