Optimal strategy involves bluffing a certain percentage of the time, and assuming that other players are bluffing a certain percentage of the time, irrespective of the behavior of those other players.
This is no more useful than saying "the optimal strategy for Settlers of Catan involves making the correct move in any given situation".
In all likelihood, the optimal strategy for Coup involves bluffing with different frequencies in different situations. Moreover, bluffing is not simply binary, because there are more than two actions in any one situation.
Optimal strategy involves bluffing a certain percentage of the time, and assuming that other players are bluffing a certain percentage of the time, irrespective of the behavior of those other players.
This is no more useful than saying "the optimal strategy for Settlers of Catan involves making the correct move in any given situation".
I have a similarly dim view of Settlers. It is a trivial game once you understand it. I personally have no desire to ever play it again except as a teaching exercise.
In all likelihood, the optimal strategy for Coup involves bluffing with different frequencies in different situations. Moreover, bluffing is not simply binary, because there are more than two actions in any one situation.
Typically, one or more of the possible actions are excluded as being objectively non-optimal, or else excluded except a small percentage of the time.
Optimal strategy involves bluffing a certain percentage of the time, and assuming that other players are bluffing a certain percentage of the time, irrespective of the behavior of those other players.
This is no more useful than saying "the optimal strategy for Settlers of Catan involves making the correct move in any given situation".
I have a similarly dim view of Settlers. It is a trivial game once you understand it. I personally have no desire to ever play it again except as a teaching exercise.
I bring up Settlers because any game is trivial once you know the optimal strategy.
The fact that an "optimal" (let's say Nash equilibrium) strategy for Coup exists and is quite likely to be a mixed strategy is really rather obvious, and quite trivial.
However, knowing that such a strategy exists is hardly the same thing as actually knowing what that strategy is.
In all likelihood, the optimal strategy for Coup involves bluffing with different frequencies in different situations. Moreover, bluffing is not simply binary, because there are more than two actions in any one situation.
Typically, one or more of the possible actions are excluded as being objectively non-optimal, or else excluded except a small percentage of the time.
It's not that you exclude single actions as being "objectively non-optimal" - if the best strategy is mixed, it's the probability distribution that is optimal rather than any single action.
Moreover, actions that would be trivially and obviously bad if played on their own can in fact be very useful when played as part of a mixed strategy. The reason is that by including the possibility of playing those actions you hide information; in short, incorporating the possibility of bad actions makes your good actions stronger. Besides that, sometimes small percentage chances can actually make a big difference.
Of course, there is a further complication, and that is that Nash equilibrium play is not really "optimal" in an overall sense, because in general the assumptions don't hold. If you know that other players can and will make mistakes, then it may often be a good idea to deviate from equilibrium play in order to exploit those mistakes.
The challenges it poses in the solving, the largely random nature of victory among skilled players, and the skills necessary to play effectively and reach that level of skill, are to me uninteresting. I have no desire to get beyond the point of "I know how I would go about solving this game, and I know what the game will be like among players who have all largely solved it." The game provides nothing, to me, that other games don't provide better.
Settlers was a great game before I analyzed it. Now it's a terrible game. I have recognized similar patterns in new games, but the mere act of solving Settlers in the first place was enjoyable. I enjoy solving that kind of game, but have zero desire to fully solve a mostly-luck mafia-esque bluffing game: they're practically their own genre at this point.
If there are many games in a shared "genre," I tend to see the most enhanced/complex/good, and separately, the most distilled, and ignore all others in the spectrum.
That I can understand, but it's clearly a matter of personal preference. Personally, I have a significant interest in games with hidden information (I am, in fact, currently doing a Master's thesis on the topic).
The presence of hidden information makes games much, much harder to analyse, both for computers and for humans; "solving" a game of imperfect information is vastly more difficult. For example, take phantom tic-tac-toe, an imperfect-information version of tic-tac-toe. Although nearly-optimal strategies are known, phantom tic-tac-toe remains unsolved in the strict sense (AFAIK).
That being said, although such games can be very interesting, I think I understand the root of your issue. Hidden information and randomness each introduce quite a lot of variance in the outcomes of the game. Mathematically speaking, that variance is essentially perpendicular to the core problem of solving the game. However, what it does do is weaken the feedback mechanisms you have available to evaluate how good you are.
Hidden information makes this problem even worse, because the optimal move for such a game is not a function of a singular game state, but a probability distribution over possible game states. This makes it far, far more difficult to evaluate the quality of your strategy in the context of only a single game, which in turn vastly diminishes your ability to solve the game simply by playing it. The end result is that, in some ways, thinking about the game becomes more interesting than playing it.
The challenges it poses in the solving, the largely random nature of victory among skilled players, and the skills necessary to play effectively and reach that level of skill, are to me uninteresting. I have no desire to get beyond the point of "I know how I would go about solving this game, and I know what the game will be like among players who have all largely solved it." The game provides nothing, to me, that other games don't provide better.
How would you go about solving the game, then?
Also, I'm not sure I agree with your concept of "what the game will be like among players who have all largely solved it". It is trivially true that games of that nature will have a lot of randomness in outcomes (typically regardless of the quality of the players), but simply knowing that randomness will be present is not very meaningful. The interesting question there is what the non-random components of the outcome (or, if you like, the long-term average) will be like, and actually knowing the nature of the strategies you need to get better outcomes - such strategies can, in fact, be very interesting.
Even in Mafia, which you've put forth as a prototypical, distilled example of this type of game, the underlying strategy (i.e. setting psychology aside) is surprisingly non-trivial once power roles are involved.
That could be fake. I don't think it's possible to be smart enough to play Eclipse while simultaneously not being smart enough to spell the word "tournament."
That could be fake. I don't think it's possible to be smart enough to play Eclipse while simultaneously not being smart enough to spell the word "tournament."
Could be true but you need to remember there kids that could fit in this demographic. Example would be a 7 year old who frequently games with dad I see at a game store and can hold his own in Catan and Modern Art.
That could be fake. I don't think it's possible to be smart enough to play Eclipse while simultaneously not being smart enough to spell the word "tournament."
There's a difference between "smart" and "educated".
I play Eclipse and probably misspell Tournament given a chance. There are multiple reasons why someone could have a spelling deficiency and still be smart.
If I wanted to? I'd start with a large number of playthroughs with multiple different sets of people and track win statistics. (Just who, nothing about how). I would play until I win a statistically significant percentage of the time against inexperienced players.
If I am able to win reliably against inexperienced players, then I have proven that the game involves skills, and that I have gained proficiency in at least one of them.
I would then play only against experienced players. If any one player wins statistically significantly more often than the other experienced players, I know that there is still a skill component over which that player has higher mastery. (It doesn't have to be me).
Eventually, one of the following will happen.
1. I win more often than everyone else
I now know that, to the limits of the possible player input into the game, I have mastered it relative to the general player pool, and that my relative mastery overcomes randomness. Barring a general up-stepping in game among the total player pool (e.h., SSF tournament play), I have nothing more of interest to learn about the game. I may keep playing it to prove my mastery, but even them I am really only hoping for someone to crush me and prove that I was wrong.
2. I continue to lose more often than everyone else
I now know that there is a skill component which I lack. I have objectively inferior strategies, and have more to learn from the game.
3. All experienced players win about the same percentage of the time
For the current player pool, randomness now trumps any player input. There are few ways forward. I could seek an ignored degenerate strategy (e.g., snaking), though this is unlikely to exist. I could seek a wider or more skilled player pool (in case my sample pool had a local equilibrium).
When 3 occurs, I usually stop playing a game. I'll use the game as a teaching tool at best. Or, I'll occasionally play it with random people to confirm that nothing has emerged since the last time I played. The game is now boring and pointless unless someone proves me wrong and beats me a statistically significant percentage of the time.
The only variable is what skills are tested in all of the above. If they are skills I wish to improve, or that I otherwise find interesting, I'll happily play a game to one of these conclusions. I was willing to master extremely far-order strategies in Advance Wars due to my intense interest in the game's mechanics and tested skills.
But, say, Settlers. The only things I could improve to fight against randomness would be dice manipulation or analysis of the specific dice used hoping for exploitable bias. Neither skill is interesting to me, so I will never bother.
Some games, like Twilight Struggle, despite ending at #2 above (me losing reliably), I still have no desire to play. To achieve local mastery, the "skill" I would need to foster the most is memorization of all the cards in the game, as well as counting cards and tracking odds of a given card coming up during a particular phase of the game. I knowwhat to do, but as I've already done that for some other game, I have no interest in doing it again just for this specific game.
I know WHAT to do in RTSs. I have no desier to become GOOD at doing it.
Also, I'm not sure I agree with your concept of "what the game will be like among players who have all largely solved it". It is trivially true that games of that nature will have a lot of randomness in outcomes (typically regardless of the quality of the players), but simply knowing that randomness will be present is not very meaningful. The interesting question there is what the non-random components of the outcome (or, if you like, the long-term average) will be like, and actually knowing the nature of the strategies you need to get better outcomes - such strategies can, in fact, be very interesting.
Yes. However, in most bluffing games, the degree of randomness far exceeds my interest in the paltry strategems that remain for players.
Even in Mafia, which you've put forth as a prototypical, distilled example of this type of game, the underlying strategy (i.e. setting psychology aside) is surprisingly non-trivial once power roles are involved.
Mafia isn't a good game. I don't particularly enjoy it from an analytic perspective anymore.
I didn't say the prototypical/distilled versions of these games are the best of these games. I seek them only so that I can explore the FINAL, CORE mechanic of these games fully. Playing Mafia is like targeted weightlifing: I'm exercising one specific muscle group.
I seek the most distilled example AND the "best" or "most fun" example. Basically, what is the core, and what larger games use that core in interesting ways within themselves?
Mafia is a good social game. It's a good party game. Adding special roles or alternative goals ruins that aspect. The game requires mastery at that point to be fun. It becomes less accessible, less social.
Mafia's beauty is that the rules are so simple that you can teach a large group of drunk strangers to play it in less than five minutes. AND, you can usually convince them to ACTUALLY PLAY. Add any roles beyond a very tiny set, and the game is already deep into cruft waters.
Now, games that are primarily random in mid-level play and up, I have no interest in anymore. If I can win a statistically significant percentage of the time (with effort and mastery), but that percentage is 2%, fuck that game. For normal numbers of plays (e.g., playing the game five times at a convention), the game is basically just random.
Fuck that noise. A game's endstate has to be interesting in the short term among a reasonable number of plays.
If I wanted to? I'd start with a large number of playthroughs with multiple different sets of people and track win statistics. (Just who, nothing about how). I would play until I win a statistically significant percentage of the time against inexperienced players.
As you've admitted, that applies rather trivially to any game at all. I was hoping for something specific...
Really, I should take issue far more with Scott, since he made a far stronger claim:
I guess there might be at least a few people on earth who are not smart enough to figure out that entire game in one play through.
In any case, Rym, I quite agree with you that there is a significant element of personal preference with respect to which skills you are interested in perfecting, and if that's your main criticism of a game there isn't really anything I can argue with there.
That being said, I think that although you can easily dismiss a game by simply saying you're not interested in the particular skills being tested, there is still reason for you to actually discuss the game in specific terms. For one thing, it's possible you may actually have the wrong picture as to what skills are being tested, or the degree to which they are tested.
Yes. However, in most bluffing games, the degree of randomness far exceeds my interest in the paltry strategems that remain for players.
Your choice to call them "paltry" is a matter of personal preference. The degree of randomness doesn't mean the strategies cannot be superior to the strategies other people are using, and it doesn't mean they can't be interesting or complex, or require genuine ingenuity to devise.
Even in Mafia, which you've put forth as a prototypical, distilled example of this type of game, the underlying strategy (i.e. setting psychology aside) is surprisingly non-trivial once power roles are involved.
Mafia isn't a good game. I don't particularly enjoy it from an analytic perspective anymore.
I didn't say the prototypical/distilled versions of these games are the best of these games. I seek them only so that I can explore the FINAL, CORE mechanic of these games fully. Playing Mafia is like targeted weightlifing: I'm exercising one specific muscle group.
If you note my terminology, I implied the exact opposite of what you seem to think I did - I said that *even* in Mafia the strategy is *surprisingly* non-trivial.
I seek the most distilled example AND the "best" or "most fun" example. Basically, what is the core, and what larger games use that core in interesting ways within themselves?
Mafia is a good social game. It's a good party game. Adding special roles or alternative goals ruins that aspect. The game requires mastery at that point to be fun. It becomes less accessible, less social.
Mafia's beauty is that the rules are so simple that you can teach a large group of drunk strangers to play it in less than five minutes. AND, you can usually convince them to ACTUALLY PLAY. Add any roles beyond a very tiny set, and the game is already deep into cruft waters.
Now, games that are primarily random in mid-level play and up, I have no interest in anymore. If I can win a statistically significant percentage of the time (with effort and mastery), but that percentage is 2%, fuck that game. For normal numbers of plays (e.g., playing the game five times at a convention), the game is basically just random.
Fuck that noise. A game's endstate has to be interesting in the short term among a reasonable number of plays.
Comments
In all likelihood, the optimal strategy for Coup involves bluffing with different frequencies in different situations. Moreover, bluffing is not simply binary, because there are more than two actions in any one situation.
The fact that an "optimal" (let's say Nash equilibrium) strategy for Coup exists and is quite likely to be a mixed strategy is really rather obvious, and quite trivial.
However, knowing that such a strategy exists is hardly the same thing as actually knowing what that strategy is. It's not that you exclude single actions as being "objectively non-optimal" - if the best strategy is mixed, it's the probability distribution that is optimal rather than any single action.
Moreover, actions that would be trivially and obviously bad if played on their own can in fact be very useful when played as part of a mixed strategy. The reason is that by including the possibility of playing those actions you hide information; in short, incorporating the possibility of bad actions makes your good actions stronger. Besides that, sometimes small percentage chances can actually make a big difference.
Of course, there is a further complication, and that is that Nash equilibrium play is not really "optimal" in an overall sense, because in general the assumptions don't hold. If you know that other players can and will make mistakes, then it may often be a good idea to deviate from equilibrium play in order to exploit those mistakes.
The challenges it poses in the solving, the largely random nature of victory among skilled players, and the skills necessary to play effectively and reach that level of skill, are to me uninteresting. I have no desire to get beyond the point of "I know how I would go about solving this game, and I know what the game will be like among players who have all largely solved it." The game provides nothing, to me, that other games don't provide better.
Settlers was a great game before I analyzed it. Now it's a terrible game. I have recognized similar patterns in new games, but the mere act of solving Settlers in the first place was enjoyable. I enjoy solving that kind of game, but have zero desire to fully solve a mostly-luck mafia-esque bluffing game: they're practically their own genre at this point.
If there are many games in a shared "genre," I tend to see the most enhanced/complex/good, and separately, the most distilled, and ignore all others in the spectrum.
The presence of hidden information makes games much, much harder to analyse, both for computers and for humans; "solving" a game of imperfect information is vastly more difficult. For example, take phantom tic-tac-toe, an imperfect-information version of tic-tac-toe. Although nearly-optimal strategies are known, phantom tic-tac-toe remains unsolved in the strict sense (AFAIK).
That being said, although such games can be very interesting, I think I understand the root of your issue. Hidden information and randomness each introduce quite a lot of variance in the outcomes of the game. Mathematically speaking, that variance is essentially perpendicular to the core problem of solving the game. However, what it does do is weaken the feedback mechanisms you have available to evaluate how good you are.
Hidden information makes this problem even worse, because the optimal move for such a game is not a function of a singular game state, but a probability distribution over possible game states. This makes it far, far more difficult to evaluate the quality of your strategy in the context of only a single game, which in turn vastly diminishes your ability to solve the game simply by playing it. The end result is that, in some ways, thinking about the game becomes more interesting than playing it.
Also, I'm not sure I agree with your concept of "what the game will be like among players who have all largely solved it". It is trivially true that games of that nature will have a lot of randomness in outcomes (typically regardless of the quality of the players), but simply knowing that randomness will be present is not very meaningful. The interesting question there is what the non-random components of the outcome (or, if you like, the long-term average) will be like, and actually knowing the nature of the strategies you need to get better outcomes - such strategies can, in fact, be very interesting.
Even in Mafia, which you've put forth as a prototypical, distilled example of this type of game, the underlying strategy (i.e. setting psychology aside) is surprisingly non-trivial once power roles are involved.
https://plus.google.com/117169641341602591955/posts/FCEGj3rFBCo
If I am able to win reliably against inexperienced players, then I have proven that the game involves skills, and that I have gained proficiency in at least one of them.
I would then play only against experienced players. If any one player wins statistically significantly more often than the other experienced players, I know that there is still a skill component over which that player has higher mastery. (It doesn't have to be me).
Eventually, one of the following will happen.
1. I win more often than everyone else
I now know that, to the limits of the possible player input into the game, I have mastered it relative to the general player pool, and that my relative mastery overcomes randomness. Barring a general up-stepping in game among the total player pool (e.h., SSF tournament play), I have nothing more of interest to learn about the game. I may keep playing it to prove my mastery, but even them I am really only hoping for someone to crush me and prove that I was wrong.
2. I continue to lose more often than everyone else
I now know that there is a skill component which I lack. I have objectively inferior strategies, and have more to learn from the game.
3. All experienced players win about the same percentage of the time
For the current player pool, randomness now trumps any player input. There are few ways forward. I could seek an ignored degenerate strategy (e.g., snaking), though this is unlikely to exist. I could seek a wider or more skilled player pool (in case my sample pool had a local equilibrium).
When 3 occurs, I usually stop playing a game. I'll use the game as a teaching tool at best. Or, I'll occasionally play it with random people to confirm that nothing has emerged since the last time I played. The game is now boring and pointless unless someone proves me wrong and beats me a statistically significant percentage of the time.
The only variable is what skills are tested in all of the above. If they are skills I wish to improve, or that I otherwise find interesting, I'll happily play a game to one of these conclusions. I was willing to master extremely far-order strategies in Advance Wars due to my intense interest in the game's mechanics and tested skills.
But, say, Settlers. The only things I could improve to fight against randomness would be dice manipulation or analysis of the specific dice used hoping for exploitable bias. Neither skill is interesting to me, so I will never bother.
Some games, like Twilight Struggle, despite ending at #2 above (me losing reliably), I still have no desire to play. To achieve local mastery, the "skill" I would need to foster the most is memorization of all the cards in the game, as well as counting cards and tracking odds of a given card coming up during a particular phase of the game. I knowwhat to do, but as I've already done that for some other game, I have no interest in doing it again just for this specific game.
I know WHAT to do in RTSs. I have no desier to become GOOD at doing it.
Yes. However, in most bluffing games, the degree of randomness far exceeds my interest in the paltry strategems that remain for players. Mafia isn't a good game. I don't particularly enjoy it from an analytic perspective anymore.
I didn't say the prototypical/distilled versions of these games are the best of these games. I seek them only so that I can explore the FINAL, CORE mechanic of these games fully. Playing Mafia is like targeted weightlifing: I'm exercising one specific muscle group.
I seek the most distilled example AND the "best" or "most fun" example. Basically, what is the core, and what larger games use that core in interesting ways within themselves?
Mafia is a good social game. It's a good party game. Adding special roles or alternative goals ruins that aspect. The game requires mastery at that point to be fun. It becomes less accessible, less social.
Mafia's beauty is that the rules are so simple that you can teach a large group of drunk strangers to play it in less than five minutes. AND, you can usually convince them to ACTUALLY PLAY. Add any roles beyond a very tiny set, and the game is already deep into cruft waters.
I prefer, AT MOST:
1. Angel
2. Archangel
3. Masons
4. Mafia
5. Psycho Killer
Again, at MOST.
I also don't play Mafia except in intensely social situations.
Fuck that noise. A game's endstate has to be interesting in the short term among a reasonable number of plays.
Really, I should take issue far more with Scott, since he made a far stronger claim: In any case, Rym, I quite agree with you that there is a significant element of personal preference with respect to which skills you are interested in perfecting, and if that's your main criticism of a game there isn't really anything I can argue with there.
That being said, I think that although you can easily dismiss a game by simply saying you're not interested in the particular skills being tested, there is still reason for you to actually discuss the game in specific terms. For one thing, it's possible you may actually have the wrong picture as to what skills are being tested, or the degree to which they are tested. Your choice to call them "paltry" is a matter of personal preference. The degree of randomness doesn't mean the strategies cannot be superior to the strategies other people are using, and it doesn't mean they can't be interesting or complex, or require genuine ingenuity to devise. If you note my terminology, I implied the exact opposite of what you seem to think I did - I said that *even* in Mafia the strategy is *surprisingly* non-trivial. Let me clarify: I mean that merely having any power roles at all makes the strategy nontrivial.
Cost me $47 after shipping, FINALLY have this board. Now about those red jungle speed cards...
Now it appears that the rules are set up soaybe I could just get this by itself, please?