Home Page > Invented Games > Fib-Fibonacci


A two-player game by Eric Treadwell and T.J. Highley (address withheld by request)


The Fibonacci sequence consists of numbers that equal the sum of the two previous numbers. The first two are defined to be 1 and the rest follow: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. This game is based on this sequence, though are parts where it deviates significantly. One of the most important factors that shaped the development of this game was the fact that it uses the cards that are left over while another group of people are playing euchre.

The deck

The deck consists of 26 cards. There are 2 jokers, 4 each of twos, threes, fives, sevens, and eights, 2 fours, and 2 sixes. (Note that there are two each of the fours and sixes - this is because presumably the euchre players are using the other two fours and sixes to keep score in their game.)


This is a two player game. Each player begins with a hand of five cards and the other cards form the draw pile. The non-dealer plays first.


The winner is the person who gets rid of all of his or her cards first.


Players alternate turns. On your turn, you must do one of two things: draw a card from the draw pile or make a legal play. When you draw a card, that is your entire turn. You must wait until your next turn to play it. There are several different types of legal plays.


Vertical versus horizontal: These terms will describe how the cards are oriented. The vertical direction runs from one player to the other. The horizontal direction runs across the table, separating the players.

Run A sequence of cards that follows the Fibonacci rules - each value is the sum of the two previous values. The cards in a run are played vertically, and the run itself grows vertically.

Base card A card that is not part of a run but must be present before a run can start. Base cards are played horizontally.

Legal plays

  1. If there are no cards already on the table, then there is only one card that can be played: the Joker. When a joker is played, it becomes a base card with the opportunity to start runs in two directions (one run growing toward one player and one run growing toward the other). Also, when a Joker is played, the same player has the bonus option of playing a card on it to begin one of the runs. The card that is played must be three or less.
  2. A two or three can be played as the first card in a run on any opening on a base card.
  3. A three or five can be played as the second card in a run, but a three cannot be played if the first card in the run was also a three. Note that the typical combinations for the first two cards will be 2-3, 2-5, or 3-5.
  4. A card may be played as the third or fourth card in a run only if the sum of the two previous cards equals the cards value. For instance, if the first two cards in the run are 2-3, the third card must be a five (2+3). Then the pile is 2-3-5. The fourth card must be an eight (3+5). Generally, runs will not reach beyond four cards.
  5. (small wild) When a four is played, it takes the place of any card that is face up on the table. The card it replaces is taken into the player's hand. For the purpose of deciding what cards can be added to the run, the four keeps the value of the card it replaced. The four is considered wild because it can take on any value. However, it takes two turns to use it to obtain a card of that value and play it.
  6. (big wild) A six can take on any value greater than or equal to zero. However, it is limited based on when it is played. If it is the first card in a run, it must take on a value less than or equal to three. If it is the second card in a run, it must take on a value between three and five (inclusive). Note that there are now 11 possible combinations for the first two cards: 0-3, 0-4, 0-5, 1-3, 1-4, 1-5, 2-3, 2-4, 2-5, 3-4, 3-5. Most of these will seldom be seen though. If the six is the third or later card in a run, it must take on the value of the sum of the two previous cards. For example, 2-3-6 is a run. The wild card (6) must take on the value of 5 since 2+3=5 and the next card must be an 8 (which could be represented by another 6).
  7. (big wild) A six can also be used to restart a run at zero. When the six is played in this manner, it is considered a base card (and should be played horizontally on the end of run to be restarted), but the player does not get to play the bonus card associated with Jokers. The six only restarts the run on the side where it is played - the run on the other side of the original base card is unaffected.
  8. If your opponent just played a 7 or an 8 on his last turn, and you hold the 8 or 7 respectively of the same suit, you may play it. It is played vertically, but shifted to the side to make it clear that it is not part of the run. This opportunity only lasts for one turn. If you draw it, you cannot play it later in this manner. Likewise, if you hold the 7 and 8 of the same suit you cannot play them in this manner since it just an opportunity for your opponent.

Note that the table layout will typically consist of columns stretching between the players with a joker in the middle and runs stretching in each direction. All the runs on both sides of the base card are common property - players can add a card to either run if it fits.

Empty draw pile

If the draw pile becomes empty, it is filled up again with cards on the table. Any run whose top card is a seven or higher is considered closed since no card can be played on it (except a wild card). All cards that are part of a closed run and all base cards are shuffled together and form the new draw pile. Runs that were not shuffled may still be played on. If there was a space to start a run, but no cards were yet played there when the base card was shuffled, that space is lost.

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Last updated: 23rd June 2006