The talon in preferans
9.1%
chance that one particular card you need is in the talon.
What to expect from the talon in preferans
Several things matter when you size up the talon: where the extra trick is really hiding, why the talon gives a weak hand more than a strong one, and when you should not count on it at all.
The "minus one trick" formula
A mariage (King and Queen without the Ace = one trick) is a special case of a general rule: a suit that lacks its top card but holds an unbroken run below it is worth exactly one trick less than its length, however long the run is:
| Cards in the suit | Guaranteed tricks |
|---|---|
| King, Queen (no Ace) | 1 |
| Ace, King, Queen | 3 |
| King, Queen, Jack, 10 (no Ace) | 3 |
| Ace, King, Queen, Jack | 4 |
The missing card does not have to sit right under the Ace, and the card that fills the gap does not have to be the highest one:
| Held in the suit | Came from the talon | Tricks on your own lead: before → after |
|---|---|---|
| Ace, Queen, 10 | King | 2.00 → 3.91 |
| King, 9, 8 | Queen | 0.49 → 2.54 |
| Jack, 10 | King | 0.00 → 1.05 |
A good talon is more often a card like this that fills a gap in a suit than the Ace itself.
You can check your own suit in the interactive calculator in the article on what to keep in mind when you declare a contract.
The chance of filling a gap: short suits against long ones
The deck has 32 cards and 10 are in your hand, so 22 cards are unknown, and the talon is 2 particular cards among them. The chance that the card you need is one of those two is 2 in 22, that is 1/11 ≈ 9.1%, whatever the length of the suit. If any of j different cards would do:
P = 1 - C(22-j, 2) / C(22, 2)
C(22, 2) = 231 is the number of equally likely pairs the talon can be among the 22 unknown cards. j is how many different cards would suit you: j=1 if you need one particular card (say, only the Ace), j=2 if either of two will do, and so on. C(22-j, 2) counts the same thing, but only among the remaining 22-j cards that do not help you, that is every case where both talon cards miss and none of the ones you need arrives. One minus that share is the probability that at least one of the j cards you need does turn up in the talon.
| How many different cards would help | Chance that at least one is in the talon |
|---|---|
| 1 (for example, the only Ace) | 9.1% |
| 2 | 17.7% |
| 3 | 26.0% |
| 4 | 33.8% |
If you need two particular cards at once, the chance drops to 1/231 ≈ 0.4%. That gives a practical rule for the "bid or pass" decision: if your hand is one trick short of the contract and you have two weak suits, each with a single gap, the chance is real (~ 2 * 9 = 18%) and bidding is justified. If you are two or more tricks short and the weak suits are too scattered, do not count on the talon: a long weak suit cannot turn strong when it has too many gaps, because the talon holds only two cards. Passing is the sensible choice here, not hoping for "a nice talon", and telling these two cases apart is exactly what separates a beginner from an experienced player.
The talon cannot make your hand worse
After taking the talon, the player must discard two cards, so the talon cannot make things worse. At worst, if the talon does not help, it goes straight to the discard and the hand stays as it was.
Misère is the exception
"The talon can only help" holds for a normal contract: misjudging the talon usually costs one undertrick, not a disaster. Misère is a different story: a single card that takes a trick can turn into a train. It is safer to declare misère on a hand that is already clean, because if the talon cards add tricks (as they very likely will), you can discard them.
"Talon in the face"
Some groups play a rule called "talon in the face" (prikup v litso): the talon can be discarded face up, and the dealer gets a penalty to the heap. This is not part of the official tournament rules but an agreement at a particular table, and the details vary from group to group. SmartPref does not use this convention: we stick to tournament rules.
What to remember
- The talon never makes your hand worse.
- The talon helps a weak but not hopeless hand more than a hand that is already strong.
- Short suits with a single gap gain more from the talon than long suits with several missing cards. A suit with no gaps is almost never affected by the talon.
- A good talon is more often the cards that fill particular gaps in your suits than just two Aces.
- It is safer to declare misère on a hand that is already clean, because the talon will almost certainly bring a trick and you will be able to discard it.
- "Talon in the face" is common in many groups, but tournaments do not use it.