Solutions
Solution to Puzzle 1
Your cards |
♠ -- ♥Q ♣T, ♣ K ♦A, ♦ K |
Concealed cards |
♠ -- ♥ T ♣ Q, ♣J ♦T, ♦Q, ♦ J |
Trump |
♠Q |
Trick points |
Hans 27, You 28 |
Despite having only 28 trick points, the first thing to consider at this juncture is whether to close the stock. A good reason to consider this is that Hans's trick point total is still under 33, so if you succeed you will gain 2 game points, even if Hans takes more tricks once the stock is closed. Another reason is that closing the stock will prevent Hans from drawing that last trump from the stock.
Suppose that you do close the stock. You don't want to be the first one to lead diamonds because, if Hans holds ♦T plus one or two other diamonds, you cannot prevent him from winning a trick with ♦T. It seems possible that you can compel Hans to lead a diamond, and perhaps that would mean you could capture the ♦T with your ♦A. You will have to eliminate whatever clubs he could lead safely, and then "throw him in" by leading ♥Q. (This scheme is called an "elimination play" and will be familiar to good Bridge players. As I mentioned, these elimination plays come up very frequently in Schnapsen.)
Let us suppose first that Hans holds the critical ♥T you need in order to throw him in. Begin by leading each of your clubs. If he follows suit to both club leads, you will be on lead from this position:
Suppose that you do close the stock. You don't want to be the first one to lead diamonds because, if Hans holds ♦T plus one or two other diamonds, you cannot prevent him from winning a trick with ♦T. It seems possible that you can compel Hans to lead a diamond, and perhaps that would mean you could capture the ♦T with your ♦A. You will have to eliminate whatever clubs he could lead safely, and then "throw him in" by leading ♥Q. (This scheme is called an "elimination play" and will be familiar to good Bridge players. As I mentioned, these elimination plays come up very frequently in Schnapsen.)
Let us suppose first that Hans holds the critical ♥T you need in order to throw him in. Begin by leading each of your clubs. If he follows suit to both club leads, you will be on lead from this position:
Your cards |
♠ -- ♥Q ♣ -- ♦A, ♦ K |
Concealed cards |
♠ -- ♥ T ♣ -- ♦T, ♦Q, ♦ J |
Trick points |
Hans 27, You 47 |
Since we are assuming for now that he has the ♥T, you will win from this position whichever two diamonds he holds. You throw him in by leading ♥Q, after which he is coerced to lead a diamond and you can win both diamond tricks. Even if his diamonds are only ♦Q, ♦ J, you will end with 47+11+4+3+2 = 67 trick points.
Still assuming that he holds the ♥T, he might not follow suit to both club leads because one of the clubs is still in the stock. If he makes the obvious ♦ J discard on your second club lead, you will be on lead from this position:
Still assuming that he holds the ♥T, he might not follow suit to both club leads because one of the clubs is still in the stock. If he makes the obvious ♦ J discard on your second club lead, you will be on lead from this position:
Your cards |
♠ -- ♥Q ♣ -- ♦A, ♦ K |
Hans's cards |
♠ -- ♥ T ♣ -- ♦T, ♦Q |
Trick points |
Hans 27, You 46 or 47 |
Now when you throw Hans in with a heart, you are guaranteed to capture his ♦T and make plenty of trick points.
If Hans has only one club, he might make the devious play of discarding ♥ T on your second club, foiling the throw-in. This would leave you on lead from this position:
If Hans has only one club, he might make the devious play of discarding ♥ T on your second club, foiling the throw-in. This would leave you on lead from this position:
Your cards |
♠ -- ♥Q ♣ -- ♦A, ♦ K |
Hans's cards |
♠ -- ♥ -- ♣ -- ♦T, ♦Q, ♦J |
Trick points |
Hans 27, You 54 or 55 |
It is true that you can no longer throw him in, but his ♥ T will have given you so many trick points that you can win just by "cashing" (that is, leading and winning) ♦A.
Finally, we come to the situation in which Hans does not hold the critical ♥ T at all, so that the elimination play fails. In that case, this is the full position when you close the stock:
Finally, we come to the situation in which Hans does not hold the critical ♥ T at all, so that the elimination play fails. In that case, this is the full position when you close the stock:
Your cards |
♠ -- ♥Q ♣T, ♣K ♦A, ♦ K |
Hans's cards |
♠ -- ♥ -- ♣Q, ♣J ♦T, ♦Q, ♦J |
Trick points |
Hans 27, You 28 |
You cash ♣T and ♣K, Hans following suit, bringing you to 28+10+4+3+2 = 47 trick points. You next lead ♥Q, hoping to throw him in, but he discards ♦ J, bringing your total to 47+3+2 = 52. Now you are the one who has to lead diamonds, but that is fine because cashing ♦A brings your total to 52+11+3 = 66.
There were many possible contingencies for you to work out, but in each one you are guaranteed to score 2 game points. You have done the hard part of working all this out in your head, so go ahead and close the stock, sit back, and enjoy the pleasure of watching your plan unfold.
Solution to Puzzle 2
There were many possible contingencies for you to work out, but in each one you are guaranteed to score 2 game points. You have done the hard part of working all this out in your head, so go ahead and close the stock, sit back, and enjoy the pleasure of watching your plan unfold.
Solution to Puzzle 2
Your cards |
♠J ♥T, ♥K ♣Q ♦J |
Hans's cards |
♠T, ♠K ♥J ♣A, ♣K ♦-- |
Trump |
♥ |
Trick points |
Hans 36, You 32 |
You cannot possibly win a spade or club trick. The most you can hope to win are two trump tricks and the diamond, which would make your trick point total 32+10+4+2+2+4+4 = 58. This means that your only chance of winning the deal is to win the last trick. (Recall that, if the stock is exhausted and no one claims 66, the winner of the last trick wins the deal.)
You cannot afford to let Hans trump your ♦ J, because that trick plus his two other winners would give him 36+2+2+10+2+11+3 = 66 trick points. Leading ♠J won't work: Hans will win ♠T and then lead ♠K, forcing you to trump. This leaves you on lead from this position:
You cannot afford to let Hans trump your ♦ J, because that trick plus his two other winners would give him 36+2+2+10+2+11+3 = 66 trick points. Leading ♠J won't work: Hans will win ♠T and then lead ♠K, forcing you to trump. This leaves you on lead from this position:
Your cards |
♠ -- ♥K ♣Q ♦J |
Hans's cards |
♠ -- ♥J ♣A, ♣K ♦-- |
Trick points |
Hans 48, You 46 |
Your only chance to win the last trick from here is to lead ♣Q, but Hans will win with ♣A and then lead ♣K, forcing you to trump again and leaving him with the last remaining trump.
Look back at the original position. The reason that leading ♠J ultimately let Hans win the last trick is that Hans has more cards in the spade suit than you do. The way to win the last trick is to leave such suits for him to lead first. (You will see this in action momentarily.) For the same reason, leading ♣Q will not work. The only possibility remaining for you is a trump lead. If you cash ♥T, you will be on lead in this position:
Look back at the original position. The reason that leading ♠J ultimately let Hans win the last trick is that Hans has more cards in the spade suit than you do. The way to win the last trick is to leave such suits for him to lead first. (You will see this in action momentarily.) For the same reason, leading ♣Q will not work. The only possibility remaining for you is a trump lead. If you cash ♥T, you will be on lead in this position:
Your cards |
♠J ♥K ♣Q ♦J |
Hans's cards |
♠T, ♠K ♥ -- ♣A, ♣K ♦-- |
Trick points |
Hans 36, You 44 |
Now, not a trick earlier or later, is the time to lead ♦ J. Hans can no longer trump it, so you do not have to worry about him reaching 66. What will happen when you lead ♦ J? Hans is "squeezed", forced to shorten one of those two longer suits to the same length as yours. You then lead whichever suit he discarded, because he no longer has more cards in that suit than you do.
Let's suppose Hans discards ♣K on your ♦ J. (Discarding his ♠K instead would be entirely dual.) You continue by leading ♣Q, the suit he discarded. After winning that trick, Hans is left on lead in this position:
Let's suppose Hans discards ♣K on your ♦ J. (Discarding his ♠K instead would be entirely dual.) You continue by leading ♣Q, the suit he discarded. After winning that trick, Hans is left on lead in this position:
Your cards |
♠J ♥K ♣ -- ♦-- |
Hans's cards |
♠T, ♠K ♥ -- ♣ -- ♦-- |
Trick points |
Hans 50, You 50 |
Hans is forced to lead from the spade suit himself. Your last trump will win the last trick, the deal, and the game.
I call this play a "tempo squeeze". Your lead of the diamond squeezes Hans into shortening one of his long suits and then, when you continue with the suit he discarded, he "loses a tempo", as bridge players say. He has to lead from the long suit himself rather than being able to use a high card in that suit as an entry into his hand. This endplay nicely illustrates the fact that the struggle for the last trick often involves very different strategy from the struggle to reach 66 trick points.
I call this play a "tempo squeeze". Your lead of the diamond squeezes Hans into shortening one of his long suits and then, when you continue with the suit he discarded, he "loses a tempo", as bridge players say. He has to lead from the long suit himself rather than being able to use a high card in that suit as an entry into his hand. This endplay nicely illustrates the fact that the struggle for the last trick often involves very different strategy from the struggle to reach 66 trick points.