Comment by IIAOPSW
8 months ago
Slightly off topic but am I the only one that approaches strategy games by making a "zeroth order approximation". Eg find the shortest path to victory under the (obviously faulty) assumption that my opponent does nothing and the board is unchanging except for my moves. Now find my opponents shortest path to victory under the same assumption. Then evaluate, if we both just ignore each other and try to bum rush the victory condition, who gets there first?
For most games, if you can see a way to an end state within 3-5 steps under these idealized conditions, there's only so much that an actual opponent can do to make the board deviate from the initial static board state that you used in your assumption. The optimal strategy will always be just a few minor corrections of edit distance from this dumb no-theory-of-mind strategy. You can always be sure that whoever has the longer path to victory has to do something to interfere with the shorter path of their opponent, and there's only ever so many pieces which can interact with that shorter path. Meaning whatever path to victory is currently shortest short circuits the search for potential moves.
On beginner level this might work, but if people are more competitive they begin to realize the benefit of not only playing the own game, but reading the enemies plan (e.g. scouting in Starcraft/AoE2) to counteract it as much as possible.
Chess against humen is different. Usually, there is no path to victory, only to remis. People just follow strategic plans that people told them would be slightly beneficial later on. Along following that strategic plan people mess up and the first one to realize that the opponent messed up usually wins. Like having a piece advantage of 2-3 is usually considered a win already.
I agree with this. My default approach to board games is basically to maximize victory points early. This usually works; when 4 people are playing a new game for the first time, I usually win. This doesn't really work when people know how to play the game specifically, though.
I think this algorithm is better than many other algorithms that people come up with, however.
(As an aside, when I play a card game I sort my cards with a merge sort instead of an insertion sort. People said you would never use these algorithms in real life, but you can if you want to!)
This comment got me thinking about how I sort my cards. I scan the whole hand, then make the biggest changes first (e.g. consolidating suits/card types), then sort the subgroups.
Huh, guess I'm doing a sort of human heuristic version of Quicksort
The interesting thing about sorting cards for a trick taking game is often standard algorithms don't directly apply, because you don't have a fixed end state. I choose the order of the suits based on how the cards are currently laid out, as long as I end up with red and black alternating.
Common advice to beginners:
"Improve the position of your worst placed piece."
For better players, determine which is most effective:
1 Improve the position of your worst placed piece.
2 Exchange or minimize the potential of your opponent's best-placed piece (e.g. trade off their bishop on a long diagonal)
3 Maximize the potential of your best-placed piece (sometimes by a sacrifice)
4 Prevent your opponent from developing some pieces
This is over-simplified, of course, but the balance of the position must be taken into account.
If you programmed this as a chess strategy, it would probably result in an engine that played the Scholar's mate every game. This is actually close to what low Elo players do in chess, but as you get closer to 800-ish ELO the probability of attempted scholar mates drop dramatically (likely due to it being an opening that isn't that good).
This is one of the canonical ways people learn chess. It's not that bad of a way to play because it emphasizes thinking about good moves, and it efficiently finds mates in N (when done by a human)
In higher level play it usually loses to opponents that are aware they're not playing alone, at least that's the case with bots that do in fact stay unaware of their opponent.
A lot of decision in chess would be like "this square would be nice for that piece, how can I get there ?" and then analyze what your opponent can do to prevent you to do that, or what counterplay that gives him. So what you are doing makes a lot of sense.
It's called the Null-move heuristic [1]. The assumption being that if a move can't win even if the opponent doesn't respond to it, then probably it is a pretty bad move. It's pretty standard in traditional chess search engine. Though I don't think AlphaZero's monte carlo search uses it.
[1]: https://en.wikipedia.org/wiki/Null-move_heuristic
This would never work in chess because there is almost always a checkmate in a few moves under the assumption that the opponent doesn't defend it. So this engine would just play way too aggressively and over-extent their pieces.
Take scholars mate for example. You can win in 4 moves from the initial position and it is an easy win if the opponent doesn't defend it but playing against someone that knows chess it is a horrible opening because it is easy to defend and leaves you in a weak position.
That's why white has a higher statistical win rate ya?
Only if you play on the Tengen point.
Can't you almost always win the game in a few moves if you plan for your opponent to make really stupid responses?
Ehh idk. Sounds like it’s prone to the beginner strategy of assuming your opponent will occasionally do something really dumb.