One of the most powerful weapons in Schnapsen is the trump marriage. This article is going to examine how strong the additional cards in your hand need to be to make closing the deck the right play. As it would be a laborious task to cover all possible situations during a game, we are just going to look at what to do if you have the trump marriage in your starting hand. The crucial factors determining whether closing the deck is the right play are the same at all times, but as a game progresses, you have to take the cards that are out of the game into account as well. Furthermore, you have to be aware of the potential payoffs. Please note that in the examples below the face-up trump is the Jt.**Starting Hands containing 4 Trump Cards**

Obviously, if you have all 4 trump cards in your hand, you should close the deck as you can be certain to score enough card points.**Starting Hands containing 3 Trump Cards**

If you have 3 trump cards including the marriage in your hand, you basically have to distinguish between hands containing the At and hands containing the Tt.**At-Kt-Qt-x-x**. We have discussed a variant of this hand before and come to the conclusion that closing the deck is the right strategy. It is very likely that you are going to have enough points after the first three tricks, therefore it does not really matter what the other two cards in your hand are.**Tt-Kt-Qt-x-x**. The exchange of the At for the Tt makes a big difference since your opponent is 36% to have the At.

First of all, let's look at how successful you are going to be if your opponent does not have the ace. In that situation, you would like to score 9 additional points in 3 tricks. Without specifying the Xs in your hand, you are just 66% to succeed. Therefore, the additional cards in your hand do matter: If you have an ace or a protected ten (meaning a ten plus another card of the same suit), it is the correct strategy to close the deck. Even if your opponent has the At, you will win the game, given that the first thing you do after closing the deck is to announce the marriage.

However, if you have low cards to go with your trump cards, you will not succeed if your opponent has the At. Furthermore, if he does not have the ace, you cannot be sure to score enough points all the time. If one of the Xs is a jack, your are 78% to succeed, which is equivalent to an overall EV of 0. If you have a jack and a queen, the percentage goes up to 83%, with 2 jacks it is even 91%. Still, the overall EV is just slightly positive in these situations.

Fortunately, there is a great alternative: announcing the marriage without closing the deck. If your opponent has the ace, he is going to decide to take the trick as he will try to limit the game points you can score. Still, this helps you in two ways: First, if you had decided to close the deck, your opponent would have scored 3 points most of the time. Now, you are very likely to win the game. Second, you can be sure to have the upper hand as far as trumps are concerned for the rest of the game. Additionally, you have two chances to get a helpful card from the deck. You are in a great position to score 2 game points.

If your opponent does not have the ace, you do not lose much by announcing the marriage without closing the deck: You take the trick, and your opponent only has an 8% chance of getting the ace. Moreover, you could get a helpful card after the first trick. Therefore, if you have low cards to go with your Tt-Kt-Qt, it is best just to announce the marriage and see what happens.**Starting Hands containing 2 Trump Cards**

Before we look at any specific hands, there is one key statistic worth mentioning: If you have the trump marriage without any additional trump cards, your opponent is just 11% to have both the trump ace and the trump ten (assuming that the face-up trump is the Jt). Therefore, if the other cards allow you to score 66 card points when your opponent does not have two trump cards, it is safe to close the deck.**Kt-Qt-As-Ah-Ad**. If you close the deck right away with this hand, you cannot lose, even if your opponent has the 2 remaining trump cards. Once all the trumps are out of the game, he will have to play a card of another suit. You will definitely take that trick and all the tricks that follow.**Kt-Qt-Ah-As-Ts**. This hand is similar to the last one. Your opponent must have both remaining trump cards and at least a couple of diamonds to put you under pressure. Your overall winning percentage is 96%. Closing the deck simply is a no-brainer.**Kt-Qt-Ah-Th-Kh**. As you will score enough points every time your opponent has fewer trump cards than you do, closing the deck is the right strategy. Your opponent might have both remaining trump cards and no hearts, but your overall winning percentage is 94%, still.**Kt-Qt-Th-Kh-Td**. With this hand, you would not like your opponent to have any combination of 3 of these 4 cards: At, Tt, Ah, Ad. 9% of the time, he is going to have one of these combinations and you are going to be in trouble. 36% of the time, he will have a combination of 2 of those cards: If he has the At and Tt, you would not like him to have 2 or 3 diamonds to go with them (36%). If your opponent has a trump and the Ah, you will score enough points all the time. Against an opponent with one trump and the Ad, you will succeed 95% of the time. Finally, if he has the Ah and the Ad, you will get beyond the 66 card point mark about 91% of the time. In total, your winning percentage is going to be about 87%. Thus, closing the deck is the right strategy.**Kt-Qt-Ah-Jc-Jd**. Even if your opponent has no trumps, it is not a given that you will score enough card points. If he actually has trump cards, it becomes even more difficult. Closing the deck is not an option with this hand.**Kt-Qt-Th-Ks-Kd**. This hand is not much better than the previous one. The main problem is that you need to score additional points by taking some tricks, but there are not that many tricks you could actually hope to take.**Defending against the Trump Marriage**

Finally, the question of how to defend against the trump marriage should be addressed. Basically, there is not much you can do: If your opponent closes the deck, play becomes almost automatic. If you have the higher trump cards and additional aces or tens, you should first take away your opponent's trump cards and then play your other cards of high value, starting with the aces. If you only have low cards to go with your trump cards, you should play your low cards first and save your last trump: Your opponent might have to trump and take a trick of low value. Later, you might be able to take a trick of high value by trumping yourself, if your opponent has aces or tens of suits you do not have.

If your opponent announces the marriage without closing the deck, the first thing to do is to somehow take a trick and thereby limit the game points he could score.

## 2010-09-26

### The Trump Marriage

## 2010-09-18

### Expected Value Part II

In the previous article, the concept of EV was introduced and applied to an actual playing situation. In this article, we will once again look at a couple of starting hands and identify the best strategies available based on EV.

Please note that in the examples below we will assume that the card that you get during the first trick is a jack of a non-trump suit if the deck is not closed right at the start.**Practice Situation #1**

Your hand is At-Tt-As-Ts-Ks. The face-up trump is the Qt.

This hand is worth 46 points, so you need an additional 20 points to get to 66 card points. Since you have the highest 2 trump cards and the 3 highest cards of another suit, you can be sure to take all the tricks if you decide to close the deck.

Is it actually a good idea to close the deck right away? As your opponent is going to have less than 20 points 18% of the time, she will score 3 game points 18% of the time. The remaining 82% of the time, you will score 3 game points. Thus, the EV of this strategy is 1.9 game points.

What other options do you have? To my mind, it would not be sensible to play a trump card as you would give up the edge you have as far as trumps are concerned. Consider these numbers: After the first trick, your opponent is 15% to have the two remaining trump cards. If you close the deck no matter what card you get after the first trick, you will not be able to get enough points the whole 85% of the time. In total, your winning percentage will have dropped below 82%.

Another alternative would be playing the ace or ten of spades, but this does not seem reasonable, either: Your opponent will have at least one trump 60% of the time, and since it should be a player's objective to secure as many high cards as possible (as noted before) she would likely decide to trump. Then, the maximum of game points you could score is 2.0 if everything goes your way, which is just 0.1 points above the EV computed for closing the deck right at the start.

That leaves playing the Ks: This is not a bad option: Your opponent cannot have any higher spades and she is unlikely to trump this early in the game. So, you will probably take the trick and have the chance to improve your hand with the next card you will get: A total of 6 of the remaining 14 cards will put you in a highly favorable position: the 2 remaining trumps, the 2 remaining spades, and the 2 remaining aces. After getting one of these cards, closing the deck will lead to 3 game points 98% of the time. Let's assume that if you receive one of those cards which do not exactly improve your hand, you still decide to close the deck. If you get a ten or a king, you will succeed 76% of the time. With a queen, you will get to 66 card points 75% of the time; with a jack, you will still succeed 65% of the time.

In short, you will score 3 game points 84% of the time. The EV has risen to 2.0 game points. Please note that so far we have assumed that your opponent will not under any circumstances try to take the first trick. This simply is an unrealistic assumption. Thus, your actual EV is not going to be higher than the EV of closing the deck at the beginning. The prime reason for this is that this hand cannot get much better than it already is.

This example illustrates an important fact: In Schnapsen, if you have the edge, you must immediately try and capitalize on it. Waiting and hoping for "better" cards will not pay off, especially if there are not many cards that would *significantly* improve your hand.

So far, we have only looked at what to do when you are to lead. But how should this hand be played if your opponent was to open the game? Obviously, if she announces the trump marriage, you have to take the trick, close the deck, and try to get to 66 card points. If she plays a spade, you take the trick, close the deck, and again try to get to 66. If she plays a high card, you should ask yourself why she would do that. She simply has to have all four remaining cards of high value and a single trump. This situation rarely occurs, and you should continue as in the previous two instances.

The most interesting situation occurs when your opponent plays a low card of a suit that you do not have: Should you trump or should you play the Ks? First of all, note that 3 marriages are still live meaning that if you let your opponent stay in command, she might sooner or later get one of those marriages and get over the 33 card point mark. However, your hand is just too good to just score a single game point with. Furthermore, you can be certain that she does not have two trumps since she could and should have announced the trump marriage. Factoring in that if she has one trump at the beginning of the game, in which case she will improve to two trumps just 8% of the time after the first trick, your overall winning percentage is 80% if you trump and then close the deck. This is equivalent to an EV of 1.8 game points. Compared to playing the Ks, which puts you in a situation in which you might score but a single point, this clearly is the superior strategy.**Practice Situation #2**

Your hand is At-As-Ts-Ks-Ah. The face-up trump is the Qt.

This hand is worth 47 points, so you need an additional 19 points to get to 66 card points. The chance that the cards in your opponent's hand are worth less than 19 points is 13%. Also note that you have but a single trump. If your opponent has more trumps than you do, which is the case 27% of the time, there is almost no way for you to score enough card points. If you decide to close the deck, you will fail to win the game 37% of the time (note that you cannot just add the 2 previous percentages up as you would count several hands twice). Still, the EV of this decision is 0.8 game points.

What alternatives do you have? First of all, it should be obvious that playing the At without closing the deck is out of the question as it would be difficult to win the game later on without trump cards. Since your opponent is 77% to have at least one trump, playing the Ah does not seem like a good idea either. A similar argument can be made against playing the As or the Ts, although this would be a slightly better strategy: As your opponent is more likely to have a heart than a spade, you might get the chance to take a trick later on by playing the Ah.

That leaves you with one final option: playing the Ks. Here, the reasoning would be the same as in practice situation #1: Unless your opponent has all 3 remaining trump cards, he is unlikely to trump. Therefore, you get the chance to take a card from the deck that improves your hand. The only question is: What cards do in fact improve your hand? Unfortunately, the only cards you really want are the other trump cards: 3 of 13 cards or 23%. Then, if you decide to close the deck, you will win the game 90% of the time, given that you play the cards in the correct order (if you get the Tt: At-Tt-As-Ts-Ah; if you get the Kt or Qt: At-As-Ts-Ah; your opponent might take a trick earlier, then play would become automatic). If you do not improve, you could still close the deck as long as the new card would allow you to take all the tricks in case your opponent has no more than one trump card. Those cards would be the Js, Qs, Th, Ac, which would be 31% of the remaining cards. Then, you would win the game 64% of the time (the actual percentage is slightly higher as you might get to 66 even though your opponent has more trumps, but 64% seems like a good enough estimate).

46% of the time, you will get a card that does not allow you to close the deck as your chances of winning would be less than 50%. Furthermore, you would likely have to play a card which enables your opponent to take the trick. This would also mean giving up the lead, which becomes an ever more important issue towards the end of a game. As you cannot be sure to have enough trumps, regaining the lead might become tricky. Moreover, at this point there are three live marriages, still.

Factoring in all these facts, it might be possible to slightly increase your EV by playing the Ks first, but as you can see, judging this decision is very complicated. Additionally, your opponent's playing style should be considered when thinking about the possible outcomes. Therefore, in my opinion, it would still be the better decision to close the deck right at the start.

This hand confirms what we saw in practice situation #1: If you have the edge early on, you should try and take advantage of it. This is especially true if you are weak as far as trumps are concerned and the other cards in your hand give you a shot at winning the game.

What if your opponent has the lead and you have the starting hand of practice situation #2? Actually, this hand becomes a lot easier to play: If you can take the first trick by playing the Ah or As, you will do just that. If your opponent plays a low club, you should definitely play the Ks. If you get the chance to take a trick that is worth more than 20 points, go ahead and trump. There really is not a lot you can do in this situation. As the game progresses, however, you should be aware of the possibility of your opponent getting the trump marriage, so you might sooner or later have to spend your trump card on a trick that is worth but few points.

## 2010-09-13

### Expected Value Part I

During a single game, you have to make a number of decisions: What cards do you get rid of? What cards do you lead with? Should you close the deck? Ultimately, these decisions should be based on the potential payoff, i.e. the game points you or your opponent might score. In a nutshell, you should always make the decision that maximizes your payoff. This payoff can be determined using the concept of expected value (EV). The EV tells you what a certain decision is worth in the long run. To illustrate this concept, let's look at an example.

Your starting hand is Qd-Jh-As-Ks-Qs. The face-up trump is the Js, you are to lead. What should you do?

First of all, let's try to classify this starting hand. It contains 3 trump cards including the marriage, which is almost as good as it gets. Then, the hand is worth 23 card points, which is below average, but recall that the trump marriage is worth 40 additional points. As for suits, you dominate the trump suit, but you definitely are on the losing side as far as the other 2 suits are concerned.

Now, what options do you have? What are the corresponding payoffs?

**Option 1: Closing the Deck**

Right at the start of the game, you could close the deck. Please note that you can be sure to reach as many as 58 card points with the cards in your hand alone: The marriage is worth 40 points, plus you will take three tricks including the As (11 points), Ks (4 points), and Qs (3 points). That leaves you 8 points short of the 66 card point mark. So, the three cards you get from your opponent should be worth at least 8 points. The best possible scenario would be your opponent actually having the Ts, which is the case 36% of the time. After closing the deck, you will lead with the As, so if your opponent has the Ts, he has to play that card as he has to follow suit. These ten additional points already are more than you actually need to win the game.

The only time you will not win the game is when the three lowest cards in your opponent's hand are worth less than 8 points. In other words, he needs one of the following card combinations: 3 jacks; or 2 jacks and a queen. In this particular situation, your opponent cannot have 3 jacks, since you hold one jack yourself and another jack is the face-up trump card, so the only scenario you should worry about is the 2J+Q scenario. Your opponent will have this combination 7% of the time.

In short, of the 64% of the time your opponent does not have the Tt, he is 7% to have 2J+Q.

So 4% of the time your opponent will score 3 points. Thus, the EV of this strategy is 2.7 game points.

Actually, I would consider this a conservative estimate for the following reason: Whenever people have to decide what cards to get rid of they tend to keep the higher cards. In our example, you could decide to lead with either the Jh or Qd after the second trick, knowing that you will definitely take the last trick since there is still one more trump in your hand and your opponent will not have reached 66 points by then. This way you might be able to score some extra points.

However, we should try and keep things simple. The EV as we calculated it is a good estimate.

**Option 2: Playing the Jh**

An alternative strategy would be not to close the deck and to play the Jh. If your opponent has the remaining trump and figures that he is in trouble, he might take the trick and limit you to 2 points at the most. But once again, let's keep it simple, ignore this scenario, and look at the more probable one: Your opponent has at least one heart 87% of the time. What's worse is the fact that he might already have a marriage or get one after the first trick. If he takes the trick with the Ah, which he has 36% of the time, he might even get to 33 points, in which case you will be able to score a single point only. So let's be optimistic and assume that 13% of the time you will still score 3 points, 83% of the time you will score 2 points, and the remaining 4% of the time you will score one point. The reason why this is an overly optimistic estimate is that we assume that you never lose this game (13% + 83% + 4% = 100%), which is impossible (you will almost always find a way to somehow lose a game). Still, your EV is 2.1 game points only.

Despite the optimistic assumptions, the EV of this strategy is 0.6 game points below the EV of the first strategy. This option definitely is inferior to the first one. Note that you will get a similar result for first playing the Qd instead of the Jh.

**Option 3: Announcing the Marriage**

A third possible strategy would be to announce the marriage without closing the deck. If your opponent has the Tt, he will definitely take the trick. Once again, he might have a marriage and thus get over the 33 card point mark. So, the probability distribution for this part is the same as it was in option 2: 4% of the time, you will score one game point and 32% of the time, you will score 2 game points.

For the sake of simplicity, let's assume that if you take the first trick, you will then close the deck no matter what card you take from the deck. Please note that if your opponent does not have any jacks in his starting hand, you will definitely get to 66 card points after closing the deck at this point. This will happen 23% of the time.

Even if he does have a jack, there is a fair chance that you will get a card that significantly improves your hand: the trump T, one of the remaining aces, or the Kd (giving you the marriage of diamonds). That is a total of 5 cards of the remaining 14 cards, or 36%. If you do not improve your hand, note that your opponent might get the Tt after the first trick (8%). If that does not happen either, you might not reach 66 card points, but only if your opponent has the remaining J and a Q, which will happen 11% of the time. Therefore, your opponent will score 3 game points 3% of the time.

The EV of this strategy is 2.4 game points.

**Option 4: Playing the At**

One last possible strategy would be to play the As without closing the deck, then announcing the trump marriage after the first trick. That puts you well above the 33 card point mark, so if you somehow manage to lose this game, your opponent can score a single point only. Please note, however, that your opponent is 42% to have the trump ten after the first trick (if you do not have it by then). The outcome of this game depends largely on the additional cards you will get during the game, but obviously you are in a good position. Your opponent might be more likely to make mistakes in a pressure situation like this. All things considered, I would estimate the EV of this strategy to be below 2.0 (without actually having calculated or simulated this situation).

**Summary**

In this article, we have looked at how to compute the payoffs of alternative strategies. The strategy with the highest EV is the one yielding the best results over the long run. Therefore, in our example, option 1 was the best strategy with an EV of 2.7 game points. Option 3 led to an EV of 2.4 game points. Some people might argue that this difference of 0.3 game points is not a particularly big difference. Actually, that is true and has to do with the strength of this specific hand. However, you should realize that all players get the same hands over the long run and should therefore try to maximize their payoff in each and every game.

Consider the following statistics: From experience, I expect a player to score one game point in 40% of games, another 40% of the time a player will score 2 game points, and in the remaining 20% of games 3 game points will be scored. That means that a player gets 1.8 game points per game won on average. Consequently, you need to win 4 games on average to win a Bummerl. If both players play equally well, a Bummerl consists of about 7 games. Now let's assume that in every single game you give up 0.3 game points in EV since you play suboptimally. In total, you give up 2.1 game points.

That is a lot, considering that you need to score 7 points to win. To compensate for this difference a huge extra effort is needed. As a player scores 1.8 game points per game won, this basically means that you give up one game without your opponent having to make any kind of effort.

All of these small correct decisions will lead to a large chunk of points in the end and might make the difference between winning and losing.

## 2010-09-10

### Card Counting and Card Points

This article is going to present a number of general facts about card counting and card points you should know. These are not exactly strategy concepts, but nevertheless, these facts are going to have an impact on your strategy.**Card Counting**

If you are new to the game of Schnapsen, you have to internalize all the basic processes and rules at first. This will help you limit the number of easily avoidable mistakes everyone makes at the beginning. Next, you should try to become proficient in card counting, which improves one's game dramatically. Specifically, you should keep track of the following things during a game:

-) How many points are the tricks you have taken worth?

-) How many points are the tricks your opponent has taken worth?

-) What cards are out of the game?

-) What cards are still live?

Under tough rules, the impact of card counting on your game will be massive: Since you must not look at the tricks you have taken yourself, you would not know at what point you would have reached the 33 or 66 card point marks if you had not kept track of your points. All you would do is guess. But even under soft rules, a player usually may not look at the tricks the opponent has taken. Consequently, it would be difficult to know which cards are still live if you did not count cards.

Now let's look at why you should be able to answer the four questions mentioned above at all times during a game.**The Players' Card Points**

As I have mentioned before, you have to keep track of the card points you and your opponent have scored to be able to estimate the potential payoffs, i.e. the game points one can still score. Consider the following example: If both you and your opponent have taken a trick, but are still below 33 points, you know that no player can score 3 game points in that game. Furthermore, depending on your opponent's card points, you might be forced to play more aggressively: Let's say that your opponent is close to 66 card points, but you are still below 33: You should try everything you can to get over that threshold fast.**Live and Dead Cards**

Keeping track of live and dead cards is important as it impacts the classification of the strength of your hand. Consider the following example: You have the Ts. Does the presence of the Ts strengthen or weaken your hand?

The answer is: It depends. If the As is dead, you know that you have the highest card of that suit, which is definitely positive. However, if all other cards of that suit are dead as well, the Ts is a problematic card: If you play it, your opponent will likely trump and secure the 10 card points (if trumps are still out there). If the As is still live, the ten is not exactly a powerhouse card.

Here is another example: You have the Qs-Qc-Qh-Qd in your hand. If all the kings are still live, you have an excellent chance to get a marriage at some point in the game. If all the kings are dead, all you have is 4 low cards worth 12 points that will not exactly help you take many tricks.

Keeping track of the live cards is vital for another reason: As a game progresses you get an ever clearer picture of the cards in your opponent's hand. Finally, once the stock is gone, you should know exactly what hand your opponent has. Furthermore, the chance of you getting certain cards increases during a game: Let's say you long for a particular card: After the first trick, you are 7% to get that card. After the third trick, your chances have increased to 10%. After the fifth trick, you are even 17% to get that card.

Sometimes it might be possible to exactly predict the last card of the deck if your opponent is to lead after the fourth trick: If a marriage is still live, you do not have any cards to that marriage, and your opponent does not announce it, you can be almost dead certain that the last card in the deck is a card that would be part of that marriage. Therefore, you can decide if you would prefer to have that card in your hand and have the lead, or if you would rather get the last trump card.**Tempus Fugit**

After having stressed the importance of counting cards, I would like to point out the following fact: If you lose the lead during a game, by the time you might regain the lead your hand will have changed dramatically.

Let's say you have a hand that on the whole does not look too bad, but you play a card that will likely allow your opponent to take the trick. Now, you take a new card from the deck and your opponent leads. You decide to take the following trick, and you get a new card again. At this point, there has been an exchange of at least one card, possibly two cards (that is 40% of the cards in your hand). A hand that might have been quite good two tricks ago may have become a loser.**Card Points**

Finally, we should take a closer look at card points: All 20 cards add up to a total of 120 card points. Since a single game can consist of a maximum of 10 tricks, the average trick in this scenario is worth 12 points. To reach 66 card points, you need to take 6 average tricks.

Obviously, the situation changes once marriages come into play. A marriage increases the amount of card points available in a game. Please note that once two 20-point marriages or the trump marriage have been announced, there is no need to be in a position to take the last trick since one player will have scored enough points by then.

Of the 120 total points, 84 points are covered by aces and tens, 36 points are covered by the remaining cards. Consequently, one of your key objectives should be to secure as many aces and tens as possible in the tricks that you take. In the previous article, I briefly mentioned the problem of an unprotected ten, i.e. a ten in your hand that is the only card of its suit: Once you are forced to follow suit and your opponent plays the ace of that suit, you have to play the ten, which is a card of high value that you would prefer not to surrender to your opponent.

Finally, towards the end of a game, aces and tens of dead suits might become problematic if you do not have the upper hand as far as trumps are concerned. If you play one of these cards, your opponent will have the chance to take those tricks by trumping.

## 2010-09-06

### Classification of Starting Hands

The first key fact to realize about Schnapsen is the importance of one's starting hand. The quality of the starting hand determines a large part of one's strategy since it contains half of the cards a player will receive during a single game. Please recall that a single game consists of a maximum of ten tricks.

The quality of a hand should be assessed based on four properties:

-) How many and which trumps does the hand contain?

-) How many points are the cards worth?

-) How many different suits does the hand contain?

-) Does the hand have any kind of marriage potential?**Trumps**

The average starting hand contains 1.2 (+/- 0.9) trumps. You will get no trumps 19% of the time. The probability to receive a single trump is 44%. The starting hand will contain 2 trumps 29% of the time and 3 trumps 7% of the time. The chance to receive all 4 trumps is less than a percent.

Of course, the number of trumps in your hand influences the number of trumps your opponent might have. If you do not have any trumps in your hand, the probability that your opponent has at least one trump is 87%. If you have one trump, the chance that your opponent has more trumps than you do is 28%. If you have two trumps, your opponent will have two trumps as well 11% of the time.**Card Points**

The average starting hand is worth 30 (+/- 7) card points. Again, what cards you have impacts the kinds of hands your opponent could have. If your hand is worth 35 points, you should expect your opponent's hand to be worth 28 (+/- 7) points. Obviously, the higher the values of the cards in your hand are, the lower will be your opponent's card point total. Please note that the exact numbers depend on the specific cards in your hand since a certain total of card points might be obtained by a number of different card combinations.

If you have the best starting hand worth 54 points (A-A-A-A-T), expect your opponent's hand to be worth 22 (+/- 6) points. As you can see, your opponent's card point total average does not change by much regardless of whether you have an average hand or a monster: The difference is a mere 8 points.

As far as total card points are concerned, hands worth more than 43 points are within the top 5% of hands. To be within the top 10%, a hand needs to be worth more than 38 points. For the top 20%, you need more than 36 points. Hands worth less than 22 points are in the bottom 20%, with less than 20 points they are in the bottom 10%.**Suits**

Obviously, you would like to have as many trumps as possible. But how many other suits would you like to see in your hand? The general answer to that question is: as few as possible. Consider the following example: Your hand is Tt-Kh-Th-Kd-Ks containing cards of four different suits. If you are to lead, all options available to you are problematic: The best alternative is to play the Kh, as the chance of your opponent having the Ah is a mere 36%. You should not play the Kd or the Ks because the chance of your opponent having either the A or T of that suit (or both of them) is 60%. What happens if your opponent is to lead? You are vulnerable because of the number of suits. If she decides to close the deck, you will in all likelihood fail to take even a single trick: The trump T is unprotected, meaning that if your opponent plays the trump ace, you have to play the trump ten. The situation of the Th is different: If your opponent decides to play the Ah, you can play the Kh, which leaves you with the possibility of taking a trick if she has another heart in her hand.

Basically, the only time a single card of a certain suit is unproblematic is when that card is the ace.**Marriage Potential**

Lots of additional points can be obtained through marriages. 21% of the time a starting hand will contain a marriage. Most of the time, you will only have parts to a marriage, e.g. either a single K or a single Q. The number of such kings and queens in your hand influences the likelihood that you will get a marriage at some point during a game. The following table displays the probabilities of you getting a marriage, given that the missing marriage cards are still live:*Example*. If your starting hand contains the Kh, the Qd, and the Qs, the chance that you will have one of those marriages either after the first trick **or** after the second trick is 41%.

Once again, the number of kings and queens in your hand impacts the chances of your opponent having a marriage: If you do not have any kings or queens in your starting hand, she is 44% to have a marriage. For each marriage that she cannot have, this number drops by 11 percentage points.**Impact on Strategy**

The quality of your starting hand influences your objective during that game. If you have a particularly bad starting hand, it might be the best strategy to just try and somehow take a single trick to limit the game points your opponent might score to 2. On the other hand, if you happen to have a particularly good starting hand, you might want to try to maximize your payoff and alter your strategy in a way that makes it almost impossible for your opponent to take any tricks.**Practice Hands**

Now let's try and judge the following hand's quality based on what we have discussed so far.**A-A-A-At-Tt**. This is a fairly easy one: There are two trumps in this hand, so your opponent cannot possibly have more trumps in her hand. The cards add up to the maximum of 54 card points. You have all suits in this hand, but you don't really care since you have all the aces. Obviously, there is no marriage potential. You know that you will take all the tricks if you decide to close the deck. Your opponent's cards have to add up to 12 points for you to get to 66. There are just 4 hands that she might have that would be worth less than 12 points: J-J-J-J-Q. There is no doubt about how this hand should be played: Close the deck and score 3 game points.**J-J-J-J-Q**. As far as card points are concerned, this is the worst possible hand. The queen gives you limited marriage potential and you have the worst cards of all suits. You have at least one trump though, which should enable you to take one trick and thereby limit your opponent to 2 game points. An interesting situation arises if the queen in this hand is the Qt and the turned-up trump is the king. You could consider forgoing taking the first trick hoping to get a card that improves your hand. If you are lucky, you might be able to take the second trick by playing that card and then marrying the trump king and queen.**Tt-T-T-T-K**. This hand contains one trump, which is not too bad, but the fact that it is the ten is worrisome. In fact, all the tens leave you vulnerable. One king means limited marriage potential. The card values add up to 44 card points, which is within the top 5% of hands. However, if you are to lead, this is a difficult hand: Basically, your only option is to play the king. If your opponent is to lead, things look different: Then, you are very likely to take the first trick and might improve your hand with the next card.**Ks-Qs-Ah-Jh-Tt**. This is a pretty average starting hand, except for the fact that it contains a marriage: It is worth 30 card points (not counting the marriage), the only trump is an unprotected ten. Still, this hand has potential.**At-Tc-Td-Kd-Qd**. You have the highest trump, a marriage which protects the ten of the same suit, and a lonely ten. This hand is worth 38 points (not counting the marriage). Once again, there is a lot of potential in this hand, especially if your opponent is to lead.**Jd-Td-Ts-Kt-Ac**. This hand contains one trump, yet only a low one. You have two tens, one of which is protected by a jack. The card point total is 37 points. Even though at first glance this hand might look familiar to the last one, it is far inferior because it lacks a marriage.**Ks-Qt-Th-Js-Jc**. This hand contains only a single low trump, is worth 21 points, and includes an unprotected ten. There is marriage potential (including the trump marriage). Still, you should try to somehow take some tricks and limit the damage your opponent might do.**Ks-Kh-Qd-Qc-Ac**. This hand has excellent marriage potential, which makes up for the fact that it is worth 25 points only. This hand can develop into a winner or a loser, depending on the cards you draw during the game. If you end up losing this game, you should be able to limit your opponent to but few game points. Note that if you want to announce a marriage, you have to be in a position to lead, so at some point during the game you will have to take a trick to be in that position. If clubs are trump and your opponent is to lead, this is a pretty good starting hand.

## 2010-09-05

### Rules

Schnapsen is played with a 20-card deck consisting of aces, kings, queens, jacks, and tens. Starting with the highest card, the card ranking is: A-T-K-Q-J. The cards have the following values: A – 11 card points, T – 10 card points, K – 4 card points, Q – 3 card points, J – 2 card points. Usually, either French style decks (suits: hearts, diamonds, clubs, spades) or German style decks (suits: hearts, bells, acorns, leaves) are used.**Before the Game Begins**

To properly deal cards in the traditional way, a specific sequence of actions must be followed: First, the initial dealer shuffles the cards and puts them face-down on the table. Then, the other player cuts the deck. Next, the dealer picks up the deck and starts dealing the cards: 3 cards to the opposing player, 3 cards to himself, 1 card face-up in the middle of the table showing the trump suit, 2 cards to the opposing player, and 2 cards to himself. Finally, the remaining deck is placed face-down on top of the trump card leaving it still visible. The deal alternates between the two players.**Basic Rules**

The player that has not been the dealer leads. Now, the dealer has two options: He can either take the trick by playing a higher card of the same suit or by playing a trump, or he can choose not to take the trick and play any card of his hand. The player that takes the trick scores the value of the two cards in the trick. Then, the winner takes the top card of the remaining deck, the opposing player takes the next. After that, the winner of the last trick leads.

Play resumes according to these rules until the stock is gone after the loser of the fifth trick has taken the last remaining trump card. Now the rules change in that players must follow suit. If they cannot follow suit, they have to trump. If they cannot trump either, they may discard any card of their hand.

Once a player believes to have reached at least 66 card points with all the tricks he has taken, he declares that he has enough points. To make sure that he does in fact have at least 66 points, his cards are counted. Now, the declaring player scores game points depending on how many card points his opponent has scored: one game point if his opponent has more than 32 card points; 2 game points if his opponent has less than 33 card points; 3 game points if his opponent has failed to take a single trick.

If the player has failed to reach 66 card points even though he said he had, his opponent scores 2 game points.

If no player manages to reach 66 card points before the last trick is played, the winner of the last trick gets one game point. In this case, it does not matter who has more card points.

Typically, the number of game points each player has scored is written down to avoid any confusion.

Three additional actions are available to players.**The Trump Jack**

First, the holder of the trump jack can exchange it for the face-up trump card if he is to lead. However, the exchange may only occur right before or after a trick.**Marriages**

Second, a player who is to lead and who holds both the K and Q of one suit may marry the two by playing one of the two cards and showing the other, while saying the number of card points the marriage is worth. Marriages are worth 20 card points except for the trump marriage, which is worth 40 card points. However, as long as the player who has announced the marriage has not scored a trick, these points do not count.**Closing the Deck**

Finally, a player who is to lead can close the deck by flipping over the turned-up trump card. From this moment on, play continues as if the stock was gone, meaning that no additional cards are taken from the deck and that suit must be followed. The player who chooses to close the deck must reach 66 points before his opponent does. He scores game points depending on the opponent's card points right before the deck was closed. If he fails to reach 66 card points, his opponent scores three points if he had not scored any points at the time the deck was closed, in any other case the opponent scores two game points.**Winning**

The first person to score 7 game points is the winner of a so-called Bummerl. Typically, the game points are counted downwards, so at the start of a Bummerl the score is 7-7. The first player to 0 is the winner.**Additional Tournament Rules**

A tournament match is usually played as either best-of-3 or best-of-5 Bummerls.

In most tournaments, some or all of the following additional rules are applied:

-) Tricks are taken by the winner, immediately turned face-down, and must not be looked at again.

-) The turned-up trump card cannot be exchanged for the trump jack right at the start of a game or if the stock is down to one card.

-) The deck cannot be closed if it is down to one card.

-) After announcing a marriage, the king has to be played.

-) Marriages may be announced only if a trick has already been taken.

-) Marriages may not be announced after the stock is gone.

Players may agree on playing according to these tougher tournament rules in normal play as well.

**References**

http://en.wikipedia.org/wiki/Sixty-six_(card_game). Retrieved on 05 September 2010.

http://de.wikipedia.org/wiki/Sechsundsechzig. Retrieved on 05 September 2010.*Waclena*: http://www.pagat.com/marriage/schnaps.html. Retrieved on 05 September 2010.

### Glossary

**Bummerl**

pronounced [bʊmʌl]; in Schnapsen, a player’s objective is to win a *Bummerl*. The first player to score 7 game points wins a *Bummerl*. Typically, the game points are counted downwards, i.e. at the start of a *Bummerl* the score is 7-7 and the first player to 0 is the winner.**card points**

All cards are worth a specific amount of *card points*: aces – 11 points, tens – 10 points, kings – 4 points, queens – 3 points, jacks – 2 points. During a single game, a player's objective is to be the first to score at least 66 *card points* with the tricks taken.**to close the deck**

to flip over the turned-up trump card and continue play as if the deck was gone; no more cards may be taken from the remaining deck and suit must be followed. The player who *closed the deck* has to reach 66 card points before the opponent does.**to cut the deck**

After shuffling the cards, the player that has not shuffled the cards *cuts the deck *by taking about half of the deck and placing the remaining cards on top of the cut-off half.**dead**

A card is *dead* once it has been played; a suit is *dead* once no more cards of that suit are live.**expected value (EV)**

in this context, the game points a player can expect to score over the long run by making a specific decision**to follow suit**

If suit must be followed, the player has to take the trick by playing a higher card of the same suit as the card with which the opponent has led. If this is not possible, a lower ranking card of the same suit must be played. If this is not possible either, the player has to trump. If none of these actions can be performed, any card may be played.**game**

a unit of play; during a *game*, a player's objective is to be the first to reach 66 card points with the tricks taken. A *game *consists of a maximum of ten tricks. The winner of a *game* is awarded a certain number of game points.**game points**

The winner of a single game is awarded *game points *depending on the card points the opponent has scored during that game. If the opponent has 33 or more card points, the player is awarded one *game point*. If the opponent has less than 33 card points, the player scores 2 *game points*. If the opponent has failed to take a single trick, the player gets 3 *game points*. The first player to score 7 *game points* is the winner of a Bummerl.**to lead**

to be the first player to play a card during a trick**live cards**

set of cards consisting of the opponent's cards, the turned-up trump card, and the remaining cards in the deck**marriage**

A player who is to lead and who holds both the K and Q of one suit may *marry *the two by playing one of the two cards and showing the other, while saying the number of card points the *marriage* is worth. *Marriages* are worth 20 card points except for the trump *marriage*, which is worth 40 card points. These points do not count as long as the player who has announced the *marriage *has not taken a trick.**trick**

A* trick* is the smallest unit of play: one player leads, then the opponent plays a card. There are three ways to take a *trick*: First, if only a single trump card is played, the player who played the trump card takes the *trick*. Next, if both cards belong to the same suit, the person that plays the higher card takes the *trick*. Finally, if both cards are non-trump cards of different suits, the player that led takes the* trick*.**to trump**

to take a trick by playing a trump card even though the opponent has led with a non-trump card**trump suit**

The *trump suit* is determined by the face-up card in the middle of the table; if only one trump card gets played during a trick, the person playing that card automatically takes the trick.**volatility**

measure of variability; higher *volatility* is associated with higher fluctuations

## 2010-09-04

### Introduction

Schnapsen is one of the most popular card games in Austria. It is played by thousands of people each and every day. Yet, articles on strategy are hard to find.

Let’s change that!

By creating this blog, I would not only like to introduce new players to this exciting game, but also provide strategy articles that might even help experienced players improve their game.

After stating the rules of Schnapsen in the first couple of posts, the main focus is going to be on strategy. The concepts to be presented will be applied to sample hands and actual playing situations in order to emphasize their importance.

Throughout the posts, I will use the following abbreviations: Capital letters A, K, Q, J, and T stand for aces, kings, queens, jacks, and tens. The letters h, c, s, d, and t designate the suits: hearts, clubs, spades, diamonds, and trumps. In Schnapsen, any suit could be the trump suit in a particular game; however, certain situations can only be correctly assessed if you know which of your cards belong to the trump suit.

Next, I would like to point out that I will provide a glossary of Schnapsen-related terms. There are two reasons for that: First, new players who are not quite familiar with all the terms might appreciate a site where the key terms are explained. Second, since a few German native speakers might be interested in this topic as well, I believe it is a good idea to explain various basic terms of trick-taking games as these terms are not part of everybody's basic English vocabulary (as a German native speaker myself I have to admit that I did not know many of the terms when I first started reading about the subject).

Last but not least, I must stress the fact that in certain playing situations there might not be one single “correct” strategy. Instead, quite a few strategies might be similarly successful. I will try to provide arguments for and against alternative strategies and thus decide what to do in those situations. Furthermore, I will try and do my best to arrive at the right conclusions. However, mistakes can happen. The reader is advised to challenge the concepts that will be presented in this blog. I will not take responsibility for any losses arising from the application of any of my statements. All posts should be viewed as an expression of my personal opinion. In the end, the only person responsible for his/her actions at the table is the actual player him-/herself.