Most Accordion players probably think of this game as having a very low win rate. And it does, if you make moves as soon as they become available (as I assume most players usually do, although that might be starting to change). However, you can significantly increase your odds of winning by dealing out the entire deck in one long chain of 52 cards, and then planning how to win using the advantage of seeing all the cards.
In 1999, I wrote a computer program to solve deals of fully open Accordion (playing as described above). I found that my solver got bogged down fairly quickly, and it would take way too long to exhaustively prove whether a game was winnable or not. So, I gave up on the idea of the solver having the capability to prove losses, and focused insteod on trying to find wins for as many deals as possible, in order to provide a lower bound estimate for what the win rate might be. It did this by playing out a given deal over and over again until it found a win or gave up due to exceeding a time limit or a specified number of tries. Each time, it played the game with a lot of random moves in the first half of the game, before using a brute-force solve to see if a win was reachable from there.
Given how difficult Accordion seems to be to win, even when playing the open style, I was very surprised to discover that my solver managed to win all of the random deals I initially gave it! I suspected that the game had a higher win rate than even FreeCell, so I kept my program solving deals for the next 16 months until it played about 800,000 games, and it still won every single game! As far as I know, I am the first to prove that Accordion has a higher win rate than FreeCell, and that nearly every random deal is winnable (or, at least the first to have such results reported on the Internet).
With an improved program and a much better computer, I can now solve over a million deals in just one day! I'm currently up to 30 million deals solved for a win, still with no losses (or inconclusive results).
| Games Won | Win Rate % |
|---|---|
| 30,000,000 | 100 |
See Accordion's Revenge for a harder variation of Accordion that I invented.
For more information about strategy for how to play Accordion open-style, and many other interesting things about this game, see Michael Keller's article here.
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Last modified March 17, 2022
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