Fibonacci - a game for two persons

There you are, not even three persons to play Pidro for three persons. What to do while you wait for the rest to arrive? Why not try Fibonacci?

Fibonacci card game

Fibonacci is a two person card game played with a standard 52-card deck without jokers. The aim of the game is to get rid of the cards in your hand by building Fibonacci series with the cards on the table. A Fibonacci series is a series where the next number is the sum of the two previous numbers. If a player can play a fitting card he must play. If the player can not play a card fitting the series, he has to draw one card from the deck and play it if it fits. After this it is the next player's turn. The game ends when a player plays the last card in his hand or when there are no more cards in the deck and no player can play a fitting card.

The structure of the game

Each player is dealt 8 cards.
Three cards are dealt face up on the table forming the seeds of the possible Fibonacci series. The rest of the deck is placed next to them face down.
The first player must if possible play one fitting card from his hand by placing it on top of one of the cards on the table. If he has no card that fits, he must draw a card from the top of the deck and if it is a fitting card he has to play it.
The turn changes and the other player plays a fitting card or draws one and plays it if it fits.
This continues until one of the players plays his last card and wins the game.
If the deck is depleted and a player can not play a card, the turn goes to the next player, who in turn must play a card if he can and then the original player may have a fitting card to be played. And so on.
If both players have cards left when no more cards can be played, the player with the fewest cards wins. An equal number of cards constitutes a draw.

Which cards fit and where can they be played

The cards have the number values printed on them and face cards as follows: Jack = 11, Queen = 12, King = 13. The ace counts as 14 in the hand but 1 on the table. The suit does not matter.

A card fom the hand can be placed in the following ways:

If a card is the sum of any two cards on the table, it can be placed on top of either of them.
If a card is the sum of all three cards on the table, it can be placed on any.
If two cards on the table form a sum bigger than 14, either of the cards can be "cut down" by playing a copy of the card sideways on top of it. The "cut down" card now counts as a 1 on the table

An example. The table reads 2,5,J. The possibilities are: 7 can be played either on the 2 or the 5; K can be played on 2 or J; Since 5 + J > 14 the 5 or the J can be cut down to 1 by either a 5 or a J respectively.

Lets say that the player also has a Q in his hand it makes sense to play the 7 on the 2 instead of the 5 because then the table would read 7,5,J, which opens a place for the Q (5+7). Of course there is the opponents turn in between so anything can happen but a table of 7,5,J gives more opportunities than 2,7,J if the player happens to have a Q. If the player had a 5 instead of a 7, he might instead cut down the 5 on the table to a 1 so then the table would read 2,1,J which also would be suitable for a Q next turn.

Some tips for playing:

Try to foresee the series. The two card series always starts from 1,1 but then depending on the players' choices take different turns
(1,1) -> (1,2) -> (1,3) or (3,2) -> (1,4) or (4,3) or (3,5) or (5,4) and so on. Depending on which card is incremented the series go through different numbers, preferrably those in your hand. The high numbers will eventually be cut down to 1 and then it starts all over again.
Sometimes all three cards are small and it is possible to play the total sum on any of them, throwing a spanner in the works of normal Fibonacci series
Count on that the opponent will have to play if he can, filling in the slots you are missing
Cutting down cards enables you to play cards separated by 1 after each other or the same card several times. Ex (Q,J,5) Play Q-> (1,J,5) Play Q-> (Q,J,5) Play J-> (Q,1,5). This may be useful if your opponent does not have any cards in the range and has to draw every turn. Remember that you can not cut down cards if they do not form a sum > 14 with exactly one other card on the table. A table (9,5,4) does not allow cutting even if the total sum is over 14 but no two cards form it.
4 and 6 are difficult numbers. 4 only occurs in the beginning of the series and is often passed by. 6 does not occur naturally, it requires all three cards or cutting down.
It is possible to exhaust a range of cards and then freeze the table so there are no more cards that can fit. If you have less cards than your opponent it may be worth the attempt when the deck is running out.

Copyright 2018. Simon Indola, Niklas Indola - the inventors of the game Fibonacci

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