Worst case scenario in 2048

Question

The game 2048 can be thought as a two player game, where one player shifts the table around to get to the 2048 tile, while the other player tries to hinder them by putting down 2s and 4s on the table. While the original game will put down the tiles randomly there are variants, such as some where this is not random, and also some where you are the one putting down the tiles, and the computer will shift the table around (not to mention the general one, where you can play both sides).
Theoretically, the worst situation is the following table, but for this the player shifting the table has to play really badly.

2
4
2
4

4
2
4
2

2
4
2
4

4
2
4
2

If however both players play flawlessly against each other, then what is the highest tile that the shifting player can achieve?

TheDoctor · Accepted Answer

When playing deterministic 2048, where a new tile is placed in the first available spot, you can get a pattern like this using left-down-left-down:

The worst I have been able to get in regular 2048 is this:

It is possible to get that worst-case scenario if your tile generator and human are working together to do so.

Worst case scenario in 2048

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