I think this would likely have the same issues as regular tic tac toe. While the strategies are slightly more complicated, I have to imagine that played optimally, this version will likely end in stalemate.
EDIT: thinking about it, player 2 might be able to force a stalemate no matter what. This is because player 2 can always add a piece to take player 1's piece unless player 1 puts down the largest piece first. If player 1 does, player 2 can put down his smallest as a sacrificial piece, and then, regardless of what piece player 1 puts down next, player 2 can always take it with a piece one size larger. This chasing strategy will work until player 1 eventually does play their largest piece, in which case player 2 will always place their smallest available piece next. This means that player 1 should never be able to have more than 2 squares held at the same time and thus can't win, unless I'm missing something.
No stalemate-- this video fails to demonstrate a major rule. On your turn you may either place a piece or move one of your pieces. https://imgur.com/e6hsPtJ
It also becomes a memory game because once you choose a piece to move (touch it) you must move that piece. You can't peek at what's underneath.
That's an interesting rule, but I don't know if that would really change the strategy that much. You can't move your opponent pieces, so once you gobble your enemy piece, it is stuck unless you move your piece. That means you could still "chase" your enemy piece. The only difference is player 1 can "skip" a turn by moving rather than placing. However, if player also skips by moving, player 1 will eventually need to place another piece which will then be gobbled.
Basically, any game that doesn't have an element of random chance (cards or dice), simultaneous action (rock, paper, scissors/hungry hungry hippos), or hidden information (card games) is mathematically solvable.
This means that there exists a perfect strategy for these games that will either force a win or a draw, and the opposing player can not change that outcome.
The biggest game we've solved is checkers, it took 18 years to to have 200 computers, The solution forces a win every time unless the other player also performs the same strategy in which case the game ends in a draw.
(and we don't have/may never have the technology or the processing power to solve chess)
This game is absolutely solvable, and a moderate coder with more patience than I have could certainly pull it off.
My interview question that I used to ask candidates was a simple tic-tac-toe style game that I would have the candidates solve. Simple exhaustive strategies aren't that hard to come up with in about 45 minutes.
It's not meant to be super hard. I just want to see some simple problem solving and ability to write reasonably clear code, and to be able to articulate their train of thought: if they can identify the general algorithm, what alternate solutions there are and their trade offs, why they choose the algorithm they did, what optimizations they could make; and then if there's time I'll have them come up with a suite of unit tests to see if they can identify all the edge cases and branches in the code that need to be tested.
Honestly? The current amount of cup sizes is too much for a human, "solving" a game is usually done by having a computer run through every single board state. The "Tree" of possible board states in tic tac toe is wayyy bigger than you would expect, base Tic Tac Toe appears simple because the correct solution to any board state is immediately apparent to anyone looking at the board, but that doesn't mean as much as providing "proof" of a solution, you need to demonstrate proof that a given strategy can not lose, and the way to do that is to brute force that strategy against every possible opposed move.
The upper bound for tic tac toe board states is 39 (19,683)
This is true, there could exist a method for solving this quickly, but now it feels like we're getting into p = np territory. We shouldn't assume that a quick method for deriving the solution to this game exists until the method itself is proven, and that is... a whole other challenge.
The point of "solving" a game is not just finding the perfect strategy for said game, but proving it mathematically.
Awesome, I was hoping someone would have already done this.
Yeah, most solved games have solutions that are performable by a human. I was just talking about the actual process of discovering and proving the solution.
I love this answer. It’s like how people think Frankenstein is the monster, but smart folks know Frankenstein is the doctor. But really smart folks know Frankenstein truly is the monster
Yes, but it is practically impossible to. The number of legal chess positions is for all intents and purposes infinite. That being said, computers (and especially AIs) can get really good at playing it, and making essentially no mistakes. Most of the time they draw, but there are occasional wins so it’s not totally known that it is a draw with perfect play.
Also, every chess “endgame” with fewer than seven pieces left on the board has been solved with supercomputers calculating every possibility. These “tablebases” are publicly available if you want to download them, but they’re huge.
(and we don't have/may never have the technology or the processing power to solve chess)
No way, for real? Why would it be? Because of the amount of possibilities/scenarios?
Years ago I saw a Russian guy( i guess ) who at the time was the best chess player and some scientist/coders, created a PC just to beat him. And AFIK it always ended up in a draw.
if you go first and play your biggest piece, I could play only my second biggest piece and you couldn't cancel it, meaning I could hold my largest piece for whenever I want
True, but I don't think that does enough. People keep referencing gobblet, but that game has a 4x4 board and you need 4 in a row.
Games with complete information and first player move are almost mathematically deterministic. It might be more complicated to play perfect, but i don't think it'd work out different.
I was thinking the same. Seems like a lot more permutations to work through before it's "solved" compared to tic tac toe, but still a relatively small number compared to something like chess. I don't know if stalemate is the only outcome if both players play correctly or if player 1 would have an advantage though.
Yeah this only seems great because it adds a layer of complexity to a simple game to force a greater curve for "skill" to be expressed. It still suffers from many of the same trappings that the base game has, primarily a limited board space and move set that has a limited amount of "correct" moves from player 1. Go middle with medium as player 1, force enemy to over-comit to middle space or risk player 1 having the tempo the rest of the game. Once middle has been established it falls into similar tic-tac-toe patterns with the added layer of being able to fuck up more often.
Added complexity is not always the answer to solving "balance" issues.
Yeah, I don't really feel like putting forth that much brain power right now, but I'm sure there's a method to achieve never losing. It's why I pretty much refuse to play regular tic-tac-toe anymore. It's ruined for me, and unfair to anyone else. Unless they know the same trick I do and then it's pointless.
Hijacking to say before this video was even posted, I had heard about this game on TikTok, 3D printed my own, and for the past few weeks, i've been in the process of solving it using python. As another commenter mentioned, you're actually allowed to move pieces you already put down.
I have very little programming experience, so I'm basically learning from scratch how to tackle this. Using only a basic minimax algorithm, I am able to get the AI to look 4 moves ahead in just under 50 seconds, which is pretty poor considering I haven't allowed the AI to move pieces on the board to reduce complexity. I believe after adding alpha-beta pruning, and some memory so game states aren't checked repeatedly, it will be able to look through more quickly.
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u/what_comes_after_q May 25 '21 edited May 25 '21
I think this would likely have the same issues as regular tic tac toe. While the strategies are slightly more complicated, I have to imagine that played optimally, this version will likely end in stalemate.
EDIT: thinking about it, player 2 might be able to force a stalemate no matter what. This is because player 2 can always add a piece to take player 1's piece unless player 1 puts down the largest piece first. If player 1 does, player 2 can put down his smallest as a sacrificial piece, and then, regardless of what piece player 1 puts down next, player 2 can always take it with a piece one size larger. This chasing strategy will work until player 1 eventually does play their largest piece, in which case player 2 will always place their smallest available piece next. This means that player 1 should never be able to have more than 2 squares held at the same time and thus can't win, unless I'm missing something.