Moving runs
FreeCell only ever moves one card at a time. Dragging a run works because the game performs those single moves for you — so a run goes exactly when you had the room to carry it card by card.
What the number counts
(1 + empty free cells) × 2^(empty columns). The cells hold cards one at a time; each empty column can hold a stack, which is why it multiplies instead of adding.
The half people forget
Moving into an empty column carries one fewer, because that column cannot help carry the run it is receiving. Three cells and one empty column moves eight cards onto an occupied pile but only four into the empty one. This is the single most common surprise in the game, and it is why the board keeps the number in front of you.
Runs are not the goal
Building a long ordered run feels productive and often is not: it locks cards together that you may need to separate. Build a run when you have somewhere to send it.
Make the room first
When a run is longer than the limit, the fix is space, not a different run. With two open cells and no empty column the limit is three. Open a third cell and it becomes four; empty a column instead and it becomes six. The number under the board updates after every move, so check it before you drag.
On a real board: deal 7
This is deal 7 after 4 hints, exactly as the board draws it. The solid outline marks the card the next hint moves; a dashed outline marks the card it is working towards.
On the board, this one reads: Moved all 3 as one run — your limit of 3 allowed it.
The hint moves 3 cards — 5♠, 4♦, 3♣ — from one column onto another in a single drag. At that moment the limit is exactly 3. With one more card in the run the board would refuse the move and tell you why, instead of quietly doing nothing.
Play deal 7. Open it and press Hint 4 times to reach this spot.