All in a Row

All in a Row is a solitaire card game that is akin to Golf and Tri Peaks, and is very similar to Black Hole. The game's objective is to put the entire deck into the foundation.

This article is about the solitaire game. For the nursery rhyme, see Mary, Mary, Quite Contrary. For the play by Alex Oates, see All in a Row (play).
A Deal of All in a Row Solitaire in PySolFC in midplay

Rules

The cards are dealt to the tableau in columns of four. The foundation (the "row") can be started from any column, and afterwards it is built with cards incremented or decremented from the previous card by one (where kings and aces wrap).

Only the top cards of each pile in the tableau are available for play.

The game ends if there are no more top cards that can be moved to the Black Hole. The game is won if all of the cards end up in the Black Hole.

Solvers and Solvability Statistics

The Black Hole Solitaire solver by Shlomi Fish was adapted to solve All in a Row deals, and was subsequently run on the first 1 million PySolFC deals.[1] The solver found that 670,676 out of the million deals were solvable, while the other 329,324 were provably impossible, yielding a winning rate of over two thirds (67%).

The median of possible positions span for the impossible deals was 192.5, which indicates that over half of them, could be determined as such fairly quickly. On the other hand, the median of the positions span for the solved deals was 677,782, which indicates that there are many dead ends in such games.

Variants

Black Hole is a related game to All in a Row. Its foundations contain one initial card, and there are 17 cards of 3 columns each.

See also
  • Black Hole
  • List of solitaires
  • Glossary of solitaire

References
  1. Statistics from the First 1,000,000 PySolFC All in A Row Deals
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.