I would like to know what are the chances of winning in both versions:
- laying out the cards one by one
- laying out the entire deck at the game start
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According to one of the biggest player on the solitaire market (SolSuite), the game of Accordion (one card at a time version) has a chance of winning in about 1 of 200 games, i.e. 0,5%
But I would actually say that there is no difference in the winning percentage (if played right) between the two versions you are talking about, since (in the one card at a time version) you could always lay out the entire deck first one card at a time before starting to play...
According to the latest publication that compute the solvability of 45 solitaire games, Accordion is almost always solvable.
Freecell, Spider, and Accordion...are all very close to 100% solvable.
At least one of each three games can be won in the version where you lay out the entire deck. Just follow these strategy tips:
You should select four cards of the same rank, clustered near each other and near the end of the layout. The strategy is to try to get all four selected cards to the end of the layout and never cover them with anything else until the very end of the game.