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Subject: Danish Tarok - Strategy
                                   
   This page was contributed by Jens Brix Christiansen. See also the
   Rules of Danish Tarok.
     * Objective of the game. 
     * Strategy when making own Ultimo
     * Strategy when preventing another player's Ultimo
     * Defending against a known enemy
     * Driving out kings
     * Strong defense with no known enemy
     * Weak defense with no known enemy
     * Going for Nolo
     * Forcing Bagud
     * Making the last trick, no Ultimo
     * Capturing Ultimo cards
     * Playing for the trick count
     * What to discard (to the skat)
       
Objective of the game.

   The objective of the game is earn as many tokens as possible.
   Since tokens are earned and paid in many different ways, several
   strategies are possible. In order of priority, they are
    1. Prevent another player's Ultimo. The pots are a common asset,
       often of considerable value. Combined with the high cost of
       paying for Ultimo and founding the empty pot, this becomes
       the overriding objective of each hand.
    2. Making own Ultimo. This is an obvious goal; but taking a
       chance on your own Ultimo should not also include the risk of
       allowing someone else's Ultimo.
    3. Forcing someone else to lose the last trick on an Ultimo Card
       (forcing Bagud).
    4. Making the last trick. In most deals, it will be clear at
       some point that Ultimo is impossible, e.g. because the 5
       Ultimo cards have all been played, or because one player
       (without the pagat) has only trumps left.
    5. Capturing Ultimo cards during play; and conversely, not
       losing tricks in which you play your own Ultimo cards.
    6. Maximizing the count.
       
   Note that playing for Nolo is not a goal in itself, since the
   reward is modest. However, the threat of Nolo is a powerful tool
   in preventing another player's Ultimo; it especially effective
   against a player who has declared many trumps.
   
Strategy when making own Ultimo

   In the jargon, the player seeking own Ultimo is called the enemy
   (fjenden), and this section describes the strategy for play by
   the enemy. By definition, making your own Ultimo amounts to
   taking the last trick with an Ultimo card. This can only succeed
   if no other player holds a trump to play at the last trick. If
   you succeed in removing all trumps from the opponents, and still
   hold the pagat in the final trick, the Ultimo is automatic, since
   the pagat will be the only trump in the final trick. If you are
   planning a king Ultimo, you will furthermore normally need to be
   on lead; the elegant king Ultimo where the winner was not on lead
   to the final trick, though possible, is rarely achieved on
   purpose.
   
   Hence, enemy play is primarily a question of driving out all the
   (other) trumps. To some extent, this can be done by leading
   trumps yourself, and for the other players it is a sure sign of
   enemy play when a player leads trumps. However, whenever someone
   else leads a suit in which the enemy is void, he must play a
   trump; therefore, an enemy who leads trumps runs the risk of
   losing control of the game because he himself has all his trumps
   driven out. He therefore should lead trumps only when the other
   four suits are fairly balanced, since he then probably will not
   have many trumps driven out.
   
   The usual way for the enemy to drive out trumps is to lead a long
   suit. Such a suit is called a whip (pisk) and leading it is
   called to whip (at piske). After a few rounds, the other players
   can no longer follow to the whip and must therefore play their
   trumps; in the jargon they are hit (ramt). Of course, a whip is
   no good to the enemy unless he is on lead, and once the whip
   becomes effective, he will lose the lead every time he plays it.
   Therefore, the enemy also needs cards that will win tricks, so
   that he can come in to lead: high cards in the side suits (i.e.,
   suits other than whip and trumps), extra length in trumps, or
   high trumps.
   
   Of course, the enemy needs to know exactly how many trumps are
   still out at the end play, so that he can choose correctly
   whether to give up his Ultimo attempt. Holding the pagat in the
   last trick and being surprised by a miscounted trump still not
   played is not only embarrassing, it is also expensive.
   
   To sum up, for an Ultimo to succeed, the enemy needs
    1. An Ultimo card that will not be driven out. A player without
       an Ultimo card is not an enemy. A king needs to be in a long
       suit (sometimes 6, usually 7) in order to be expected to
       survive until the last trick.
    2. A useful whip. 6 cards are the shortest feasible whip, 7 are
       usually needed.
    3. Trumps. 8 are sometimes enough, although 9 are usually the
       minimum.
    4. Winners in the side suits.
       
   A rule of thumb to start with for novices is that the whip and
   the trumps together should total 16 of the 25 cards if an Ultimo
   attempt is to succeed. Many high cards in the side suits and a
   fairly even distribution of the side suits can reduce the
   requirement by one or two. Conversely, a void in a side suit and
   lack of winners in other side suits are bad signs, since the
   enemy risks having his trump length reduced too fast.
   
Strategy when preventing another player's Ultimo

   Players whose goal is to prevent an Ultimo are called defenders.
   Successful defense usually requires that two players agree to
   defend. Their strategy varies completely with the circumstances.
   Important questions when selecting the strategy are the
   following:
   
    1. Is there a known enemy?
    2. Are you a strong or a weak defender?
    3. Should you play for Nolo?
       
Defending against a known enemy

   Simply put, a known enemy exists when there is a declaration of
   trumps. The player declaring trumps announces both how many
   trumps he has and whether he holds the pagat. This information
   (and simple arithmetic) allows the two other players to determine
   how many trumps they each hold, and to know who holds the pagat.
   At the opening lead, the enemy is thus well defined, and the
   division of roles between the defenders is also well defined. The
   primary defense strategy is:
   
     * The defender with the long trumps retains a trump for the
       final trick. This is known as holding on (at holde spillet).
       
   If that seems impossible, the secondary defense strategy is to
   ensure that
     * All the enemy's Ultimo cards are driven out before the final
       trick.
       
   When the defenders play to hold on, they usually have little room
   for error: The success of the defense often rests on marginal
   events like the untimely loss of the lead. They should
    1. Keep leading the suit in which the enemy is short (to drive
       out his trumps).
    2. Not allow the enemy to gain the lead unduly often (i.e.,
       control the tempo).
    3. Not lead a suit that forces the strong defender to use a
       trump.
    4. Ensure that the strong defender has a chance to play his spot
       cards early in the game.
       
   It is normally risky for the weak defender to lead his own long
   suit -- if his ally is short, this may lose the fatal tempo for
   the defense. It is necessary for the defenders to exchange
   information about their suit lengths. This is done by the
   following carding convention:
     * Following high-low to the two first rounds of a suit signals
       3 or 2 cards in the suit. Following low-high signals 4 or
       more cards in the suit. (Novices beware: even when signaling,
       the red 10s are low and the 1s are high).
       
   Another carding convention is also used between defenders:
     * From a sequence of equivalent cards, the convention is to
       lead the highest. When a defender leads the C, for instance,
       the other defender knows that he does not hold the D.
       
   If he has the opening lead, a weak defender should lead a suit of
   neutral length (i.e., 4), in order to get a length signal from
   his ally. If his partner shows 4 or more cards, the suit can
   safely be continued when he later gains the lead.
   
   The strong defender should normally play much like the enemy,
   leading his whip whenever possible. It should not usually matter
   that his partner is short in his whip; what is important is
   whether the enemy is short in the whip. If the weak defender
   plays to the strong defender's whip before the enemy, the weak
   defender should normally play his highest trumps, in order to
   promote his partner's trumps so that the enemy cannot draw them
   without losing the lead.
   
   When the whip for the defense has been identified, the weak
   defender should support the whip by leading it himself as long as
   he can. Not only is this a good use of the tempo, it also makes
   it difficult for the enemy to identify the strong defender; this
   can help the defenders, for when the enemy has a choice of two
   suits each of which will drive out trumps from only one of the
   defenders, it can be crucial that he attacks the strong defender.
   
   A defender gains on the trick count when he makes his high cards,
   and he does not risk a penalty for not making a king when he
   plays it early. Such temptations must be resisted when they risk
   costing a fatal tempo for the defense: the high cards must be
   used for controlling the game until it is obvious that an Ultimo
   is no longer possible.
   
   As the game progresses, the role of enemy can change. For
   instance, when it is clear (from the declarations and the play)
   that the enemy no longer holds an Ultimo card, there is no need
   to maintain an alliance against him, and indeed some other player
   who still holds an Ultimo card may now be the greatest threat.
   
Driving out kings

   You cannot really drive out the pagat from an enemy without
   totally stripping him of trumps. But kings can be driven out, and
   especially when the defenders know that the enemy does not hold
   the pagat, their primary goal is to drive out kings.
   
   Driving out a king is (simply) a question of leading the suit
   until the king has been played. However, the defense does not
   necessarily have the tempo to drive out all kings, and they are
   also in trouble if the enemy has a king that heads a long suit of
   6 or 7 cards.
   
   The declarations may have placed all the kings, but when they
   have not, it is important that the defenders exchange information
   about what kings they hold, so that they can concentrate on the
   kings held by the enemy. The convention is that defenders play
   their kings early, and specifically that they never hold their
   kings back from a trick where the enemy has played a knight or
   queen. Also, if the defender holds the pagat, he should play it
   early if there could be the remotest suspicion that he is
   otherwise trying to make it Ultimo.
   
   Even when the enemy holds one more card in a suit with a king
   than any defender, the defence still has a chance to drive out
   the king. This is achieved by holding back the fool until the
   long defender's suit is exhausted and then playing an extra round
   of the suit by leading the fool and naming it appropriately. This
   is especially elegant when one defender has the long suit and the
   other defender has the fool. Often the declarations will allow
   the defenders to infer who has the fool, but sometimes the
   defence simply has to assume that the fool is available. It can
   be good play by the enemy to hold on to the fool when this leads
   the defenders to assume that each other might hold it.
   
Strong defense with no known enemy

   If you hold 7, 8, or 9 trumps, and there has been no declaration
   of trumps, you will normally be a strong defender against an
   unknown (possibly non-existing enemy). The other two players will
   be in a similar position and each will decide whether he is
   strong or weak (or possibly an enemy). Since there was no
   declaration, each of the other players can hold at most 9 trumps;
   this information may be helpful in the play.
   
   Your best strategy as strong defender with no enemy is to play
   like an enemy, and hold on to the game. Your potential ally will
   not be able to distinguish you from an enemy, but this usually
   cannot be helped: if you falter from leading your whip, you may
   find out who the real enemy is, but you may also yield the fatal
   tempo at the same time.
   
   The strong defender should signal suit lengths honestly; it may
   become clear at some point to a weak defender that you are not an
   enemy, and the information available should then be as useful as
   possible.
   
   If a strong defender holds the pagat, he may concentrate on
   driving out kings, but this can be dangerous since it is not
   clear which kings are important to drive out, and the loss of
   tempo may result in losing control of the final trick. Note that
   playing in this way effectively forces the two other players to
   treat you as an enemy.
   
Weak defense with no known enemy

   If you hold 6, 5, or 4 trumps, and there were no declarations of
   trumps, the outstanding trumps (including the fool) number 16,
   17, or 18, and they must be divided no more unevenly than 9-7.
   Your goal is to ensure that both the other players have a trump
   in the last trick. One of the other players is likely to be your
   ally, but (see above) you probably won't find out who that is for
   some time.
   
   The weak defender plays in such a way that the other players'
   trumps are conserved. The worst possible play is to lead a suit
   that both must trump, and the best play is to lead side suits
   that both can follow to. The weak defender keeps track of the
   number of trumps left in each of the other players' hands (with
   the inherent uncertainty) and chooses to favor the player who
   seems to be losing the race to conserve his trumps; early in the
   game, the weak defender normally will not lead a whip, since this
   risks driving out trumps. If one of the other players keeps
   playing Ultimo cards, the weak defender can be tempted to
   consider him his ally; but an enemy with several Ultimo cards can
   play at that game too. Only if when all Ultimo cards are
   accounted for can the weak player be certain that no enemy lurks.
   
Going for Nolo

   Against overwhelming trump length (which is, of course,
   declared), a successful Nolo may be the only counter-measure
   available to the defense. For a Nolo to be successful, the
   following criteria are important:
    1. The other defender must actively support the Nolo.
    2. The defenders must agree to play Nolo immediately.
       
   A player (i.e., the weak defender) going for Nolo usually must
   have no high cards in his very short suits and usually must be
   short in trumps (successful Nolo with 5 or more trumps is rare).
   Moreover, it is normally necessary for the weak defender in
   general to have trumps that can be beaten individually by the
   strong defender. The defenders will know at the opening lead that
   Nolo is a possibility. A strong defender invites Nolo by leading
   a high trump at this first opportunity, and the weak defender
   accepts the invitation by following with a high trump (not

   winning the trick, of course); the weak defender rejects the
   invitation by overtaking the high trump. A weak defender invites
   Nolo by leading a trump, but he must not be overly zealous lest
   the strong defender lose a tempo in rejecting the invitation.
   
   The strategy at Nolo is for the strong defender to draw the weak
   defender's trumps before the enemy can force him to trump his
   whip. Then the strong defender plays his whip or more rounds of
   trumps, with the understanding that the weak defender then gets a
   chance to play other dangerous cards. The strong defender must
   guard his entries carefully, so that he can protect against the
   enemy's attempt to give the weak defender a trick.
   
   The fool is a very strong card in the weak defender's hand at
   Nolo, and conversely it is a dangerous weapon against the Nolo in
   the enemy's hand. For the strong defender, the fool is a minor
   liability: he must ensure that he does not give the weak defender
   a trick when he plays it.
   
   The weak defender normally signals suit length as usual, but the
   signal is possibly better used as encouraging/discouraging, e.g.
   with low-high signifying "yes, continue with this suit".
   
   When the dealer wins a Nolo, he still holds the skat in his trick
   pile; this sometimes confuses the enemy, who may overlook that
   the dealer did not win any trick.
   
Forcing Bagud


   This is not so much strategy as it is tactics. You cannot plan to
   force Bagud early in the game, but if Ultimo cards are still in
   near the end of the game, they can sometimes be forced Bagud.
   This happens when the holder of the Ultimo card is kept off lead
   in the end game. Forcing Bagud requires reliable knowledge about
   the cards left on each player's hand, which is not always
   possible and never easy, bearing in mind that three cards are in
   the skat.
   
   The risk of being forced Bagud (not necessarily on purpose)
   illustrates the importance of holding cards that take tricks so
   that you are on lead.
   
Making the last trick, no Ultimo

   A strong defender or an enemy who is forced to give up his
   Ultimo, will normally make the last trick if he was dealt mondo.
   Overall the most frequent outcome of a hand is for the player
   with mondo to make the last trick, but until that happens a
   series of thrusts and parries have been made to attempt and
   prevent Ultimo.
   
   In some cases, where a strong player has neither an Ultimo card
   nor mondo, he may drive out higher trumps by means of enemy
   strategy, thus scoring the last trick anyway.
   
Capturing Ultimo cards

   It is a minor source of income and satisfaction to capture an
   opponent's king with a trump. A trap can be set by choosing cards
   from a short suit for the skat. This is dangerous for a would-be
   strong defender, who may lose control of his trumps in this way,
   but it can be sound play for a weak defender if he happens to
   deprive the enemy of entries in this way.
   
Playing for the trick count

   Any player would rather play his king on a queen and a knight,
   since that trick counts 10 points in all. Holding back high cards
   until they are likely to yield good counts is marginally
   profitable (and also sometimes risky, if you don't cash your high
   cards until it is too late). It is, of course, a grave error to
   lose a fatal tempo to an enemy while pursuing the extra point in
   the trick count. It is also bad play to hold back a king when
   trying to drive out the enemy's kings, unless it is clear to the
   ally from a declaration that the enemy does not hold this
   particular king. However, it is accepted to use the highest point
   card of equals when following to a trick -- e.g. to win with the
   D when holding D C V of a suit.
   
What to discard (to the skat)

   This depends on how you plan the play of your cards. This can
   often be a difficult part of the game. But there are a few rules
   of thumb:
   
   The easy answer is to keep your whip, keep your trumps, balance
   the side suits. But if you are about to become a weak defender,
   your whip is not so important, and you should worry more about
   protecting entries and you might gamble on discarding from a
   short suit. And if you might be about to play Nolo, you should
   discard high cards from short suits, or possibly (all) your
   trumps.
   
   A strong player with a very long whip may be better off
   discarding from the whip than discarding from side suits. This
   seems to be true when the whip is so long that it is unlikely
   that there will be entries to play all the cards in it. Normally
   only 8 cards in a whip will be useful.
     ____________________________________________________________
   
   Return to Rules of Danish Tarok.
     ____________________________________________________________
   
   Return to General Index of Card Games site
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    This page is maintained by John McLeod
    (john@pagat.demon.co.uk).
    Last updated 21st May 1996