Undertricks
one down
almost every lost contract in SmartPref Pro goes down by a single trick.
What to keep in mind when you declare a contract
You have won the talon, and now it is time to choose your discard and name the contract, which means sizing up your cards. Most players judge hand strength simply: they add up how many tricks each suit is worth. It is a simple approach that works, but it misses a few important points we will go through now. First, it matters who leads. Second, the estimate of tricks itself can be done more accurately.
The assumption behind the numbers
Further on we will work out how many tricks a suit takes on average, and how likely each outcome is for a given layout. For that, we need to agree how the counting works.
We assume that as long as you hold at least as many cards of the suit as the opponent who just won a trick, the right to lead the suit again comes back to you, as if you always had an entry in another suit to get back and play the long suit to the end. This is the standard assumption for playing out a long suit: what you care about is playing it correctly.
Who leads
The player who leads first is called "first hand". The next player is "second hand", and the last one is "third hand". The first lead, like the first bid in the trade, passes clockwise from player to player every deal.
The cards in your hand are the same either way, so why would it matter who leads? It does, and it can be worth a whole trick in your contract. In our statistics, most lost contracts in preferans go down by exactly one trick.
Let us take one suit apart from the rest of the hand and go through every possible split of the missing cards between the opponents, weighting each split by its real probability. This full search of the plays, which skips branches that are clearly worse, is called alpha-beta pruning. Every number in this article was calculated this way, including the calculator at the end of this section. Below are a few layouts, from simple to tricky, each counted twice: when you lead the suit, and when an opponent leads it first.
| Your cards | Missing | Tricks, your lead | Tricks, opponent's lead |
|---|---|---|---|
| A K Q 8 7 | J 10 9 | 5.00 5: 100% |
5.00 5: 100% |
| A Q 10 8 | K J 9 7 | 2.67 2: 33%, 3: 67% |
3.42 3: 58%, 4: 42% |
| K J 10 8 | A Q 9 7 | 2.12 2: 88%, 3: 12% |
2.54 2: 46%, 3: 54% |
| K J 10 | A Q 9 8 7 | 1.05 1: 95%, 2: 5% (*see below) |
1.33 1: 67%, 2: 33% (*see below) |
| K J 9 | A Q 10 8 7 | 1.00 1: 100% (*see below) |
1.14 1: 86%, 2: 14% (*see below) |
Note the K J 9 and K J 10 cases. On paper this is a sure trick, but because the suit is short and is often not played out in a row, it is safer not to rely on it and count it as half a trick rather than a whole one.
Work it out yourself. Mark at least two cards of one suit that you hold. The algorithm will go through every possible split of the missing cards between the opponents and work out the result for each one; the weighted average is at the top of the table.
Mark at least two cards of the suit, but not all eight.
What the trade has already told you about the opponents' cards
When a player drops out of the trade, they are in effect telling the table about their cards: "I don't have a suit this strong, but I probably have the previous one, where I passed." That is why it is better to raise the contract step by step while you bid, so you don't give your cards away to the opponents at once.
So when you choose your contract, take into account what has already happened in the trade: at what point your opponents passed. If both opponents passed straight away without bidding, they have no long suits. And the other way round: if someone bid against you up to seven diamonds and then dropped out, they probably have long clubs (the suit just below diamonds).
Take "K Q 8 7" as an example: the Ace, Jack, 10 and 9 are missing. The mariage, as you know, takes one trick. After that the split matters: if the opponents' cards lie 2-2, both small cards will make tricks. If it is 3-1, only one of your two remaining small cards will make a trick, because the other one is spent knocking out the defenders' last card. A 4-0 split is the least likely, but you have to allow for it too: if an opponent bid up to this suit, that suit is probably long in their hand. The bottom line: if you suspect the suit is long with an opponent, your cards in it will bring you one trick. If not, two. Counting on three tricks is still a big risk.
Count losers, not tricks
The hardest part of the count is judging how many tricks a suit with a less than perfect layout will take. The difficulty is that you need to estimate exactly how the unknown cards are split between the two opponents, and a full search like the one in the section above is not practical to do in your head at the table.
For short suits there is a simpler way: instead of counting how many tricks you will take, count how many you are sure to give away. Count the sure losers in each suit, subtract the total from 10, and that is your contract.
For example, "A K J, K Q 7 8, A K Q". The easiest estimate goes like this: in the first suit the J is most likely a loser, because if an opponent's Queen is guarded they will hold on to it, while the A K will make two tricks; in the second suit the 7, 8 and Q are losers; the third suit has none. That makes 10 - 4 = 6, so you should declare six with trumps in the long suit.
This is easier than averaging or guessing how the opponents' cards lie: just go through your cards once from the bottom up and ask about each one, "is this a loser or not?"