Card games
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by Martin Tompa
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Schnapsen is an exceptionally tight card game. It has similarities to other trick-taking games such as Bridge and Pinochle. I like to think of Schnapsen as "Bridge in miniature": it is played with only 20 cards, it needs only two players, and one game takes only 15 minutes or so. Despite its miniature size, Schnapsen involves challenging strategy and every game is rife with thought-provoking situations.
Schnapsen is the national card game of Austria and Hungary, with variations played throughout Europe. The earliest known written reference to the game was over 300 years ago, but it was undoubtedly played long before that. It is truly a classic.
I will outline the rules of the game and then offer two find-the-winning-play puzzles that exemplify the thought-provoking situations that arise in every game. To really appreciate the strategy issues in this game, you should take some time to work out what you think is the best play before reading my solution to each puzzle.
If, after finishing the article, you want to face a terrifying opponent in a game of Schnapsen, I encourage you to play against Doktor Schnaps, the best Schnapsen-playing program on the internet. It was written by Artificial Intelligence expert Florian Wisser of Vienna, is freely available, and is devilishly hard to beat.
The Rules
Schnapsen is played with just five cards—Jack, Queen, King, Ten, Ace—from each of the four suits. This listing of the five cards specifies the order of the cards in each suit from lowest to highest: the Ten comes between the King and Ace in rank. Each card has a trick point value:
Schnapsen is the national card game of Austria and Hungary, with variations played throughout Europe. The earliest known written reference to the game was over 300 years ago, but it was undoubtedly played long before that. It is truly a classic.
I will outline the rules of the game and then offer two find-the-winning-play puzzles that exemplify the thought-provoking situations that arise in every game. To really appreciate the strategy issues in this game, you should take some time to work out what you think is the best play before reading my solution to each puzzle.
If, after finishing the article, you want to face a terrifying opponent in a game of Schnapsen, I encourage you to play against Doktor Schnaps, the best Schnapsen-playing program on the internet. It was written by Artificial Intelligence expert Florian Wisser of Vienna, is freely available, and is devilishly hard to beat.
The Rules
Schnapsen is played with just five cards—Jack, Queen, King, Ten, Ace—from each of the four suits. This listing of the five cards specifies the order of the cards in each suit from lowest to highest: the Ten comes between the King and Ace in rank. Each card has a trick point value:
Card rank |
Trick Points |
Ace |
11 |
Ten |
10 |
King |
4 |
Queen |
3 |
Jack |
2 |
You may have played some games with tricks (such as Bridge or Hearts) and perhaps played games with trumps. For those who have not, I will start with an explanation of these concepts. One player is on lead, selects a card (called the lead) from his or her hand, and plays it face-up on the table. The other player (the follower) then selects a card from hand and plays it face-up on the table. These two face-up cards comprise the trick. The winner of this trick is determined as follows. First, one of the suits has been designated (as explained later) to be the all-powerful "trump suit" and the cards in this suit are called "trumps." If neither player played a trump to the trick, then whoever played the higher-rank card of the suit that was led wins the trick. If either player played a trump, then whoever played the higher-rank trump wins the trick. (As an example, suppose that spades are trump. If the player on lead plays ♣Q and the follower plays ♦A, then ♣Q wins the trick. The follower can win this trick only by playing a higher club or a trump.) The winner of the trick collects the two trick cards, places them face-down in front of him or her, and is on lead to the next trick.
A Schnapsen game consists of a sequence of deals. The goal of each deal is to collect enough cards in your tricks to total at least 66 trick points. As soon as that happens, you declare 66 and the deal is over.
The player who is dealer alternates from deal to deal. The dealer deals five cards to each player, deals one card face-up on the table (the suit of this card is the trump suit for this deal), and places the remaining nine cards face-down on the table. The ten cards on the table are called the "stock." The face-up trump card is treated as though it were the bottom card of the stock, that is, it is the last card that will be drawn from the stock.
The nondealer is on lead at the first trick. The player on lead can select any card in hand to lead. The follower may be constrained, depending on the state of the stock. Initially the stock is open. (The other possible states of the stock are closed and exhausted, discussed later.) When the stock is open, the follower's choice of card to play is completely unconstrained. For example, the follower is allowed to play a trump on a nontrump lead, even if the follower holds cards in the suit that was led.
Assuming the stock is open, the winner of the trick draws one card from the top of the stock and then the loser does likewise. This order matters when there is only one face-down card remaining in the stock, because then the loser of the trick draws the face-up trump. Because of this drawing mechanism, each player will have five cards in hand at the beginning of each trick, provided the stock is open.
Whenever you are on lead (including before trick 1), you have three options before leading, and you may do any combination of them:
1. If the stock is open and the player on lead holds the Jack of trumps in hand, that Jack may be exchanged for the face-up trump on the table.
2. If the stock is open, the player on lead may close the stock. This is indicated by placing the face-up trump card on top of the face-down stock pile. The significance of closing the stock will be discussed later.
3. If a player holds the King and Queen of the same suit in hand, those two cards constitute a marriage. Whether or not the stock is open, the player on lead may show such a marriage to the opponent. The player on lead is required to lead one of those two marriage cards, returning the other one to his or her hand. Marriages so declared immediately add extra trick points to the player's total, 20 points for a nontrump marriage and 40 points for the trump marriage. If these extra points bring your total to 66 or more, you can declare 66 and end the deal before leading. You may only declare one marriage each time you are on lead, even if you happen to hold two marriages in your hand.
Only the player on lead has these options.
If the stock is not closed during the first five tricks, then the last cards in the stock will be drawn at the end of the fifth trick. From this point, the stock is no longer open, it is exhausted. When the stock is either closed or exhausted, the rules for the follower become much more restrictive: you must follow suit and win the trick, if possible. More precisely,
1. If you have any card of the led suit that ranks higher than the one led, you must play such a card.
2. If not, if you have any lower card of the led suit, you must play such a card.
3. If not, if you have any trump, you must play a trump.
4. If not, you may play any card.
If the stock is closed or exhausted, no more cards are drawn from the stock. Play continues with these restrictive rules until either some player declares 66 or both players run out of cards. If the stock is exhausted and both players run out of cards, whichever player took the last trick wins the deal. If the stock is closed and both players run out of cards, the closer loses the deal. Notice that the player that closes the stock can lose the deal in either of two ways: by failing to reach 66 trick points, or if the opponent declares 66 before the closer does.
When the deal is over, the winner of the deal scores some number of game points, and the first player to accumulate seven game points wins the entire game. If the stock was not closed, the winner of the deal is awarded game points as follows:
A Schnapsen game consists of a sequence of deals. The goal of each deal is to collect enough cards in your tricks to total at least 66 trick points. As soon as that happens, you declare 66 and the deal is over.
The player who is dealer alternates from deal to deal. The dealer deals five cards to each player, deals one card face-up on the table (the suit of this card is the trump suit for this deal), and places the remaining nine cards face-down on the table. The ten cards on the table are called the "stock." The face-up trump card is treated as though it were the bottom card of the stock, that is, it is the last card that will be drawn from the stock.
The nondealer is on lead at the first trick. The player on lead can select any card in hand to lead. The follower may be constrained, depending on the state of the stock. Initially the stock is open. (The other possible states of the stock are closed and exhausted, discussed later.) When the stock is open, the follower's choice of card to play is completely unconstrained. For example, the follower is allowed to play a trump on a nontrump lead, even if the follower holds cards in the suit that was led.
Assuming the stock is open, the winner of the trick draws one card from the top of the stock and then the loser does likewise. This order matters when there is only one face-down card remaining in the stock, because then the loser of the trick draws the face-up trump. Because of this drawing mechanism, each player will have five cards in hand at the beginning of each trick, provided the stock is open.
Whenever you are on lead (including before trick 1), you have three options before leading, and you may do any combination of them:
1. If the stock is open and the player on lead holds the Jack of trumps in hand, that Jack may be exchanged for the face-up trump on the table.
2. If the stock is open, the player on lead may close the stock. This is indicated by placing the face-up trump card on top of the face-down stock pile. The significance of closing the stock will be discussed later.
3. If a player holds the King and Queen of the same suit in hand, those two cards constitute a marriage. Whether or not the stock is open, the player on lead may show such a marriage to the opponent. The player on lead is required to lead one of those two marriage cards, returning the other one to his or her hand. Marriages so declared immediately add extra trick points to the player's total, 20 points for a nontrump marriage and 40 points for the trump marriage. If these extra points bring your total to 66 or more, you can declare 66 and end the deal before leading. You may only declare one marriage each time you are on lead, even if you happen to hold two marriages in your hand.
Only the player on lead has these options.
If the stock is not closed during the first five tricks, then the last cards in the stock will be drawn at the end of the fifth trick. From this point, the stock is no longer open, it is exhausted. When the stock is either closed or exhausted, the rules for the follower become much more restrictive: you must follow suit and win the trick, if possible. More precisely,
1. If you have any card of the led suit that ranks higher than the one led, you must play such a card.
2. If not, if you have any lower card of the led suit, you must play such a card.
3. If not, if you have any trump, you must play a trump.
4. If not, you may play any card.
If the stock is closed or exhausted, no more cards are drawn from the stock. Play continues with these restrictive rules until either some player declares 66 or both players run out of cards. If the stock is exhausted and both players run out of cards, whichever player took the last trick wins the deal. If the stock is closed and both players run out of cards, the closer loses the deal. Notice that the player that closes the stock can lose the deal in either of two ways: by failing to reach 66 trick points, or if the opponent declares 66 before the closer does.
When the deal is over, the winner of the deal scores some number of game points, and the first player to accumulate seven game points wins the entire game. If the stock was not closed, the winner of the deal is awarded game points as follows:
Loser's State |
Game Points |
Loser took no tricks |
3 |
Loser's tricks and marriages sum to fewer than 33 trick points |
2 |
Loser's tricks and marriages sum to at least 33 trick points |
1 |
Note that if the loser declared a marriage at trick 1 but never took a trick, the deal is still worth 3 game points, not 2.
If the stock was closed and the closer won the deal, then game points are scored as in the table above, except that the loser's state is measured not when the deal ended, but rather when the stock was closed. That is, if the loser had no tricks at the time when the stock was closed, the closer is awarded 3 game points, even if the loser accumulated some tricks after the stock was closed. Similarly, if the loser had fewer than 33 trick points at the time when the stock was closed, the closer is awarded 2 game points, even if the loser surpassed 33 trick points after the stock was closed.
Knowing when to close the stock is one of the aspects that makes Schnapsen challenging. You may want to close the stock in order to force your opponent to follow suit, or because you don't want to allow your opponent to draw any more cards from the stock, or because your opponent has not yet accumulated 33 trick points and you want to guarantee that you win 2 (or 3) game points. The risk of closing the stock is that you must reach 66 trick points (before your opponent does), and you will be penalized at least 2 game points if you fail. In particular, if the closer loses the deal, the closer's opponent wins 3 game points if he or she had no tricks at the time when the stock was closed, and otherwise the closer's opponent wins 2 game points.
Puzzle 1
I am calling these challenges "puzzles", but don't get the wrong idea. They are not cleverly contrived in order to be interesting. They are exact situations that came up in games I played. In fact, I chose this first puzzle because it represents one of the most important and frequent endgame situations you will encounter in Schnapsen. In any of these endgame situations, when you're at the table it's thrilling to plan and execute the winning play.
You are playing Schnapsen against Uncle Hans, an expert opponent, and find yourself in the following position:
If the stock was closed and the closer won the deal, then game points are scored as in the table above, except that the loser's state is measured not when the deal ended, but rather when the stock was closed. That is, if the loser had no tricks at the time when the stock was closed, the closer is awarded 3 game points, even if the loser accumulated some tricks after the stock was closed. Similarly, if the loser had fewer than 33 trick points at the time when the stock was closed, the closer is awarded 2 game points, even if the loser surpassed 33 trick points after the stock was closed.
Knowing when to close the stock is one of the aspects that makes Schnapsen challenging. You may want to close the stock in order to force your opponent to follow suit, or because you don't want to allow your opponent to draw any more cards from the stock, or because your opponent has not yet accumulated 33 trick points and you want to guarantee that you win 2 (or 3) game points. The risk of closing the stock is that you must reach 66 trick points (before your opponent does), and you will be penalized at least 2 game points if you fail. In particular, if the closer loses the deal, the closer's opponent wins 3 game points if he or she had no tricks at the time when the stock was closed, and otherwise the closer's opponent wins 2 game points.
Puzzle 1
I am calling these challenges "puzzles", but don't get the wrong idea. They are not cleverly contrived in order to be interesting. They are exact situations that came up in games I played. In fact, I chose this first puzzle because it represents one of the most important and frequent endgame situations you will encounter in Schnapsen. In any of these endgame situations, when you're at the table it's thrilling to plan and execute the winning play.
You are playing Schnapsen against Uncle Hans, an expert opponent, and find yourself in the following position:
Your cards |
♠ -- ♥Q ♣T, ♣ K ♦A, ♦ K |
Concealed cards |
♠ -- ♥ T ♣ Q, ♣J ♦T, ♦Q, ♦ J |
Trump |
♠Q |
Stock |
Open, one face-down card |
Game points |
Hans 5, You 5 |
Trick points |
Hans 27, You 28 |
On lead |
You |
Before you can tackle this puzzle, we need to discuss how to read the card diagram. The table shows all the cards you have not yet seen (under the heading Concealed cards) and the cards that you are currently holding in your hand (Your cards). If the stock is exhausted, then the concealed cards are the cards that Hans is holding. But if the stock is either open or closed, then the concealed cards contain Hans's cards plus all the face-down cards in the stock. As a good Schnapsen player, you know the concealed cards exactly, because you have been keeping track of what cards you have seen played.
The card shown under the heading Trump is the card that is currently face-up on the table. If the stock is exhausted, there will just be a suit symbol under this heading with no particular card of that suit shown. Under the heading Stock is the state of the stock and the number of face-down cards remaining in the stock.
In Schnapsen, Game points are counted down from 7 to 0. In the diagram above, the game point score is 5-5, meaning that each player needs 5 more game points to win the game.
Finally, there are headings for the number of Trick points each player has already accumulated (including any marriages declared) and an indication of which player is On lead for the next trick.
Do not get confused: the six cards listed as concealed are not Hans's cards, they are all the cards you cannot see. One of those cards is still face-down in the stock, and the other five are in Hans's hand, but of course you do not know which five.
One of your challenges in planning the play is to take into account the six possible hands Hans may be holding at this point.
Now go back to the card diagram above and plan your play for the remainder of this deal. When you think you have a good plan, you can read my solution here.
Puzzle 2
A few deals later you find yourself in this position:
The card shown under the heading Trump is the card that is currently face-up on the table. If the stock is exhausted, there will just be a suit symbol under this heading with no particular card of that suit shown. Under the heading Stock is the state of the stock and the number of face-down cards remaining in the stock.
In Schnapsen, Game points are counted down from 7 to 0. In the diagram above, the game point score is 5-5, meaning that each player needs 5 more game points to win the game.
Finally, there are headings for the number of Trick points each player has already accumulated (including any marriages declared) and an indication of which player is On lead for the next trick.
Do not get confused: the six cards listed as concealed are not Hans's cards, they are all the cards you cannot see. One of those cards is still face-down in the stock, and the other five are in Hans's hand, but of course you do not know which five.
One of your challenges in planning the play is to take into account the six possible hands Hans may be holding at this point.
Now go back to the card diagram above and plan your play for the remainder of this deal. When you think you have a good plan, you can read my solution here.
Puzzle 2
A few deals later you find yourself in this position:
Your cards |
♠J ♥T, ♥K ♣Q ♦J |
Hans's cards |
♠T, ♠K ♥J ♣A, ♣K ♦-- |
Trump |
♥ |
Stock |
Exhausted |
Game points |
Hans 1, You 1 |
Trick points |
Hans 36, You 32 |
On lead |
You |
You each need only one more game point to win the entire game, so this deal will determine the champion. This time the stock is exhausted, so you know exactly which five cards Hans is holding, thanks to your ability to track the cards played. How hard can it be to find the best play when nothing is concealed? Give it a try before reading my solution.
♠♥♣♦
The header image shows equipment used in Schnapsen for keeping track of marriages declared and the game score. [Public domain image by Roland Screecher.] For any readers interested in a more detailed investigation of Schnapsen, the best source of information is Dr. Tompa's own book, Winning Schnapsen, reviewed in this issue. ~ Ed.