| What has consistently worked for me is to mostly use 3 directions, forcing all of the large tiles to the bottom row, and crowding the space above the largest number(s) so going in the fourth direction keeps those large numbers along the bottom. All the way to 1024 is autopilot by just keeping small numbers out of the bottom row. Then, the thinking begins---plan each move to keep the 32s, 64s, 128s on the same edge of the board until you make an inevitable mistake or have bad luck working in the remaining 2x4 or 2x3 section. This last section is where your analysis algorithm would really add value. Plus, using just three directions until it's time to condense large blocks should reduce your computation a lot. Do you think regular use of all four directions is necessary to get more consistently to higher values like 16k or 32k? (Actually, is 32k possible?) I feel like once you have most of the blocks on board to get to 8k except for perhaps one 256, you can't really have a random 2 or 4 in the corner or it's Game Over in 10 moves or fewer. Moving in the fourth direction makes the 'corner small number' a guarantee when the board is filled like this. Playing all large numbers on the bottom also means you can calculate an optimal play (using the smaller numbers) in small (2x3, 2x4, 3x3) regions as long as the result comes out at the same grid location consistently---near the smallest large number. Then, optimization of the large numbers becomes a separate problem. Do you put everything sequential in the bottom row? 4096-2048-512-128 Or do you put high values at the ends? 4096-128-512-2048 Or low values at the ends? (This is not the answer. Getting a medium value from one end to the other---consistently---without messing everything else up is not probable and probably not possible.) Or should the high values make a wedge along two sides? 512 4096-2048-128 In summary, I don't think trying to solve the full state space makes sense. This game feels like two separate isolatable optimization problems---small and large numbers---plus a little bit of glue when the isolation breaks down: starting a game, fixing a stuck situation, or collapsing a series of large numbers. Have you thought about using your worst cases to find rules to make Evil 2048 even more evil? Or see how an MDP works against Evil 2048 to get the best outcome in worst case scenarios? Oh-- Great article and analysis, by the way. |