Accordion is an insanely difficult game of solitaire that you’ll probably never finish – assuming you can find enough space to play it.
The objective is to get the entire deck of cards into one pile. Shuffle the deck of cards. Now deal them out, left to right, face up, in a line. All of them. What? You don’t have room? Well, that’s okay; a standard variant allows you to deal out the first twelve cards and then make moves, dealing new cards after each move as space becomes available. Even with this, you're probably going to have to zigzag your line of cards.
You may move a card onto the card immediately to its left (which I will call a "step"), or onto the card three spaces to the left (which I will call a "jump"). Matching is by suit or by value.
Example of Accordion (using a twelve card layout)
♦8 ♥4 ♠K ♥6 ♣4 ♥Q ♠A ♥J ♣7 ♦7 ♣8 ♠4
The ♣4 can be placed on the ♥4:
♦8 ♣4 ♠K ♥6 ♥Q ♠A ♥J ♣7 ♦7 ♣8 ♠4 ♦J
Possible moves now are ♥Q on ♥6; ♠A on ♠K; ♦7 on ♣7; or ♦J on ♦7 - The second option looks best, giving:
♦8 ♣4 ♠A ♥6 ♥Q ♥J ♣7 ♦7 ♣8 ♠4 ♦J ♥K
If we compress that block of hearts, we get:
♦8 ♣4 ♠A ♥J ♣7 ♦7 ♣8 ♠4 ♦J ♥K ♥7 ♣Q
Which leaves a variety of options to go on with.
There is an even more difficult variant, called Idle Year, where you deal the cards one at a time, making moves as soon as one becomes available. If you have a choice between stepping or jumping, you may do whichever pleases you. Of course, the forced moves will send you crazy very quickly.
Actually, any variant of Accordion is difficult to win, so you can set arbitrary victory conditions based on the number of remaining piles left. I consider two piles to be a small victory in itself.
You can play accordion online (a quick Google search will find several sites), but I found it painful on my eyes, so I recommend a deck of cards. Accordion is quick to learn and fast to play, as long as you don't mind rearranging piles of cards when you run out of room. I enjoy it, even if I haven't finished it properly... yet.