For and against binary goals in strategy games (and against high score)

#21
While no such game exists, I can imagine a game where none of the shorter arcs are directly tied to success at the match length arc. In such a game a player can and should 'lose every battle' in order to 'win the war' so to speak. That is make sub-optimal choices in terms of tactics, and short to mid term strategy, because although worse now, those choices lead to their victory at the longest term goal. For this type of game (and no other), I think giving the player a reward for any of the short and medium arcs, will subvert the strategy of the game, shifting it away from the longest arc, which should be the games only focus.

I think that broadly this is the type of game Keith now advocates for. And I hope he and other pursue it. But I think that the vast majority of potential strategy games do not fall into their narrow category, and for those, other goals will be better. (And I have lots of new ideas on this topic maybe we can talk about if we ever resolve this very long running conversation). I think understanding game and goal design as I started to lay out in my first post in this thread, in terms of the quality and length of arcs and how they are incentivised is probably necessary for both of these things.
 
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#22
Imo, one notable quality of par systems is that can cause a state where the player would rather play more conservatively in order to lose small, if there's a ~5% chance of winning vs a ~95% chance of losing big. And as Keith suggests, it could create temptation for a player to select strategy/tactics that let them win big, rather than safer plays with a stronger chance of winning small.

Using Starcraft as an example, it certainly isn't bad to overwhelming crush your opponent. But when players are rewarded for how decisively they won, it creates the unique conditions above (imo, not inherently good or bad).

I don't see this as something to be avoided inherently. To my own sensibilities, this seems less suited to long (15+ hour) scenarios (like Civilization), and more suited to shorter scenarios (a level/round in a game). In tournament play, it could result in games that are less exciting to watch, if a player decides to resign early to prevent a larger loss if they try to play out a risky game state.
I think that par system and similar scoring systems only make sense for single player games. Since we do not wish to punish the losing player unduly.
I'm not sure I follow the argument you (and previously) keith make about percentages. As Hopenager explained players should choose the strategy which gives them the highest Expected Value.

Your suggested score system for 4x sounds interesting, I'll have to think about it more.
 
#23
While no such game exists, I can imagine a game where none of the shorter arcs are directly tied to success at the match length arc. In such a game a player can and should 'lose every battle' in order to 'win the war' so to speak. That is make sub-optimal choices in terms of tactics, and short to mid term strategy, because although worse now, those choices lead to their victory at the longest term goal. For this type of game (and no other), I think giving the player a reward for any of the short and medium arcs, will subvert the strategy of the game, shifting it away from the longest arc, which should be the games only focus.
If this is ever the case, it simply means you have your "win" and "loss" labels inverted at the tactical level. The output of a tactic isn't win/lose, so much as some specific results that are beneficial or not to the overall strategy.
 
#24
Yes, thats why i used the term sub optimal. To indicate that the player isnt making the worst tactical choices, just not the best tactical choices.
 
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#25
That is make sub-optimal choices in terms of tactics, and short to mid term strategy, because although worse now, those choices lead to their victory at the longest term goal. For this type of game (and no other), I think giving the player a reward for any of the short and medium arcs, will subvert the strategy of the game, shifting it away from the longest arc, which should be the games only focus.
This is not the way I think of score systems. For the record, I am in favor of the same type of game Keith is, where performance is measured primarily on the longest arc, and I think we should use score systems for those types of games too.

It sounds like you are saying that in a score game, the score should essentially be a tally of their successes/failures on the medium/short arcs, but since in a game with a focus on the match-length arc we only care about the success/failure on that arc, so we shouldn't take into account the lower arcs and should just give a win/loss for the longest. Is that correct? Let me know if I'm misinterpreting you.

If that's your argument, I think that you are actually kinda making the same mistake that Keith is: you are assuming that the outcome of a plan for an arc must be measured as a "success" or a "failure". Success/failure is not inherent to a plan. A plan (strategic or tactical) does not inherently "fail" or "succeed", plans merely have outcomes, and success/failure are measurements imposed on those outcomes. But they are NOT the only type of measurement, and I have seen no good argument that they are the best type. My view is not that we should be tallying binary measurements of mid-length arcs to get score, but instead score should be a scalar measurement of performance the longest arc.

As an example, consider again the problem of digging a ditch 100 feet long. Say I come up with a plan to do that, and execute it, and end up with a ditch 101 feet long. Did I succeed for fail? You might be tempted to say that I failed because I didn't get exactly 100 feet, but under that criteria any possible outcome would have been a failure, since it's never going to be exactly 100 feet, at best it'll be 100.001 feet or something. So, one might say, we could define success/failure like so "You are successful if you are within 1 foot of 100 (so between 99 feet and 101)".

The very fact that we can think about different definitions of success/failure means that success/failure isn't inherent to the outcome. Success/failure is a measurement from the outside, and we could just as easily provide a different measurement, e.g. a score based on the absolute value of the difference between your outcome and 100 feet. The idea that you (and Keith) seem to have, that the outcome of a plan must always be thought of as a win/loss, is mistaken.
 
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#26
Thanks to some discussion on the discord where some of us were able to reach a shared understanding, I think this is a good opportunity to step back and re-frame things. I'm going to talk about the relationship between arc, goals, and types of scoring.

First lets define an old and a new term:
Binary win/loss: When a game gives the player a single point for successfully completing the longest arc in a game.
Accrued points: When a game gives the player points each time they complete a small and/or medium arc in a game.


Now lets talk specifically about strategy games which focus almost exclusively on a single long (match length) arc.
Since such a game focuses so heavily on its long arc, the shorter arcs in the game, may provide little to no information about the long arc, and may even provide contradictory information. For example, success at a short tactical arc may actually predict failure at the long arc. Because of this generating a score based upon any but the longest arc in such a game will harm the games design. It will provide incentives to the player that contradict the focus of the game the single long arc.

Therefore such a game should NOT use accrued points. Binary win/loss in such a case is superior to accrued points.

Now lets introduce a new term:
Post-hoc points: These points are awarded on completion of an arc, based upon the remaining resources the player has left over.

So as an example a upon completion of a match a player may get extra points based on having leftover time, troops, or other resources that were not used. Now keep in mind these bonus points are contingent upon the players success at the long arc. I think of these as rewards for efficient completion of an arc (efficiency points).

The relevance of these points to the players feedback is fundamentally different based on whether they won or lost. And so, we shouldn’t award points the same way for a win or a loss. Instead determine which resource indicate efficiency and which measure progress towards success and value them accordingly. Also note that winning should be worth a lot more points than these efficiencies.

Okay now lets discuss whether such a game should use binary win/loss or Post-hoc points.

It seems clear to me that if it is possible in the game you're designing to implement post-hoc points, then doing so will drastically increase the information available to your players about how to succeed and how to improve further (in preparation for high ranks/difficulty). So think about what resources the player needs to succeed and whether using fewer of those resources represents greater player skill (which will be further reflected at high ranks where such efficiency is necessary to succeed.)

Now I expect some disagreement on that last point so feel free to stop reading there and respond to the issue of binary win/loss vs post-hoc points.

For the rest of us, lets read the next post and see where else this way of thinking takes us.
 
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#27
Now you've probably already noticed that goals and points are linked to arcs, your short term goals are to complete the short term arcs well, your medium term goals are to complete the medium term arcs well, and most importantly your long term goal are to complete the longest arc as successfully as possible.

So arcs have implicit goals, but the goals of multiple arcs of different lengths may coincide or may conflict. In most modern strategy games success in the short and medium arcs of games actually tells you a lot about success at the longest arc. So for the moment lets ignore the most extreme strategy games that focus single-mindedly on their longest arc, and talk about their much more numerous brethren.

Now lets think about designing a scoring system that encourages players to improve on the path towards their final goal, the end of the match. The first thing to notice is that points should be linked to goals, upon completing a goal, whether short term or long term we can award the player with a point (we could even reward them with some post-hoc points). And if points are linked to goals that means they're linked to arcs, so lets talk about awarding points based on the outcome of specific arcs in a game.

Now, for strategy games to figure out how many points to award for a specific arc we need to now how much the success at that arc will transfer over to success at the longest arc. If these arcs are highly correlated, we should give a large amount of points than if they are poorly correlated. We should also give more points to arcs that occur less frequently (i.e. that are longer). As a starting point maybe [ correlation * 1 / expected repeats]. So our shortest least important arcs will be worth the least and our longest more important arcs will be worth the most. But, there's a couple of important points to consider before you lock in your scoring system.

a) Points incentivise player behavour
b) scoring elegance is: the amount of information your final score imparts divided by the number of ways of scoring points.

Each way of scoring you add to your game give the player one more thing they should try and remember. And its probably not even a very interesting thing. So really make sure to pick the 100% super cool things you want players to focus on as the things that give score.

Speaking of which anything you make worth points in your game will fundamentally warp player behaviour. We compensated for this a bit using our correlation value, but even still you want to be really sure the arc you making worth points is something you want the player to be thinking about all the time.

So make sure to trim the list of points right down so its just the most important most interesting stuff you want your players to think about. From this I think we can conclude that reward the most basic actions in the game is a waste of everyone's energy. Then we've got our short arcs, the tactics, maybe there's a couple of these we want to reward, but more likely we only want to reward them if they contribute to a medium arc, so medium arcs are probably the most likely place the find good targets for accrued points, things like growing a and harvesting a berry, dunking a group of monsters in a short time, or singing to a group of mana-mad creatures to calm them down.

The result of this is we end up with a fairly strategic game, but one that isn't purely strategic. So think about your game, think about what you want its purpose to be and decide how to want to scoring system to work.

The exception to prove the rule: Okay so you've got this cool strategy game but you really want it to be about some specific interaction. So it's a game about winning, but maybe you want to also be about coordinating with your friend , or hugging cute animals, or helping old ladies across the street. Whatever it is, you can use the super power of giving it points to make it important, heck you could even build your whole game around that thing as the core way of scoring points then build out a long arc to constrain it and force players to be strategic.

Check back in soon as I've got some more ideas that I'll add to the bottom here.
 
#28
Still following this with high interest, but at this point I don't think I can really contribute in the terms being used. Incentivising, rewarding players etc. for going down gameplay paths we want them to, hmm. Disagreements of how best to do that seem to be disagreements directly about the nature of what players might find fun, and hence probably quite subjective.

So just to inject another spicy angle to this thread, it occurred to me that when there's a goal-type goal ('do X thing to win') the ending moment of a match comes directly from player agency. The X thing is done, and the game ends then, with the player who did it as the winner. With a highscore game or par system as discussed here, there is no such moment, and the end comes because of the operation of some mechanic imposed by the game which determines the longest arc. You keep scoring points as hard and as long as you can, but at some point the mechanics can't be resisted further.

I haven't really thought through the implications of this so I don't know if it's 100% or even 1% relevant here! But it does seem a clear difference. The nature of gameplay might be expected to lean towards more 'active' or 'reactive' kinds of thought processes, and so that might recommend one or other system for any given game, in addition to the other things being suggested above about incentives. I'm not sure I see any reason why either kind of gameplay should be less 'strategic' than the other, although maybe that'd come down to definitions of the word.
 

keithburgun

Administrator
Staff member
#29
Batlad's stuff here is great! If I had more time I would dive into some of the details of it - maybe I can later.

For now, here is another angle. Gonna get much less technical and much more just, player-perspective for a second: Doesn't it just *feel* completely different to play a win/loss thing than it does a score-based thing? When I am playing a win/loss thing, I feel a constant pressure to try and achieve that goal. With a score-based thing I feel more like I'm playing WITH the thing. I don't really feel pressure to do anything in particular. I mean I know "this is a game where I do X", but it's not remotely the same kind of "you NEED to do X really good or else you lose!" kind of thing.

So this is why it's weird to me that there is a discussion of one of these things being "better" than the other. They're qualitatively different. I think they're both good, for different purposes. For a strategy game, I think you should want that feeling (again this isn't my only reasoning!) of tension toward a specific final outcome. For a toy, you should want that feeling of just getting some kind of quantity of how much you explored/did after you're done playing with it.
 
#30
@Batlad
I think that the general process you are describing, of taking a binary game and changing it to use a score system, is a lost cause. Changing something as fundamental as the way performance is measured, in a tight strategy game, will cause tons of problems. So many problems that the effort required to solve all of them probably won't be much less than the effort required to just make a new, equally deep, game. The performance evalutaion needs to be decided very early in the process of designing a game, since it's so fundamental. You shouldn't have a detailed idea of how the game should be played before you have the score system and then construct a score system to match that idea, instead the score mechanism should be a very basic feature of the system (e.g. "collecting one berry gives you one point") and the way that the game is played should arise, naturally, out of it.

Also, I don't think that we need to have multiple mechanisms at different arc levels that explicitly provide points. A high-level arc doesn't need be rewarded directly with points in order for it to be important to the process of gaining points. More generally, an event can be important for gaining points, even if the event itself doesn't provide points, by helping you gain more points in the future than you otherwise could have (In other words, an event can raise EV(score at the end of the match) without just directly raising the current score). So we don't need a special mechanism to reward long arcs, long arcs can just be rewarded by the way they influence the process of getting points in the shorter arcs. For a concrete example, consider BBB: One long-arc thing you will want to do is "cover most of the map with green tiles". But the reason that you will want to do it is not that you are rewarded with some number of points if you do it, but just because it gives you more opportunities to collect berries in the future.
 

keithburgun

Administrator
Staff member
#31
I feel like all these ideas are coming from the fact that Auro, the world's first single player Elo system, wasn't perfect. Like that it took sometimes too many games to level you up, or if it leveled you up it got a bit too hard and then you'd be pushed back down. I didn't have time to solve them, but these are solvable problems and I will show that in ETO, and probably Jelly Bomber too. Here are the solutions:

- Takes too many games to level you up/down: reduce the number of XP or whatever that it costs to level up. It could be that you only have to win like 2 or 3 games at a given level to level up or something.
- When it levels up it's too hard: increase the number of levels. It could be that there's like a fuckload of levels, like 100 or something. Auro had VERY few, like 15. Not nearly enough resolution in hindsight.

The only reason we didn't do these things with Auro was that doing anything was hyper-hard with that codebase and we had no coders really anyway.

QUESTION: If there was a version of the SP Elo system with the issues fixed, would you still be wanting to do some other system like "par" or this new Batlad one?
 
#32
@Hopenager Sorry if I gave the impression that I'm advocating for changing existing games, it is only my intention to advocate for designing new games. Since changing any single part (especially of their goals) has massive implications on the rest of the system and would require commensurate changes to them.

As to the rest of your post I think I agree, I think that elegance is an important consideration when designing goal systems, and so less is often more.

@keithburgun Ugh I've got to play one or two more matches when I'm convinced this rank is too easy for me, that sounds terrible :p

But yes I recognise Auro was the first prototype and there are many improvements to be made to the ranking system. (I think adding more ranks just runs into a problem hopenager outlined in his article on the par system though, since ranks become indistinguishable from points). But yes I'd much rather move up and down multiple ranks after each match, than wait multiple matches to move a rank.

That being said I think that in principle many different games would be better with post-hoc points and a par metagame system than binary win-loss and a ranking metagame system. Ultimately though there are limits to how far we can get with theory alone, but I at least want to encourage people to consider all the (reasonable) alternatives and come to their own conclusion based upon the features of their game.
 
#33
It's perhaps worth explicitly pointing out that any win-loss game is equivalent to an EV game with only two final scores (1 and 0). Equivalent in the sense that it would be impossible to tell, by watching their play, if a rational player considered the game to be a win-loss game or an EV game.

So of course I don't think that EV games are fundamentally limited in how deep or strategic they can be, but I do think that there are some human reasons to prefer win-loss. Like Keith said earlier, playing a win-loss game just feels quite different from playing an EV game. I think, in the context of games, EV just doesn't click with people in the same way that win-loss does. It doesn't help that the vast majority of would be EV games don't explicitly prescribe EV as the correct valuation function and even encourage alternative valuation functions by putting so much emphasis on the player's all time best score.
 

keithburgun

Administrator
Staff member
#34
It's perhaps worth explicitly pointing out that any win-loss game is equivalent to an EV game with only two final scores (1 and 0).
I don't think this is worth pointing out, because an EV game with "two final scores" is a binary goal (or, a win-loss game). It's not that "a viewer couldn't tell the difference", it's that "there is no difference". I don't think this tells us anything about the quality of EV games *as distinct from binary goals*, because we've just converted them to binary goals.

I worry about the "clicking" argument because actually I think most people are probably more used to high score, especially for single player. I think people are kinda like "what" when it comes to winning and losing matches of single player games. Hopefully I'm wrong about that, and I personally can't stand to play a match based thing that doesn't have a binary outcome, but I don't think I'm in the majority on that. My general feeling is that binary is ideal but that players might have to get convinced of this fact.
 
#35
There would be a difference in the way the rules were written. One would say "try to win" and the other would say "maximize EV". But yes they are functionally identical which shows that maximizing EV can be just as good as trying to win.

But if that's not good enough for you, any binary EV game can be arbitrarily closely approximated by a non-binary EV game. So any win-loss game is basically equivalent to a set of non-binary EV games as well.
 

keithburgun

Administrator
Staff member
#36
"Maximizing EV" can be just as good as "trying to win", when it is converted into "trying to win" (by having a binary outcome). I don't know, it just sounds like you're saying "binary is non binary when you make it non binary". If you have a nonbinary system of integers (0123456...) and you say "ok now you can only use 3 and 4" or something, then it becomes a binary system.

But yes they are functionally identical which shows that maximizing EV can be just as good as trying to win.
This is where I feel like you're doing some accidental slight-of-hand. "Maximizing EV" can only be "as good as" binary outcomes when it IS a binary outcome. If it's a non-binary outcome, it's way worse.
 
#37
"Maximizing EV" can only be "as good as" binary outcomes when it IS a binary outcome. If it's a non-binary outcome, it's way worse.
You're missing the part where I said win-loss games are basically equivalent to a set of non-binary EV games as well as being perfectly equivalent to a binary EV game.

Yes, my argument so far leaves open the possibility that non-binary EV games are only good to the extent to which
they approximate a binary game. But the reason I bring it up is that many of your arguments against EV games (e.g. "How to decide what score to go for?", "How to decide how much risk to take on?", "What to do when you reach the score you're going for?") suggest that you think that EV is not even capable of producing a well defined game. So by showing that win-loss games are equivalent to binary EV games, and basically equivalent to a set of non-binary EV games I have shown that EV is, in fact, capable of producing a well defined game with any property you may care about.
 
#38
If you have a nonbinary system of integers (0123456...) and you say "ok now you can only use 3 and 4" or something, then it becomes a binary system.
A closer analogy would be that I think you're saying that base 2 numbers are the only numbers that make sense, so I'm showing that each base 2 number is actually equivalent to a base 10 number in order to demonstrate that base 10 can also be used to represent all the sensical numbers a base 2 lover may want.

Where the analogy falls short is that EV can also be used to define a set of games that can't be defined using win-loss, and my argument also makes some limited claims about that set of games.
 

keithburgun

Administrator
Staff member
#39
You're missing the part where I said win-loss games are basically equivalent to a set of non-binary EV games as well as being perfectly equivalent to a binary EV game.

Yes, my argument so far leaves open the possibility that non-binary EV games are only good to the extent to which
they approximate a binary game. But the reason I bring it up is that many of your arguments against EV games (e.g. "How to decide what score to go for?", "How to decide how much risk to take on?", "What to do when you reach the score you're going for?") suggest that you think that EV is not even capable of producing a well defined game. So by showing that win-loss games are equivalent to binary EV games, and basically equivalent to a set of non-binary EV games I have shown that EV is, in fact, capable of producing a well defined game with any property you may care about.
With "a win loss game is equivalent to a set of non-binary EV games" you have not shown that EV is capable of producing a well defined game. You may have shown that EV is capable is producing a well defined SET of games. There's a huge difference there, though.

A closer analogy would be that I think you're saying that base 2 numbers are the only numbers that make sense, so I'm showing that each base 2 number is actually equivalent to a base 10 number in order to demonstrate that base 10 can also be used to represent all the sensical numbers a base 2 lover may want.
If the base 2 lover loves 0 and 1, yes. If the base 2 lover wants "there to only be two numbers", no.
 
#40
With "a win loss game is equivalent to a set of non-binary EV games" you have not shown that EV is capable of producing a well defined game. You may have shown that EV is capable is producing a well defined SET of games. There's a huge difference there, though.
Since you seem to agree that win-loss games are equivalent to binary EV games, surely you also agree that EV is capable of producing well defined binary score games. More generally, EV is capable of producing well defined score games (binary or otherwise) because EV itself is usually well defined. It would take a rather unusual score distribution to make EV an undefined quantity. So if we only consider games with reasonable score distributions, then the player can always assign each of their options a quantity equal to the EV of that option. The player can then use those quantities to unambiguously rank their available options and pick the best one. This procedure resolves all the questions like "How many points to go for?", "What to do after a given point threshold?", and "How much risk to take on?". The answer to each one is "pick the option with the most EV". Therefore games with the goal "maximize EV" are well defined (i.e. you can actually pursue those games' goals in an unambiguous way).

The part about the non-binary EV games approximating win-loss games is a separate claim that won't make sense if you don't already agree that EV can produce well defined games.

If the base 2 lover loves 0 and 1, yes. If the base 2 lover wants "there to only be two numbers", no.
That's not the way the analogy works. Edit: To expand on this, in my analogy each number represents a game. So no one would have the position "there should only be two numbers".
 
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