I’m working on creating an AI bot for the 2048 puzzle game using the expectimax approach instead of traditional minimax. The thing is, my game tree only has maximizing nodes (player moves) and chance nodes (random tile spawns), but no minimizing opponent.
Since alpha-beta pruning usually needs both max and min players to work properly, I’m not sure if it can be used here. Is there a way to make alpha-beta pruning work with just max and chance nodes?
If alpha-beta pruning isn’t suitable for this situation, what other methods can I use to cut down on unnecessary branches and make the search more efficient? I want to avoid exploring parts of the tree that won’t help find the best move.
Any advice or suggestions would be really helpful. Thanks in advance.
Alpha-beta pruning doesn’t work with expectimax because it needs adversarial min/max nodes to create bounds. Chance nodes can’t be pruned the same way since they’re probability distributions, not worst-case scenarios. I hit this exact problem building my 2048 AI last year. Here’s what actually worked: Depth-limited search with iterative deepening to control computation, plus transposition tables to cache board states (2048 revisits similar positions constantly). Probability thresholding was huge - I’d just cut branches with super low probability. Beam search also helped by only exploring the best branches at each level. Combined, these cut my search space by 70% without hurting move quality.
You’re correct that standard alpha-beta pruning isn’t applicable here due to the absence of an adversary creating bounds. However, I have discovered effective alternatives during my experience building game AI for 2048. One method is modified expectation-based pruning, where you track running averages of subtree values and prune branches that significantly underperform compared to your best expected outcome. It’s not as efficient as traditional alpha-beta pruning, but it substantially reduces the search space. Another method is to implement progressive deepening with time limits instead of fixed depth limits. This allows you to obtain decent moves quickly while exploring deeper when time permits. Additionally, caching evaluation scores for board states is crucial since 2048 often revisits the same configurations from various move sequences, yielding considerable computational savings. Overall, while you can’t prune as aggressively as with minimax, you can still streamline the search by concentrating on key branches.
Just dealt with this exact scenario optimizing our game AI pipeline at work. Other answers are right - alpha-beta doesn’t work with expectimax.
What saved me was combining a few techniques. First, star1 pruning works specifically with chance nodes. You can cut branches where the max possible value is worse than your current best expected value.
Second was probability mass pruning. I’d calculate cumulative probability of all pruned branches and only continue if the remaining probability mass could actually affect the final decision.
The real game changer was a hybrid approach. Use expectimax for the first few levels, then switch to heuristic evaluation for deeper nodes. Gets you accuracy where it matters while keeping computation reasonable.
Monte Carlo Tree Search is perfect for this since it naturally handles 2048’s randomness.
One more tip: focus on move ordering. Put promising moves first in your search tree. Even without traditional pruning, you’ll find better solutions faster and can cut search early when you hit time limits.
Alpha-beta pruning works because one player maximizes while the other minimizes - this creates clear bounds for cutting off branches. But expectimax deals with expected values, not worst-case scenarios, so those traditional bounds don’t work. For my 2048 bot, I used a cutoff threshold based on move utility instead. I’d track the weighted average of good-looking branches and stop exploring when a subtree’s best possible outcome dropped below a certain percentage of my current best move. Branch ordering plus early termination also helped a lot. I’d evaluate moves that usually work well in 2048 first - like keeping high tiles in corners. This gives you strong baselines fast, then you can use confidence intervals to decide when more searching won’t actually change which move you pick. Transposition tables are a must since 2048 boards repeat constantly through different move sequences. This alone gave me huge speedups without needing any fancy pruning tricks.
nah alpha-beta won’t work here since expectimax calculates expected values, not min/max bounds. try monte carlo tree search instead - it handles chance nodes really well for 2048. also look into pruning low-probability branches early, saved me tons of computation time when i built mine
