[khafra]

It sounds like you're thinking he suggested just greedily taking the best possible move. But that's not what he suggested; he suggested evaluating the actual distribution of the opponent's moves and making the move with the highest expected value.

[saurik]

No, I entirely understood that. I am quite happily willing to believe that I misunderstand the ramifications of that algorithm (I spent a lot of time talking about game theory in college, but it was not my field, and that was a long time ago), but that is the algorithm I inferred. (I would respond more, but you didn't leave me with any specific complaints to respond to, so all I can really say is "no".)

[Anderkent]

The question is do you want to have the shortest expected number of turns until you win, or a 100% win rate. Playing safe (min-max) is what ensures the 100% win rate, but you might be making games longer on average.

[feral]

It doesn't have a 100% win rate as it stands.

Mini-max isn't even 'playing safe'.

Consider the following choice of moves, each leading to one of 5 random tile inserts:

Move A, which leads to 5 possible moves with the following game state goodnesses: ['Loss','Win','Win','Win','Win']

Move B, resulting in: ['99%CertainLoss','99%CertainLoss','99%CertainLoss','99%CertainLoss','99%CertainLoss']

Minimax is never going to choose A. Is that really what you want, even if your strategy is 'play it safe'?

[Anderkent]

Fair enough; I only ran it a couple times and it got to 2048 so I assumed it's a guaranteed win.

[khafra]

Min-max optimizes your chance of winning under the assumption of a rational adversary. That chance will be lower than "certain victory," especially in un-solved, symmetric games, because a rational adversary will also be playing min-max. The guarantee min-max provides is that it will do even better against a non-rational adversary than it does against a rational adversary; not that it will do better than any other algorithm against non-rational adversaries--which is the way I think it often gets parsed.

Also, we should note that the "value" in "expected value" doesn't have to mean "score." It could be the logarithm of your score, or your chance of winning against a rational adversary, or even the enjoyability of the game to spectators (if you have a precise metric for that).