Mark Gritter (markgritter) wrote,
Mark Gritter

No Thanks!

"No Thanks!" (aka "Geschenkt") is a card game played with a set of cards numbered 3 through 35. At the beginning of play the deck is shuffled and nine random cards are removed from play. Each player is given a 11 number of starting chips, and one player turns the first card face up.

Each turn, a player must either take the card in front of him, with all accompanying chips, or decline it by placing one chip on the card and the choice passes to the next player. The player who takes the card turns over a new one and chooses again. If a player has no tokens left he must take the card. (Note that a player with zero chips will pick up at least one chip from the card, so he doesn't have to automatically take the rest of the deck.)

Cards add their value to the player's score at the end of the game. However, only the lowest card in a sequence counts--- if a player holds 33, 34, and 35 then only 33 points are added to his score. Tokens subtract from the score. The player with the lowest score wins.

Is this game trivial or not? The rules suggest that the number of tokens each player has be kept secret (but cards are not) but this is just a minor impediment to perfect play if a suitable strategy could be defined.

Suppose each player had a very large number of chips available. Is there any strategy to this variant, or does all of the interest come from the limited chip supply?

If a card comes that will decrease your score (because its chips exceed the card's value to you), you should plan to take it. Note that except at the end of the game, you have to pay one chip to avoid taking the next card from the deck anyway. But, given the choice between taking a zero-valued card (net +1 if you decline the next one) or passing on it (+1 now) it is better to take the card, to have a chance at matching it up later.

However, you should certainly calculate the value of a card to your opponents as well. A card which has positive value (i.e., bad) for all of your opponents should be sent around again to pick up more chips. For example, if you already hold the 34 and you are given the option of taking the 35--- which will not increase your card count at all--- you may want to wait and force your opponents to place more chips on the card (or take it and increase their score.)

This works both ways. If it is your turn and the card is the 10, but with 8 chips on it, you may wish to take it to prevent an opponent with an 11 or 9 from collecting 9 chips, at the cost of gaining 3 points yourself.

With two players, it seems like the unlimited-chip variant would be trivial. With three or more players, though, the possibility exists for 'spoiler' play or decisions based on ranking. A player might be faced with a choice like that described above (gaining three points to avoid giving an opponent a favorable negative play) but decline because it would move him down in the rankings.
Tags: game theory, games
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