2048 isn't won by clever single moves. It's won by never undoing your own progress. Everything below follows from three rules.
Your biggest tile is your whole board. Every move either feeds it or hurts it. You lose when that tile gets dragged out of its corner and buried, not when the board fills up.
Put your largest tile in a corner and treat that corner as home. A corner tile has only two neighbours, and — if you're careful with directions — it can never be moved. Anchor it bottom-left.
With home in the bottom-left, swiping Left or Down keeps the anchor where it is. Swiping Up or Right drags it out of the corner. So from here on, those are your only two moves — even when another swipe looks tempting.
Keep your rows and columns getting smaller as they leave the corner. Then two big tiles can only ever slide into each other — they never get walled off by a small tile in between. This ordered layout is the classic "snake", and it's the shape you want most of the time.
Two small tiles want to merge in a column. You can reach them with Up or Down — both merge them. Pick the direction that doesn't move your anchor.
That pair started as 0,0,0,2 / 0,0,0,2 / 0,0,0,0 / 128,64,32,4. The lesson: when two directions both merge, the tie-breaker is always "which one keeps the anchor?".
Anchor is the 128, bottom-left. Which way, and why?
1. Two 2s sit in the top row: 2,0,0,2 / 0,0,0,0 / 0,0,0,0 / 128,64,4,0
Left. It merges the two 2s into a 4 and keeps the 128 in its corner. Right would merge them too, but it slides the anchor off the corner. Down keeps the corner but leaves the two 2s stranded apart.
2. A column of pairs: 0,0,2,0 / 0,0,2,0 / 0,0,4,0 / 128,64,4,0
Down. Both pairs merge into the bottom two rows (2+2→4, 4+4→8) close to the anchor. Up does the same merges but lifts the 128 to the top — never trade the anchor for a merge.
3. A tempting horizontal pair: 0,0,0,0 / 0,0,0,4 / 0,0,8,8 / 128,0,4,2
Left. It merges the two 8s into a 16 and leaves the 128 at home. Right merges them too, but the gap after the 128 lets the anchor drift right, off the corner. Rule 2 saves you here: Right is simply never an option.
If the anchor does leave the corner, stop chasing merges and spend two or three moves shoving it back with Left and Down alone. Better to lose a little score than to lose the whole game.