Is it possible for a game on BGA to last forever?

[FrankJones]

There are some games in which it is possible to hand an indefinite "standoff".

For example, Earth. A game I have discussed much in the other threads regarding conceding.

If both players have 13 cards planted, whoever takes the plant action next will LOSE the tableau bonus (a 14+ point swing), which might lead both players to not plant.

In this situation, it's a "standoff", and the optimal pay for each player would be to spam whichever non-plant action is best for them. But if that exchange would still result in the players being close together, it could reach a true stalemate.

Both players would eventually fill their sprouts and growths, and if the game is still so close that it would be decided by whoever does NOT plant first, it would be a true stale met, and would be a draw, similar to stalemate in chess.

The higher rated player should bear the onus of not allowing this situation to occur, since a draw would be a good result for the opponent and a bad result for the higher rated player.

[MarkSteere]

The "solved" topic comes up every so often. Like Hex is now solved for size N boards. Oddly, it's always assumed that the game is now ruined at that size.

[Meeplelowda]

The "solved" topic comes up every so often. Like Hex is now solved for size N boards. Oddly, it's always assumed that the game is now ruined at that size.

It's only ruined if a human can memorize all optimal paths through the game tree. Otherwise it's no more ruined than checkers is even though it is (weakly) solved.

[Fuchur]

The "solved" topic comes up every so often. Like Hex is now solved for size N boards. Oddly, it's always assumed that the game is now ruined at that size.

It's only ruined if a human can memorize all optimal paths through the game tree. Otherwise it's no more ruined than checkers is even though it is (weakly) solved.

As far as i understand the problem checkers is strongly solved (for the same reason that it is weakly solved : Anywhere in the decision tree you've got only a finite number of steps to follow), besides the fact that no one knows the solution.

[Fuchur]

Hi, can you give any examples of games with incomplete rules (= not preventing this case) on this site ?
(Chess, for instance, terminates in a draw if you make 50 moves without capturing any piece (if i remember that special rule correctly))

There are lots of games whose end is triggered by a player achieving a certain number of victory points; for example Catan. In Catan, if at some point all players decide to pass every turn without doing anything to acquire VP, I believe the game could go on for an arbitrary, unlimited length of time.

By the way, I don't agree with your implication that this means Catan has "incomplete rules".

Ok, i guess i haven't choosen the right words : A game seems incomplete to me if a situation can arise where no player has any advantage in bringing the game to the end and no one is forced to do anything about it.

[Meeplelowda]

As far as i understand the problem checkers is strongly solved (for the same reason that it is weakly solved : Anywhere in the decision tree you've got only a finite number of steps to follow), besides the fact that no one knows the solution.

This paper announcing the result says that it was only weakly solved: "With this paper, we announce that checkers has been weakly solved." They go over the definitions for ultraweakly solved, weakly solved, and strongly solved, so it stands to reason they chose their words carefully. I couldn't find an update to that result, and for what it's worth, the Wikipedia article on "Solved game" categorizes checkers as weakly solved. And I checked the Talk page for that article, and given the nature of the internet, you'd better believe it would be a subject of debate if it were at all controversial whether checkers was strongly solved.

I'm actually most fascinated by ultraweakly solved games, because I find the concept of being able to prove the truth of a statement, e.g., "player 1 can always win with optimal play" without being able to define how this is achieved intriguing. It reminds of me of proofs of the existence of an infinite number of integers with certain properties, such as widely digitally delicate primes, that we possibly have only one example of.*

*Last I'd looked at this topic there were no examples. But apparently now there is possibly one example. I say "possibly" because the result is published on arXiv and one of the corrections posted in v2 was that the first announced example in v1 was wrong. But apparently it was reviewed by a referee (who pointed out the error), and I surely am not qualified to detect any other errors.

[Fuchur]

As far as i understand the problem checkers is strongly solved (for the same reason that it is weakly solved : Anywhere in the decision tree you've got only a finite number of steps to follow), besides the fact that no one knows the solution.

This paper announcing the result says that it was only weakly solved: "With this paper, we announce that checkers has been weakly solved." They go over the definitions for ultraweakly solved, weakly solved, and strongly solved, so it stands to reason they chose their words carefully. I couldn't find an update to that result, and for what it's worth, the Wikipedia article on "Solved game" categorizes checkers as weakly solved. And I checked the Talk page for that article, and given the nature of the internet, you'd better believe it would be a subject of debate if it were at all controversial whether checkers was strongly solved.

Yes, sorry, i hadn't understood the meaning of "solved" game (see https://en.wikipedia.org/wiki/Solved_game) (and i've mixed up checkers with chess)

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[teallite]

Any game that's dependant on the players actually playing the game and doesn't have a fixed number of rounds, of which there are many - Terraforming Mars for example doesn't end due to a scoring condition, but due to terraforming completion. You can pass every round and never terraform Mars. But why is a person playing a game if they're not actually going to PLAY the game? For a game to be worth playing, the rules should not have to account for if the players decide to just sit there doing nothing.

OP is not asking about some deliberate choices to make infinite turns for the sake of it. If two or more consenting players want to spent the rest of their lives infinitely skipping turns, then let them have their "fun". OP asked about situations where making any move (or making any non-repetitive move if passing is not allowed) puts every player at a guaranteed disadvantage. In other words, where the only non-losing move is not to play. And rules should account for that. Terraforming Mars accounts for that. You can pass completely for the round, but you can't skip single turns.

Let's say in some games, the rules grant players the choice to skip turn(s) voluntarily without any consequences. If at some point of the game, both players decided to skip turns indefinitely because making a move puts them at a disadvantage; and if the players both refuse to abandon the game, nor do the game rules offer a game termination condition in this scenario, can this game last forever on the BGA server? If one of the players wants to abandon the game but the other refuses, how can the player get out of the situation without losing points?

Most games don't allow such situations to occur by design. But if a game or its digital implementation on BGA is flawed then you can't get out of the situation you described without losing points.

[nik592]

Any game that's dependant on the players actually playing the game and doesn't have a fixed number of rounds, of which there are many - Terraforming Mars for example doesn't end due to a scoring condition, but due to terraforming completion. You can pass every round and never terraform Mars. But why is a person playing a game if they're not actually going to PLAY the game? For a game to be worth playing, the rules should not have to account for if the players decide to just sit there doing nothing.

OP is not asking about some deliberate choices to make infinite turns for the sake of it. If two or more consenting players want to spent the rest of their lives infinitely skipping turns, then let them have their "fun". OP asked about situations where making any move (or making any non-repetitive move if passing is not allowed) puts every player at a guaranteed disadvantage. In other words, where the only non-losing move is not to play. And rules should account for that. Terraforming Mars accounts for that. You can pass completely for the round, but you can't skip single turns.

Sometimes you may make a less than optimal move in order to progress your game (and yes, often that's because you've made one or more poor decisions leading up to that point). I've definitely looked at a board state and said, well, all of my options are pretty poor, so I'll take this one that will at least give me some resources (or something) that mean I have better options later. I've sometimes felt sure that taking said moves are going to put me at a disadvantage, but that's not always the case. I guess that means your move is not a guaranteed disadvantage?

I've also been in situations where the better choice is to pass for a round (or a turn), even if it means my opponent does the same. Admittedly, in the case of TM, it's pretty rare that you'd follow passing a round with also passing out the next round where you have refreshed resources. There is the situation that FrankJones described above in Earth, where both players are at 13 cards and the next player to plant will lose the tableau bonus. Two players could spam their other actions forever, even when those actions no longer grant any real benefit. But I would assume after a few rounds of both players essentially passing because no one wants to "take the hit", someone would eventually do something. I would definitely get to that point. But then I'm here to play games, so I'd rather be playing and looking at a potential loss than sitting in a stalemate making pointless moves. I know there are some who would rather pass forever than take a move that's going to probably mean they lose the game, but not everyone feels that way.

[FrankJones]

Any game that's dependant on the players actually playing the game and doesn't have a fixed number of rounds, of which there are many - Terraforming Mars for example doesn't end due to a scoring condition, but due to terraforming completion. You can pass every round and never terraform Mars. But why is a person playing a game if they're not actually going to PLAY the game? For a game to be worth playing, the rules should not have to account for if the players decide to just sit there doing nothing.

OP is not asking about some deliberate choices to make infinite turns for the sake of it. If two or more consenting players want to spent the rest of their lives infinitely skipping turns, then let them have their "fun". OP asked about situations where making any move (or making any non-repetitive move if passing is not allowed) puts every player at a guaranteed disadvantage. In other words, where the only non-losing move is not to play. And rules should account for that. Terraforming Mars accounts for that. You can pass completely for the round, but you can't skip single turns.

Sometimes you may make a less than optimal move in order to progress your game (and yes, often that's because you've made one or more poor decisions leading up to that point). I've definitely looked at a board state and said, well, all of my options are pretty poor, so I'll take this one that will at least give me some resources (or something) that mean I have better options later. I've sometimes felt sure that taking said moves are going to put me at a disadvantage, but that's not always the case. I guess that means your move is not a guaranteed disadvantage?

I've also been in situations where the better choice is to pass for a round (or a turn), even if it means my opponent does the same. Admittedly, in the case of TM, it's pretty rare that you'd follow passing a round with also passing out the next round where you have refreshed resources. There is the situation that FrankJones described above in Earth, where both players are at 13 cards and the next player to plant will lose the tableau bonus. Two players could spam their other actions forever, even when those actions no longer grant any real benefit. But I would assume after a few rounds of both players essentially passing because no one wants to "take the hit", someone would eventually do something. I would definitely get to that point. But then I'm here to play games, so I'd rather be playing and looking at a potential loss than sitting in a stalemate making pointless moves. I know there are some who would rather pass forever than take a move that's going to probably mean they lose the game, but not everyone feels that way.

The Terraforming Mars example (given in the post above yours) is a bit odd. It's difficult to envision a scenario where a game of Terraforming Mars reaches a standoff because neither player wants to do anything (from a strategic standpoint).

As noted, "Earth" could potentially reach a standoff situation in which each player chooses non-plant actions to avoid surrendering the tableau completion bonus (a 14-point swing). If neither player has a non-plant action that is superior enough to the other player's non-plant actions to make it possible to give up the tableau completion bonus, the game could essentially become a stalemate/draw.

Perhaps more games should have an "offer draw" button. I think only one game I play has such a button.