Why four reserves instead of one big one?

Because how many cards you can reach matters more than how many cards there are. Twelve cards in one pile give you one playable top; the same twelve split into four piles give you four. Duke exists to make that difference the game, and it is why it plays nothing like Storehouse despite a similar deal.

Does an emptied column refill itself?

No, and this is the second thing that sets Duke apart from most of the Canfield family. There is no forced fill at all. An empty column stays empty until you choose to put something in it, and any card may go there, which makes spaces the most valuable thing on the board.

Can I move a card from one reserve to another?

No. Reserves are sources only. A card leaves a reserve for a tableau column or a foundation, and nothing is ever placed onto a reserve from anywhere.

How many times can I go through the stock?

Three times in all: the first pass plus two redeals. Cards are turned one at a time, so you see every card on each pass, which makes the early passes useful for planning even when you cannot play much.

Do the foundations wrap past the King?

No. Duke uses plain Ace-to-King foundations in suit with no wrap, and the tableau does not wrap either, so a King cannot be packed onto an Ace. That is a difference from Canfield proper, where both do wrap.

What is the most common mistake?

Playing from whichever reserve happens to fit, which drains all four piles evenly and leaves you with fewer live tops as the game goes on. Spend from the pile whose next card you actually want, and leave the others alone.

Duke Solitaire - Play Online & 100% Free

Play Duke Solitaire — Four Small Reserves, Four Free Choices

Duke asks a question the rest of the Canfield family never does: does it matter how a reserve is divided? Twelve cards under a single top card give you one choice at a time. The same twelve cards split into four piles of three give you four, every turn, all game. That is the whole design. Four little spreads sit face up beside four single-card columns, an emptied column is never refilled, and the stock turns one card at a time with two redeals. Free in your browser, no sign-up.

How Do You Play Duke?

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

Setup

Deck: one standard 52-card deck.
Reserves: four piles of three, dealt one card to each in turn, all face up and spread. Only the top card of each is playable.
Foundations: four, and all four start empty. They wait for the Aces.
Tableau: four columns of a single card each.
Stock: the remaining 36 cards, turned one at a time to a waste, with two redeals.

Rules

Foundations build up in suit from the Ace. Nothing wraps: a King ends a foundation.
Tableau columns build down in alternating colours, and a packed run moves as a unit.
An emptied column is never refilled. It is a space, it is yours, and any card may enter it.
Only the top card of each reserve may be played, and only to a column or a foundation.
Nothing is ever played back onto a reserve, and the foundations are one-way.
Three passes through the stock in total: the first deal plus two redeals.

Duke Strategy

Four reserve tops and four columns means eight cards you can act on at any moment, in a game with only 52. That is unusually generous, and the difficulty sits somewhere else: in what you spend those choices on.

Do not level the reserves. The temptation is to play from whichever reserve offers a fit, which grinds all four down evenly. Resist it. A reserve you have emptied is a choice you no longer have, and four choices is what makes this game playable. Leave the piles you do not need alone.
Read all twelve cards first. Everything is face up. Look for the Aces and 2s: an Ace on top of a reserve is nearly free, an Ace at the bottom of one costs you two plays you may not want to make.
Spaces are yours — collect them. With no forced fill, an empty column is a genuine holding bay. Two open columns turn an awkward reserve top into a solvable one, because you can park a card and come back to it.
Four columns is very little building room. Long alternating runs eat your board. Prefer short columns and keep at least one clear if you can, especially before you start unloading a reserve.
Use the redeals as scouting. Turning one card at a time means the whole stock passes under your eye three times. On the first pass, note where the low cards are rather than forcing plays; on the second and third, you know what is coming and can hold a space open for it.
Aces first, always. The foundations start empty and nothing banks until an Ace shows. Getting all four Aces up is the opening, and every choice before that should be judged on whether it moves an Ace closer.

Why Splitting a Reserve Changes Everything

Compare Duke with Storehouse, which buries thirteen reserve cards under one playable top. In Storehouse the reserve is a queue: it comes out in one order and you either can use the next card or you cannot. In Duke the reserve is a hand. Twelve cards, four of them live, and you choose which one to spend — so a card that is useless right now can simply be left alone while you work another pile. That is a completely different kind of decision, from an almost identical pile of cards.

It also changes what a bad deal looks like. A Storehouse deal dies when the queue jams. A Duke deal dies when all four tops are dead at once, which is rarer and takes longer to arrive — so Duke plays slower, feels more controllable, and punishes the specific mistake of draining your own options. Players who like FreeCell's open information but want a stock to work with usually take to it quickly.