How is Single Rail different from Double Rail?

Only by the deck count. One pack means four foundations, four columns and a 48-card stock instead of eight, five and 99. The build, the run move, the free spaces and the single pass are identical. The smaller board makes it faster and considerably luckier.

Why is it called Auxiliary Sequences?

Because that is what the columns are. You build descending sequences on them not for their own sake but as a staging area, so that cards coming off the stock have somewhere to wait until their foundation is ready.

Does the suit matter at all?

On the foundations, yes: each builds up in its own suit from the Ace. On the tableau, no: any card one rank lower may be placed on a column top regardless of suit.

No. Forty-eight cards are turned once. A card you leave on the waste can still be played later if the board opens for it, but the stock does not come back.

Can I win Single Rail reliably?

Not reliably. PySolFC rates it mostly luck, and with four columns the order of the stock decides many deals. Undo is unlimited here, which turns a lucky-or-not game into one you can study.

Single Rail Solitaire - Play Online & 100% Free

Play Single Rail Solitaire — Four Columns, One Deck, One Pass

Single Rail is Double Rail with one pack of cards: four columns instead of five, four foundations instead of eight, and forty-eight cards in the stock instead of ninety-nine. The rules are the same — build down by rank in any suit, move runs as a unit, put any card into a space, one pass through the stock. The board is smaller, and so is the room for error: PySolFC rates it mostly luck, and it plays like a fast, sharp sort with very little slack. Also called Auxiliary Sequences. Free in your browser, no sign-up.

How Do You Play Single Rail?

Goal: build all four foundations from Ace to King by suit.

Setup

Deck: one standard 52-card deck.
Tableau: four columns of a single card, face up.
Foundations: four, empty.
Stock: the remaining 48 cards, turned one at a time to a waste. No redeal.

Rules

Build tableau columns down by rank, in any suit: any 6 on any 7.
A packed run moves as a unit.
Any card may enter an empty column.
Foundations build up by suit from the Ace and are one-way.
One card off the stock at a time, and no redeal.

Single Rail Strategy

Forty-eight cards will come past you once, and four column tops are all you have to catch them with. Every decision is about which four ranks the board shows next.

Four tops, four ranks. Never let two columns show the same rank if you can help it; you are throwing away a quarter of the board. Spread the tops so that as many of the next few stock cards as possible have a home.
Watch the waste as a fifth column. A card on the waste can be played later if the board changes to accept it. Sometimes the right move is to leave a card there and play the column top that will make it playable next turn.
Aces are the whole game. Four foundations and four Aces; an Ace that lands under a run needs the run moved to a space to free it. With one deck there is no second copy to rescue you.
Runs are cheap to build and cheap to move. Because suits do not matter, almost any descending pair is a run. Build them long on purpose and keep one column short so you always have somewhere to start a new descent.
Use a space to re-sort, then close it. A space lets you split a run at the exact card you need. Four columns is too few to leave one open for more than a move or two.

Single Rail, Double Rail and the Forty Thieves Line

PySolFC registers Single Rail as a one-deck game with four rows, derived from Double Rail, and gives it the alternative name Auxiliary Sequences — a good description of what the tableau is: sequences you build only so that the stock has somewhere to go on its way to the foundations. It sits with Ali Baba and Fortune's Favor as one of the few one-deck games in a family built around two.

Like every game in this family here, the first stock card is left for you to turn rather than dealt to the waste at the start.