One of the rewarding aspects of Schnapsen is that it is played with such a small deck that, with some practice, you can remember all the cards that have been played and know exactly what cards remain to be seen. This is particularly important when the stock has been exhausted, at which point it is a great advantage if you know exactly what cards your opponent is holding. (If you are playing against a computer, you can be sure that the computer knows exactly what cards you hold at this point, and it will be important to counter this by knowing exactly what cards the computer holds. If you are playing against a casual human opponent, there is a good chance that you will know much more than your opponent at this point.) Good bridge players can remember all the cards that have been played using a 52-card deck, and in Schnapsen there are only 20 cards to remember, 5 in each suit.
To make it even simpler, in all but the most serious tournaments, players are allowed to look back at their own tricks at any time during the deal. This means you only have to remember the cards in your opponent’s tricks, if you so choose. I find, though, that it helps me visualize my opponent’s cards clearly if I remember all the cards that have been played, both in my tricks and my opponent’s, so I will talk about techniques for accomplishing this. I will occasionally look back at my own tricks if I have a lapse of memory.
At the time the stock is exhausted, only 10 cards will have been played (you are each still holding 5 cards), so your task is to remember only 10 cards. At this point, you can construct your opponent’s hand in your mind and can (and should) switch to remembering those 5 unseen cards rather than the cards that have been played.
This may sound daunting if you are a beginner, but it really can be mastered. You should start practicing by remembering just the trumps that have been played. This is really quite simple: you are probably looking at one or two in your hand and there is one on the table, so all you have to remember are a few other trumps. Visualize them with respect to how they rank with the ones you can see. For instance, if you can see the trump ten in your hand or on the table, when the trump ace is played you will register the fact that that ten is now the master trump. Once you can keep track of the 5 trumps, add the 3 other aces as cards that you track. Then add the 3 other tens. Once you can track these 11 cards, you will have the skill to add the remaining cards. Do the same sort of visualization in each of the four suits. For example, you will remember that the diamond ace has been played and your ten is high, and the heart queen has been played so you don’t have to worry about retaining your king for a possible marriage. You only have to picture 5 cards in each suit. If you use this method of visualization, you will find it quite easy to switch from remembering the cards played to visualizing your opponent’s hand at the point when the stock is exhausted.
I use another trick that I find helps me manage all these cards in my head: I never remember more than 2 cards per suit. At first I remember the cards that have been played, but as soon as I have seen at least 3 in the suit (including any in my hand), I switch over to remembering the cards I haven’t yet seen. Since each suit has only 5 cards, I never have to remember more than 2. A benefit of this method is that, by the time I get to trick 5 or so, I’ve completely switched over to remembering all the cards that I haven’t seen, which is exactly the view needed to plan out the endgame.
See The Schnapsen Log column Schemes for Remembering Cards to read detailed methods for remembering which cards have been played and which still remain unseen.
The principle that guides much of Schnapsen’s strategy is the control of trumps once the stock is closed or exhausted. Your goal at this point is to be able to pull any remaining trumps from your opponent and then run your winning cards, collecting trick points from your opponent and crossing the 66 point threshold. If the stock is exhausted, you will of course know which of your cards are winners, since you know your opponent’s hand exactly.
Under normal conditions, you would only have this type of trump control in about half the deals, your opponent having control in the other half. What can you do to improve your chances?
An anecdote from my childhood is relevant to this question. My father taught me Schnapsen and we played fairly often. The strategy I learned from him was a passive one. Early in the deal, he would lead out his nontrump jacks in order not to give away many trick points. When he ran out of jacks, he would lead queens or kings, trying if possible to select ones where he wasn’t giving up his chance to catch a marriage later. There would be some jockeying to lose the last trick before the stock was exhausted, in order to collect that trump showing on the table. This often meant leading a nontrump ace or ten to this trick, so that it would be costly for the other player to duck the trick and draw the trump. After the stock was exhausted, whoever happened to have trump control usually pulled trumps and won.
I remember one Sunday when my father’s younger brother, Uncle Tibor, came to visit and I played Schnapsen with him while my father and brother watched. Whenever Tibor was on lead, he would lead out a nontrump ace or ten, a play unthinkable in my family. I would trump, gleefully collecting all those points in my tricks, and return a jack. The result was that Tibor nearly always had trump control when the stock was exhausted (or he closed the stock), because I had used most or all of my trumps to capture his aces and tens. Because of this trump control, Tibor won nearly every deal. From that Sunday on, we all adopted Tibor’s Schnapsen strategy.
Like Tibor, you can improve your odds of obtaining trump control by leading nontrump aces and tens early in the deal, daring your opponent to trump. You will find that this often puts your opponent in a very awkward situation.
Consider first of all where the trumps are likely to be when the cards are dealt. There are 5 trumps, one of which is face up on the table. That leaves 4 trumps distributed among your 5 cards, your opponent’s 5 cards, and the 9 cards face-down in the stock. The expectation (that is, what you expect on average) is that you each hold one trump, and there are two left in the stock. There is a fair chance (about 25%) that your opponent holds no trump at all initially, in which case you will collect the points for your ace in your tricks and happily lead another, if you have one. (This is one place where there is a difference between the 5-card game Schnapsen and the 6-card game Sixty-Six. With 6 trumps, there are 5 of them distributed among your 6 cards, your opponent’s 6 cards, and the 11 face-down in the stock. This means that, on average, each player starts with 1.3 trumps, so there is a smaller probability that your opponent holds no trumps at all in the initial deal.)
Even if your opponent holds a trump, it may be a bit of torture to use it. The ace and ten of trumps are important cards for pulling trumps later in the deal, and it feels wasteful to use them to trump early in the deal. Your opponent will be reluctant to trump with the king or queen, giving up the chance for the very lucrative 40-point royal marriage. Finally, trumping with the jack gives up the opportunity to exchange it for whatever valuable trump is showing on the table. If your opponent yields to this reluctance and refuses to trump your ace, you will again happily lead another, if you have one, and watch your opponent squirm. Occasionally your opponent will be holding the trump marriage in hand with no other trump, and you can reel off a great number of winners, because you are playing with 5 cards in your hand and your opponent is playing essentially with only 3. (If you are the unfortunate opponent holding that naked trump marriage in your hand, and you have little chance to win the lead with your other 3 cards, it is better to break up the marriage sooner than later, when your opponent will have accumulated a large number of trick points.)
Most of the time, though, your opponent will trump your aces. Each time your opponent uses a trump and you do not, it dramatically increases the chance that you will have more trumps in hand when the stock is exhausted.
If you run out of high cards to lead, you can always return to the passive play of leading low cards in nontrump suits.
It is important that you keep track of the number of points you and your opponent have in tricks. As mentioned earlier, with the exception of the most serious tournaments, players are allowed to look back at their own tricks at any time during the deal. This means you really would only need to keep track of your opponent’s trick points, if it doesn’t disrupt your thinking too much to recount your own trick points.
When I play, I keep the two scores in my head, updating them explicitly after each trick. I will, for example, say to myself, “14 to 26”, always listing my score first in order to avoid confusion. The reason it is important to track points is that your strategy should change when one of you nears a threshold of 33 or 66 points. For example, if winning the current trick would put your opponent over 66, you must win it at all costs, even if it means trumping when your normally wouldn’t. If your opponent is near 66 and you have fewer than 33 points, you must do whatever you can to cross the 33 point threshold. If your opponent is near 66 and you have no tricks, you must do whatever you can to win a trick. If you are near 66 points and your opponent does not yet have 33 points, you may well want to close the stock in order to increase your ultimate score for the deal, or search for a way to end the deal without giving up any more trick points, such as by cashing high trumps.
It is also important to keep the game points in mind, though these are always written down so that no memory work is required. If either player is within one deal of reaching 7 game points, this impacts your strategy. For instance, if your opponent has only 1 game point remaining to win the game, it no longer matters whether you cross the threshold of 33 trick points: you must win the deal at all costs, and this may mean taking some risks. As another example, if you each have only 2 game points remaining to win the game and your current hand is bad, your primary goal should be to make 33 trick points: there is no difference in outcome between making 32 trick points and making 0 tricks.
There are three great advantages to closing the stock: (1) you force your opponent to follow suit or trump, (2) the game points (if you win the deal) are frozen so that they will not decrease even if your opponent wins additional tricks, and (3) you prevent your opponent from drawing more cards, including the face-up trump in the stock. The downside is that you must reach 66 points in your tricks without the benefit of drawing any more cards yourself, and you risk losing 2-3 game points if you fail to do so.
The two criteria you should use in deciding whether to close the stock are trump control and trick points. Your playing strategy, once the stock is closed, most likely will be to pull trumps and then play out your winners. If that is your plan, your trump holding should be strong enough to pull trump, though early in the deal you may be willing to gamble that one or even two of the trumps are face-down in the stock rather than in your opponent’s hand. As for trick points, when deciding whether to close the stock, add the points already in your tricks to the trick points in your hand that are winners. Add to this sum an estimate of how many trick points you will collect from your opponent in your tricks. For instance, if you believe that you will win all five remaining tricks, then it is fairly safe to assume that you will find your opponent with at least one 10- or 11-point card in hand, so you can probably figure on at least 22 trick points contributed by your opponent, and perhaps closer to 30. (For a more accurate formula to estimate how many trick points your opponent will contribute to your tricks, see The Schnapsen Log column How Much Help Can You Expect?) If the sum at which you arrive is at least 66 and you can pull trumps, then you should close the stock. Occasionally you will lose the deal because you have overestimated the trick point total, but this will be offset by the increased scores you gain by closing the stock on other deals. If you win every time you close the stock, you are not closing the stock often enough!
Source (http://psellos.com/schnapsen/strategy.html#formoreadvancedplayers)