Most people play 2048 the same way: move in whatever direction seems useful at the moment. They reach 512 or 1024, hit a wall, and restart. Then they do it again. The scores barely improve because the approach is fundamentally reactive.
There is a better way. It's called the corner strategy, and it's the reason some players regularly reach 4096 or 8192 while others never break 1024.
Pick one corner — bottom-left is the most common choice. Your largest tile lives there permanently. Your second-largest tile lives next to it. Your third-largest next to that. You're building a descending chain that snakes across the board.
Notice the snake pattern. Large tiles in the first row, descending left-to-right. Smaller tiles building up in rows below. This arrangement maximizes your ability to merge large tiles together.
Once you've picked your corner (say, bottom-left), you predominantly make only two moves: left and down. These keep your large tiles anchored to the corner.
Move up or right as rarely as possible. Every time you do, your largest tile risks moving away from the corner, breaking the chain and likely ending your game.
It will happen. The board fills up, and your only available move is up or right. When this occurs:
The goal is to have your tiles in a descending order along the top row. As you fill the top row from left to right with merging tiles, the bottom rows serve as a "nursery" for smaller tiles that will eventually merge upward.
Never let a tile in your top row be smaller than a tile below it in the same column. That creates a blockage that prevents future merges in the top row.
Never move your highest tile away from the corner. If the next move would displace your 2048 tile from the corner, find another move. If no other move exists, make the displacement but recover immediately.
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