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.