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Tipping points

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jwarrend
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Joined: 08/03/2008

I'm working on a game right now where the math seems to work out there's no easy way to balance the game while having rewards be integer amounts. The reward for a certain action may need to be worth 1.333, say, to be fair in comparison with another action whose reward is 1.0. Now, the obvious way to handle this is to just scale up the points, however, even that won't really solve my problem, and moreover, doing so may add more complexity than I want.

As a result, the way I've chosen to handle this is to incorporate "combo" based scoring. For example, "You get 3 points for every 2 of X that you acquire". This means that each X is worth 1.5 points, BUT that doesn't mean you actually get 1.5 points for each X you acquire; you only get points for sets of 2. This introduces what I'm calling a "tipping point" (or actually, in this case, several of them). Collecting 3 X's is worth no more than collecting 2 X's, but collecting 4 is worth substantially more.

What I'm interested in is whether other people have ever had scoring systems that included similar tipping points, and whether they felt this was a good or bad route to go.

I think this is kind of similar to the effect Jonathan Degann described in his article on "the Bomb" (incidentally, he would be a good "expert" to interview in a Chat sometime...), but I think what I'm talking about may be subtely different. Maybe not.

The interesting effect this has on the game in question is a discretization of scoring opportunities which may not be the same for all players. For example, I have the card mentioned above, "You get 3 VPs for every 2 X you collect." You have a card that says "You get 2 VPs for every Y you collect". So right away, you're capable of scoring 0,2,4,6,8, etc points whereas I'm only capable of scoring 0,3,6,9, etc.

Now, to me, what should be balanced is the difficulty of scoring equivalent numbers of points. So, to score 6 points, I need to acquire 4 X's, whereas you need to acquire 3 Y's. As long as it's equally difficult to acquire 4 X's or 3 Y's, I think it's ok. But some don't see it that way, because our scoring potentials are not the same; you have more "increments" in your scale than I do, meaning that your scoring is slightly less "all or nothing" than mine. (Making this worse, I have a couple of cards that say "get 5 points if you did Z", and Z is "tough enough" that those 5 points are well-earned, but you get nothing if you don't perform Z.

So, I guess this post is actually about 2 things -- tipping points in scoring, and discretization in scoring associated with different players having different scoring opportunities.

With regard to the former, can a game be considered "fair" if its scoring systems have tipping points? With regard to the latter, can it be considered fair if different players have different tipping points, and thus, different scoring potential, even if the difficulty of achieving the same number of points is the same? In other words, what should be controlled, the points potential all players have access to, or the difficulty of achieving X points, even if not all players could achieve exactly X points in principle?

I welcome any thoughts on the subject!

Thanks,

-Jeff

Sebastian
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Re: Tipping points

jwarrend wrote:
I'm working on a game right now where the math seems to work out there's no easy way to balance the game while having rewards be integer amounts. The reward for a certain action may need to be worth 1.333, say, to be fair in comparison with another action whose reward is 1.0. Now, the obvious way to handle this is to just scale up the points, however, even that won't really solve my problem, and moreover, doing so may add more complexity than I want.

In a game I helped design, I put an inordinate amount of effort into trying to make the rewards for various actions be fair. The person I was designing with then, over the course of several prototypes, ripped all the fairness out and left a completely unbalanced result. The game still worked happily, and lacked the complexity that I'd attempted to introduce to keep fairness.

Sebastian
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Re: Tipping points

jwarrend wrote:
As a result, the way I've chosen to handle this is to incorporate "combo" based scoring. For example, "You get 3 points for every 2 of X that you acquire". This means that each X is worth 1.5 points, BUT that doesn't mean you actually get 1.5 points for each X you acquire; you only get points for sets of 2. This introduces what I'm calling a "tipping point" (or actually, in this case, several of them). Collecting 3 X's is worth no more than collecting 2 X's, but collecting 4 is worth substantially more.

What I'm interested in is whether other people have ever had scoring systems that included similar tipping points, and whether they felt this was a good or bad route to go.

One thing to keep in mind is that you want people to have flexibility in strategies. In a game I'm currently working on, I used to have a system in which the more tokens you had, the more points you got. This meant that when considering strategy, you had to decide 'getting tokens' or 'not getting tokens' - and once you'd decided that it was difficult to change strategies. I'm switching to a system with lots of little tipping points that you get when you complete sets, which I suspect will give better results.

zaiga
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Tipping points

Hi Jeff,

It's that "Disciples" game you are talking about, right? ;)

I think "tipping point" or "set based scoring" are a great way of bringing tension into a game.

However, the "problem" in your game is that every player will have a different kind of scoring and that players don't have any control over what goal they end up with. This means that you, as a designer, must make sure that all goals are, more or less, balanced, so that a player won't feel slighted when he gets that "difficult" goal.

Giving each player a set based scoring goal, with different increments (ie. 0-2-4-6-8 vs. 0-6-9-12) makes it unbalanced from the outset. The real question is whether this is a big problem. I don't think it has to be, as long as the scoring is volatile enough. If a "normal" score is around, say, 7 or 8 points then it's much more unfair to the player who has the 3 increment scoring, then when a normal score would be in the 20's (for example).

Furthermore, if there is some alternative way of scoring points, that is equal for all players (the Deeds in your game?), then that gives a player the option to pursue that road at the end of the game, if he thinks he will not be able to complete his last set.

Finally, I think it's OK to have a bit of luck in a game and you will never be able to make a game with different, hidden goal cards completely balanced. And even if you can, there will always be someone who will complain that he lost because he got such a horrible goal card, even when that is not true. It can even be fun to have an unbalanced setup. In "BANG!" for example, the Renegade hardly ever wins, but it is still fun to play the Renegade and it's all the more satisfying when you do pull it off!

Luck and inbalance are of course more torable in a shorter, light game then a long, heavy, strategy game. If your game is the latter kind then some kind of bidding or drafting mechanism for distributing the goal cards might fix the problem.

- René Wiersma

jwarrend
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Tipping points

zaiga wrote:
Hi Jeff,

It's that "Disciples" game you are talking about, right? ;)

Naturally! But, since this is my first game with "inidividual goals", I thought I'd ask the question from a more academic standpoint. I think the question is equally valid if one is talking about reward schedules that are common to all players, even. (or at least the question about "tipping points" is -- the issue of goals with different scoring potentials is a separate issue, and one that I don't think I've seen many games that provide good examples.)

Quote:

I think "tipping point" or "set based scoring" are a great way of bringing tension into a game.

However, the "problem" in your game is that every player will have a different kind of scoring and that players don't have any control over what goal they end up with. This means that you, as a designer, must make sure that all goals are, more or less, balanced, so that a player won't feel slighted when he gets that "difficult" goal.

Yes, I agree completely. But my question is whether the game could be considered fair if the goals have different scoring potential but equivalent difficulty. I guess below you outline an answer that basically says, "fairness" depends a little bit on the context...

Quote:

Giving each player a set based scoring goal, with different increments (ie. 0-2-4-6-8 vs. 0-6-9-12) makes it unbalanced from the outset. The real question is whether this is a big problem. I don't think it has to be, as long as the scoring is volatile enough. If a "normal" score is around, say, 7 or 8 points then it's much more unfair to the player who has the 3 increment scoring, then when a normal score would be in the 20's (for example).

Furthermore, if there is some alternative way of scoring points, that is equal for all players (the Deeds in your game?), then that gives a player the option to pursue that road at the end of the game, if he thinks he will not be able to complete his last set.

I think that's a good point; I think the discretized scoring is only a problem if it's the only way that you get points. I'm trying to think of whether there are any games out there that use differently discretized individual goals. The only "individual goals" games I'm thinking of are games like Dune or Illuminati, that are more like "if you do X you win." and X varies from player to player.

Quote:

Finally, I think it's OK to have a bit of luck in a game and you will never be able to make a game with different, hidden goal cards completely balanced. And even if you can, there will always be someone who will complain that he lost because he got such a horrible goal card, even when that is not true. It can even be fun to have an unbalanced setup. In "BANG!" for example, the Renegade hardly ever wins, but it is still fun to play the Renegade and it's all the more satisfying when you do pull it off!

I think this is definitely a question of player styles. Some people will enjoy the challenge of trying to win "against the odds", while some will cry "foul!" that they drew a goal/faction/whatever that was so "difficult". An interesting aspect of the game in question, and probably most games with similar ideas, is that "difficulty" is somewhat related to common scarcity, and thus, will vary slightly from game to game, thus a "whiner" may just be a victim of the common interaction of the other players in a way that coincidentally conspired to make the game difficult for that player. I've seen this happen in Puerto Rico, for example -- a player gets completely closed out of every single opportunity, through no clearly identifiable mistake of his own. The danger here is that by giving players a card that defines their scoring opportunities, you're also giving them a scapegoat if they score badly!

Quote:

Luck and inbalance are of course more torable in a shorter, light game then a long, heavy, strategy game. If your game is the latter kind then some kind of bidding or drafting mechanism for distributing the goal cards might fix the problem.

Yeah, I'm not sure exactly where this game is going to end up in the "light/heavy" scale. I think it's fairly light, but I think it also has the possibility of having enough strategic depth that probably a drafting mechanic for more "advanced" players will be a necessary thing to include. Possibly something we'll try out next time.

Thanks for the thoughts!

-Jeff

Anonymous
Re: Tipping points

Well, Jeff, I do have a game that has a set-collection mechanic (associated with trade between players), and the problem that I'm running into is that when a player has a set of X (IOW, is at the tipping point), s/he's less likely to trade for another because it is, essentially, worthless to him/her until the next tipping point. Whether that applies in your case or not, I don't know, but I thought I'd throw it out as perhaps another perspective.

My other concern is based on an example you gave:

jwarrend wrote:
So right away, you're capable of scoring 0,2,4,6,8, etc points whereas I'm only capable of scoring 0,3,6,9, etc.

Now, to me, what should be balanced is the difficulty of scoring equivalent numbers of points. So, to score 6 points, I need to acquire 4 X's, whereas you need to acquire 3 Y's. As long as it's equally difficult to acquire 4 X's or 3 Y's, I think it's ok.

Getting to 6 may very well be equally difficult, but what if I fall short...or go long? The player with the "higher resolution" progression will likely score more points, as falling short by one X will give you 4 points while falling short by one Y will yield only 3. Likewise, going long by 2 X's gives 8 points, while going long by 2 Y's gives still just 6. Now, the rarity of X and Y may make the probabilities of these outcomes relatively equal, but I think generally speaking it would be easier to score on a "smoother" scale than on a more "granular" one.

My pair of Lincolns.

jwarrend
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Re: Tipping points

MikeDew wrote:
Well, Jeff, I do have a game that has a set-collection mechanic (associated with trade between players), and the problem that I'm running into is that when a player has a set of X (IOW, is at the tipping point), s/he's less likely to trade for another because it is, essentially, worthless to him/her until the next tipping point. Whether that applies in your case or not, I don't know, but I thought I'd throw it out as perhaps another perspective.

It doesn't apply to my game at least from a trading aspect, but the principle is the same; once you have a "set", advancing towards the next "set" becomes "worthless" until you reach some point where that goal actually becomes achievable.

In the sense of a trading game, this is certainly one of the problems that I've seen happen in my limited exposure to Settlers; if everyone has what they need, no need to trade. I think it's more a problem of lockup than fairness. I don't foresee a gridlock problem with my game.

Quote:

My other concern is based on an example you gave:

jwarrend wrote:
So right away, you're capable of scoring 0,2,4,6,8, etc points whereas I'm only capable of scoring 0,3,6,9, etc.

Now, to me, what should be balanced is the difficulty of scoring equivalent numbers of points. So, to score 6 points, I need to acquire 4 X's, whereas you need to acquire 3 Y's. As long as it's equally difficult to acquire 4 X's or 3 Y's, I think it's ok.

Getting to 6 may very well be equally difficult, but what if I fall short...or go long? The player with the "higher resolution" progression will likely score more points, as falling short by one X will give you 4 points while falling short by one Y will yield only 3. Likewise, going long by 2 X's gives 8 points, while going long by 2 Y's gives still just 6. Now, the rarity of X and Y may make the probabilities of these outcomes relatively equal, but I think generally speaking it would be easier to score on a "smoother" scale than on a more "granular" one.

Yes, I certainly agree that it would be easier the "finer-grained" your scoring scale is. And I think you've hit on the problem; it isn't just a question of equality of difficulty, but of "what happens if you don't meet your goal?" If both players are going for the 6 pt payoff but both fall short, one player will get 4 pts and the other will get 3. Now, I still contend that this will (in principle) be a "fair" outcome -- ie, that those 4 points the one player got took more work to achieve than the 3 points of the other player. But it's "unfair" from a default scoring potential perspective; is that a problem?

I'm honestly not sure. My feeling is that some people will absolutely hate it and some won't be bothered. I would guess it would be more of a problem among "serious" players than among a more casual crowd.

Thanks for your thoughts!

-Jeff

Scurra
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Tipping points

Wild suggestion time...

Would "grading" the goals be a (semi-) solution to this? For instance, imagine giving them all a star-rating from 1* (easiest) to 3* (hardest), with, say, one or two 1*s and one or two 3*, the rest being 2*.
At the end of the game, players get a bonus VP score of the total difficulty of their goals. Now this will only result in a swing of maybe one or two points (since most players will have 4* but some may have 2* or even 5*) but this might be enough to affect the final outcome.
(plus it might allow the drafters to aggressively pursue difficult or easy goals!)

And new players would get an idea about which goals they should be concentrating on, without needing to ask ahead of time about how the different goals stack up.

jwarrend
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Tipping points

Quick note -- the idea of "grading goals" is more specific to my game than the broader subject I was trying to address, namely, "Are tipping points and/or discretized scoring 'fair'?" That said, obviously since your point is pertinent to my game I want to address it.

On the surface, this sounds like a great idea; I like the idea that it's a minor correction, yet can give someone who gets two real doozies a bit of an edge over someone with two cupcakes. Yet, I have two concerns. One is that this encourages sloppiness on the part of the designer -- instead of properly balancing the game, he's giving himself a pass to leave it imbalanced and try to cover it up (with another mechanism that he will, of course, need to balance!). However, as I mentioned, the discretized nature of scoring may make "true balancing" difficult so this could be a good compromise.

The bigger concern is that the luck associated with drawing a "difficult" or "easy" goal is overwhelmed by the luck of drawing two complementary goals vs. two goals that don't mesh very well. There are some pairs of goals that are great together, others that are ok, and others that are downright contradictory. I like the challenge that each draw presents -- getting a great combo means I should be able to rack up a great score; getting a tough combo means I'll have to work hard. I find this fun, yet it could be problematic from a "serious player's" standpoint. The obvious solution is to allow drafting as a variant, but I think even better might be to assign a relative value to each pair (probably on a scale from 1 to 5 or some such). Of course, we're talking about a lot of pairs of goals here! But if the scale is kept small, I think just eyeballing a given pair gives you a sense of whether it's easy or hard. It's just a lot of work to go through each pair and assign it that value. Again, probably a variant, a table that could be posted on the web or something.

So, yes, rating the goals could definitely be ok, but (a) it's an extra rule (though a simple enough one and (b) you still have to balance the ratings and (c) all that stuff goes out the window if you get 2 goals that mesh fantastically well even if individually they are difficult.

Bottom line, this is a really tough balancing act I'm trying to pull off. But, I think it will be worth the effort in the end; already, things are crystallizing nicely, it's just still an open question of whether we have a "game" or a "toy". I think it's definitely en route to the former, but maybe not all the way there yet...

Thanks for the thoughts,

Jeff

Scurra
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Tipping points

I appreciate your point, but it's hard not to discuss things in terms of specific examples (I keep wanting to talk about "All for One" in this discussion for instance, but it would be amusingly inappropriate :))

It was also that I mostly agreed with the point about lucky draws vs scoring potential. "Lucky" draws shouldn't exist in a game in which the scoring potential is large enough to balance it out; but then if the game were big enough to properly encompass that, it would probably be too big!

I think it's worth noting that it's also worth examining when people are competing for the same things for different reasons. If you have two resources X and Y, and player A is collecting X=2 and Y=1 and player B is collecting X=1 and Y=2 then each resource is going to be worth different things to the different players. In those circumstances, X and Y have to be equally easy to obtain as otherwise one player has an unfair advantage. But that doesn't mean you don't make it easier for player A to obtain resource Y and player B to obtain resource X...

jwarrend
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Tipping points

Scurra wrote:
I appreciate your point, but it's hard not to discuss things in terms of specific examples (I keep wanting to talk about "All for One" in this discussion for instance, but it would be amusingly inappropriate :))

No, I understand, and don't mind delving into specifics (including, if you wish, "All for One"!). I simply don't want someone to feel like to get in on the discussion about "tipping points" or "discretized scoring", they have to talk about my game specifically. I think it's a subject that's of broader interest than that, certainly any game with secret goals some of these issues would come up.

Quote:

I think it's worth noting that it's also worth examining when people are competing for the same things for different reasons. If you have two resources X and Y, and player A is collecting X=2 and Y=1 and player B is collecting X=1 and Y=2 then each resource is going to be worth different things to the different players. In those circumstances, X and Y have to be equally easy to obtain as otherwise one player has an unfair advantage. But that doesn't mean you don't make it easier for player A to obtain resource Y and player B to obtain resource X...

I know what you mean. In my game (as you know) there's no difference between the players provided by "special powers" or the like; in fact, there's really only one "commodity", the "Deed" cards, each of which have different attributes. So, everyone wants that commodity, but the goals steer you towards preferring cards with specific attributes. So in a sense, an "easy" goal could become very difficult if players choose to all prefer the specific attribute you're going for because of other attributes those specific cards may have, or just because those cards are easy to acquire, etc. I think that this will lead to an "every game is different" effect, but it also suggests that there is some hyperfine imbalance that I'll overlook/ignore, that someone with way too much time on his hands will discover and declare the game "broken"! But I think it all depends on how fine-toothed your comb is...

-J

sedjtroll
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Tipping points

I say you do what you think is right, and don't worry too much about what whiners might whine about. They're whiners, they're going to whine anyway. If you think the game is fair, and you've put a lot of thought into making it so, then you probably know better than the whiner who lost his first game.

I know what you'll say, that you'd like to reduce that possibility. My point is that you can't. Not without changing to a system where everyone's path to victory can be compared linearly- apples to apples. But that's the opposite of what you want.

- Seth

jwarrend
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Tipping points

sedjtroll wrote:
I say you do what you think is right, and don't worry too much about what whiners might whine about. They're whiners, they're going to whine anyway. If you think the game is fair, and you've put a lot of thought into making it so, then you probably know better than the whiner who lost his first game.

I know what you'll say, that you'd like to reduce that possibility.

That's right. Or maybe more correctly, I don't want someone to dismiss the game and never play it again simply because they drew some "tough" goals. But I agree with you in principle that you can't build your life around certain gaming sensibilities. A good example of this is the "perfect planners", who will dramatically increase the playing time of any game. You can try to make the game play quickly, but only up to a point; after that, you really have to just say "it is what it is, and perfect planners are going to make it long no matter what." Your point is well taken.

Quote:

My point is that you can't. Not without changing to a system where everyone's path to victory can be compared linearly- apples to apples. But that's the opposite of what you want.

It's not the opposite of what I want so much as the opposite of what I can have with the way I'm currently doing things. Again, the discretized scoring is a consequence of certain increments of "goal progress" being non-integers. But, I tentatively agree with you that it's probably inevitable if I continue with that scoring concept. And you know, while I'm thinking about just expanding the point scale so as to allow for finer-graining of the scoring, I kind of like the "tipping points" as a source of tension...

It's probably also important to ask whiners to keep in mind that the game isn't meant to be "Tigris and Euphrates", but a medium-weight (at most!) family-style game; that might solve some problems.

Thanks,

Jeff

Anonymous
Tipping Points

The scoring you mention reminds me of Bohnanza. Some beans are worth points at the 4/6/8/10 level, others at 3/6/8/9, etc. (You have to collect that many to get 1/2/3/4 points.) It certainly works well to induce tension.

Another way to do fractional scoring (that may or may not be appropriate to your game) would be to give the player a random chance at points. E.g. half a point is worth a 50% chance at a real point. While adding luck, it adds an incentive to try for an extra item that would otherwise be worthless.

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