Drunk 2048 clone idea - as time goes on probability your move will be replaced with a random move grows.

For example:

after 2 seconds: [0, 1, 0, 0]* => [0.1, 0.8, 0.1, 0]

after 4 seconds: [0, 1, 0, 0] => [0.15, 0.6, 0.15, 0.05]

after 8 seconds: [0, 1, 0, 0] => [0.25, 0.25, 0.25, 0.25]

* Probability of [left, up, right, down] move.