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Original post by Kylotan Quote: Original post by AngleWyrm The Witcher tried to implement defensive moves in their bar-fight mini-game. It boiled down to: 1.Click Attack 2.Hold Defend button until enemy attacks 3.Repeat Did you enjoy the mini-game? ie. The combat system in Oblivion...

I think that system would have benefited greatly from some twitch based mechanics. IE, forcing you to anticipate an attack to counter it, instead of just standing there and waiting for it. Something as simple as a half-second window would have been a huge improvement. Basically, if you pressed block less than a half second before the attack hits, it would stumble them.

Yes, maybe with a Feinting ability that performs an animation that looks like an attack, so the opponent may choose to block. The higher your Feint skill, the more convincing it looks (to AI opponents) and the quicker you recover from the move, modified by weapon weight.

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The problem is, they do go into a lot of interesting depth here, but ultimately it just yields a system with a fairly trivial optimal strategy, even if that strategy is a mixed one.

Yes, but they do say that by itself that kind of system is fairly shallow. They also go on to explain ways to improve it. For instance: By adding in situational sensitivity, in that certain situations/choices can change the relationships between the main components/moves.

In the case of the game under discussion, this could be in the form of having two different types of defences (the percentage based and the damage reduction based), or by having another Scissors/Paper/Rock relationship over the top of it (in the system described we have the Fire/Water/Earth system and then we could have a Leg Sweep/Forward Kick/Stop on top of that).

Intransitive relationships can form a good base for a system, but they can't be the whole system.

Unfortunately, my mathematical side just takes the old optimal strategy, looks at the new elements (eg. situational sensitivity, etc), and comes up with a new optimal strategy. It doesn't actually get any harder to do, just more long-winded. I've wondered in the past whether just layering on these things is sufficient. Perhaps we're too obsessed in game development with maintaining some sort of balance that we always go for these cyclic relationships, when there may be a more interesting option?

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Unfortunately, my mathematical side just takes the old optimal strategy, looks at the new elements (eg. situational sensitivity, etc), and comes up with a new optimal strategy.

But the optimal strategy changes with the situation. When the situation changes, the optimal strategy changes.

In a simple (unlayered) system, if I was to play A, you would play B. But in a layered system, If I play A, but if you had previously taken action Z which makes action C able to beat A and then take action C.

Have a look at that Gamasutra Article (here again: http://www.gamasutra.com/view/feature/1733/rock_paper_scissors__a_method_for_.php) that I linked to earlier in this thread. It talks about how Signalling, Separating the Signal from the attack (faking) and the RPS system can lead to very interesting and fun gameplay. It is well worth the read and it will answer your concerns about RPS and how to make it actually interesting without an optimal strategy.

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Original post by Edtharan Quote: Unfortunately, my mathematical side just takes the old optimal strategy, looks at the new elements (eg. situational sensitivity, etc), and comes up with a new optimal strategy. But the optimal strategy changes with the situation. When the situation changes, the optimal strategy changes.

No, you just have an optimal strategy that takes the situation into account. The strategy is essentially a mapping of all possible states to actions, and can still be trivial. Imagine turn-based RPS, as simple proof of this. Player 2 has 3 different situations he may face, but it's still simple to come up with a simple set of rules that guarantees victory.

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In a simple (unlayered) system, if I was to play A, you would play B. But in a layered system, If I play A, but if you had previously taken action Z which makes action C able to beat A and then take action C.

Unfortunately you can just reduce this down to a simple list of states in and actions out. You have a combinatorial explosion of possible antecedent states (26x26 instead of just 26) but ultimately that's just a quantitative change, not a qualitative one.

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Have a look at that Gamasutra Article (here again: http://www.gamasutra.com/view/feature/1733/rock_paper_scissors__a_method_for_.php) that I linked to earlier in this thread. It talks about how Signalling, Separating the Signal from the attack (faking) and the RPS system can lead to very interesting and fun gameplay. It is well worth the read and it will answer your concerns about RPS and how to make it actually interesting without an optimal strategy.

I've read it before (at the time of the last thread of mine which I linked) and I disagree on a game theoretic level. It relies on human inability to estimate probability, which is fine for one on one games but as the number of players increases to MMO standards it becomes possible to see just how much signalling is optimal.

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No, you just have an optimal strategy that takes the situation into account. The strategy is essentially a mapping of all possible states to actions, and can still be trivial. Imagine turn-based RPS, as simple proof of this. Player 2 has 3 different situations he may face, but it's still simple to come up with a simple set of rules that guarantees victory.

Yes, I can see that only looking at the rules in a mechanical fashion, that this is a valid conclusion. What you are forgetting is the psychological element.

If all you did was react to the situation, then there is an optimal strategy, but a skilled player will attempt to direct their opponent along a particular strategy and then take advantage of it.

Actually, why shouldn't there be an optimal strategy. An optimal strategy is how you win (I assume that there needs to be a winner at some point).

The thing with an intransitive system is that if one player plays an optimal solution, then there will be another optimal solution to beat them. So the real optimal solution will be to psychologically manipulate your opponent. Oh, but wait, that is the point that I am making...

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I've read it before (at the time of the last thread of mine which I linked) and I disagree on a game theoretic level. It relies on human inability to estimate probability

As it is designed for human vs human contest, this is a good thing, not a bad thing.

In any game of repeated intransitive encounters, where the past history of such encounters are known to players and the future decisions can be inferred from past actions (or other data like character selection), then there will always be a psychological element in these games where you try to second guess what your opponent is going to do. The player who can best read their opponent is the better player and may the better player win.

The alternative is to make a game where all options are equal and it comes down to blind luck as to who wins. Me, I'll take the one where player skill is important.

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, which is fine for one on one games but as the number of players increases to MMO standards it becomes possible to see just how much signalling is optimal.

Signalling and reading that signalling is an important skill in these kinds of combat systems. In these games, only at the top most level is sheer button mashing speed important. When you encounter players of roughly equal skill at button mashing, then there needs to enter another factor that decides the outcome.

You could make it random luck (eg have slight variations in the amount of damage dealt), but I think it is better if the winner or looser is determined by player skill.

As we are considering two equally physically skilled (or closely skilled) players, then there must be some kind of psychological edge that one player has over the other. This would be the ability to out think your opponent and read their intended actions.

Such systems as these intransitive systems cater for that. And as this is their intended outcome, I see absolutely no problem with that. What more could you ask for, something that does exactly what it is intend to do.

You might think that if all else is equal, that you could at least tie with an opponent by using a random button mashing strategy. However, the whole signalling part means that this strategy is actually quite poor. In a random button mach, you don't exploit the signalling system to outwit your opponent. Instead, because you are not faking out the signal, your more skilled opponent can wait for your signal and react to it and easily beat you.

This is why in most beat-em-up games, a skilled player will win against a random button masher. If your concerns about this system were valid, this could not occur. In an intransitive system without signalling, a random choice will at least tie with any other strategy. This is how you can tell it is an intransitive and a balanced system.

However, once you introduce the signalling, it creates a way for a good player to exceed this issue and extend the strategies from merely the mechanics into reading and bluffing against their enemy.

For instance, the mechanics of poker are set and there is optimal betting strategies based on your hand and the actions of your opponent that can be followed. But players using these methods should, at best if only the mechanics are involved, equal each other. Why then do some players, even when not using these strategies against players who do use these strategies, come out as definite winners.

How can someone using a non optimal strategy beat a player playing an optimal strategy?

Easy, psychology.

If a player is using a predictable strategy, and that strategy can be influenced or reacted to by your opponent, then that opponent can manipulate the situation and the data that they give out to beat the optimal strategy.

In short, predictable (optimal) strategies can be exploited. All things being equal (or similar enough), if psychology can have an effect, then it will be the deciding factor.

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Original post by Edtharan What you are forgetting is the psychological element. If all you did was react to the situation, then there is an optimal strategy, but a skilled player will attempt to direct their opponent along a particular strategy and then take advantage of it. Actually, why shouldn't there be an optimal strategy. An optimal strategy is how you win (I assume that there needs to be a winner at some point).

The problem is that the optimal strategy takes the psychological element into account. And it's not all that hard to do. It doesn't mean 'guaranteed to win', or 'the best strategy for any given choice the opponent makes' but 'the best strategy given that the opponent also picks the best strategy'. A lot of human game interaction revolves around one player deliberately playing worse in the hope that the opponent will follow their strategy in a way that they believe will be better but is actually worse. The answer is not to do this, and generally speaking, if you throw enough players at a problem, eventually that's exactly what they'll do. Evolutionarily stable strategies emerge. That's why Starcraft strategy sites are so specific; people have found pretty much exactly what you need to do, and significant deviation from that in the name of bluffing is a sub-optimal approach that you can only get away with in the face of an inexperienced opponent.

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there will always be a psychological element in these games where you try to second guess what your opponent is going to do. The player who can best read their opponent is the better player and may the better player win. The alternative is to make a game where all options are equal and it comes down to blind luck as to who wins. Me, I'll take the one where player skill is important.

I don't entirely agree. I believe there is another category of games (although arguably one that overlaps with both the above) where there is no attempt at bluffing and no element of luck, but where the complexity is high enough that understanding what the opponent is attempting is impractical. I consider chess to be in this category, for instance. It's this category I'm most interested in.

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How can someone using a non optimal strategy beat a player playing an optimal strategy? Easy, psychology.

That doesn't hold true, because an optimal strategy does not mean doing the same thing all the time. For example, the optimal strategy in RPS is to play each an equal number of times, completely randomly. And in poker, the archetypical psychological game, the optimal strategy would be a mixed strategy, and it is used by computerised poker bots which do very well at making money online.

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That doesn't hold true, because an optimal strategy does not mean doing the same thing all the time. For example, the optimal strategy in RPS is to play each an equal number of times, completely randomly.

This is true in a game with no signalling.

If you used a random action strategy (using each action with an equal random chance), then I could use signalling to win. I would wait until you start to move and then using the signal, I would respond with the counter and beat you.

With signalling, random is the worst strategy, not the best.

With signalling, psychology is extremely important. Faking a signal allows you to trick your opponent.

With your poker bot example this is not an example with signalling even though I used poker as an example of signalling. With the poker bots, it is not a valid counter argument because they do not provide any signalling. As poker bluffing is all about signalling and the ability to see through your opponents faked signals. Poker bots do not5 give any signals, so the use of signals, or your ability to fake a signal becomes irrelevant.

As the discussion was about how signalling can elevate this kind of gameplay beyond the mere mechanical "optimal strategy", the whole poker bot example actually supports my argument. By eliminating the whole signalling aspect from a game that relies on signalling, you end up with a game that has an optimal strategy. But if you include that signalling aspect, the game becomes so much more and looses the optimal strategy.

Lets go back to Scissors/Paper/Rock.

When you play this game you don't provide any signals. You both secretly choose what you are going to play, and then you both show your choices at the same time.

There is no signalling. Even if you played Rock last round, this is not a signal as it doesn't actually influence any future actions.

But what if before each player players their choice, you had an opportunity to ask your opponent a yes or no answer about their choice, then after hearing each other's answer you both could change your choice, but inform your opponent that you had changed your choice.

What would the optimal strategy be now? It is certainly not random that is for sure. It would be one that took into account both the question you asked you opponent, the answer they give and whether or not they decided to change their choice.

It is actually impossible to compute an optimal strategy because it is self referential. It means that any optimal strategy that is calculated then creates an optimal strategy that will beat it which the opponent can take, but then that creates an optimal strategy that you know and can take, which creates and optimal strategy that your opponent can know about and take...

This is why it is non-computable, and that no optimal strategy can exist as the existence of an optima strategy cancels its self out because of the feedback loop created by the signalling.

It is mathematically explicit, that if you use signalling, then there will be no optimal strategy if the underlying mechanics are balanced. It is exactly the same mathematics that you use to show that there is an optimal strategy in a non signalling game.

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I don't entirely agree. I believe there is another category of games (although arguably one that overlaps with both the above) where there is no attempt at bluffing and no element of luck, but where the complexity is high enough that understanding what the opponent is attempting is impractical. I consider chess to be in this category, for instance. It's this category I'm most interested in.

First you are arguing that it we shouldn't consider the limitations of the player, that we should only consider if a game has a computable optimal strategy. then you argue that because some games are so complex that a human can not compute the optimal strategy then these are in a different category.

The only reason you are considering chess as being outside this is that nobody has computed an optimal strategy for it.

Checkers/Draughts was once in this category too. But they have now computed an optimal strategy for it. Theoretically Chess has an optimal strategy to it, it is only that the computations needed to so it are so complex that we just haven't done it.

I am talking about a completely different class of mechanics. One that create a self referential paradox that makes an optimal strategy not only practically uncomputable, but theoretically as well. Chess is theoretically computable, but just not practically computable.

These mechanics that I am talking about make the game practically and theoretically uncomputable.

The problem with these assumptions is that it is treating signalling as some special psychological aspect that is orthogonal to normal game play. It is not. It is just another possible move in the game tree, and utility values can be assigned to it just as for any other move.

The poker bot issue is relevant because it shows that by ignoring sent signals you can optimise your strategy. Humans can choose to do this too. So you can't rely on signalling to add interest to your game.

"It is actually impossible to compute an optimal strategy because it is self referential." - this isn't true; mathematically you can still work it out. That is how you can work out the optimal mixed strategy for RPS even though it's completely cyclic. It is important to appreciate the difference between a mixed strategy and a pure strategy, when applied to iterative game-playing. Sometimes the mixed strategy is bland or obvious enough to be uninteresting, but that isn't the same as being incalculable.