I just read the short book, “Uncertainty in games,” by Greg Costikyan. It was interesting. His main point, which makes sense to me, is that uncertainty a key part of the appeal of any game. He gives interesting examples of different sources of uncertainty. For example, if you’re playing a video game such as Pong, the uncertainty is in your own reflexes and reactions. With Diplomacy, there’s uncertainty in what the other players will do. With poker, there’s uncertainty about all the hole cards. With chess, there’s uncertainty in what the other player will do and also uncertainty in the logical implications of any position, in the same way that I am uncertain about what is the 200th digit of the decimal expansion of pi, even though that number exists. I agree with Costikyan that uncertainty is a helpful concept for thinking about games.
There’s one thing he didn’t discuss in his book, though, that I wanted to hear more about, and that’s the way that time and uncertainty interact in games, and how this factors into game design. I’ve been thinking a lot about time lately, and this is another example, especially relevant to me as we’re in the process of finishing up the design of a board game, and we want to improve its playability.
To fix ideas, consider a multi-player tabletop game with a single winner, and suppose the game takes somewhere between a half hour and two hours to play. As a player, I want to have a real chance of winning, until close to the end, and when the game reaches the point at which I pretty much know I can’t lose, I still want it to be fun, I want some intermediate goal such as the possibility of being a spoiler, or of being able to capitalize on my opponents’ mistakes. At the same time, I don’t want the outcome to be entirely random.
Consider two extremes:
1. One player gets ahead early and then can relentlessly exploit the advantage to get a certain win.
2. Nobody is ever ahead by much; there’s a very equal balance, and the winner is decided only at the very end by some random event.
Option #1 actually isn’t so bad—as long as the player in the lead can compound the advantage and force the win quickly. For example, in chess, if you have a decisive lead you can use your pieces together to increase your advantage. This is to be distinguished from how we played as kids, which was that once you’re in the lead you’d just try to trade pieces until the opposing player had nothing left: that got pretty boring. If you can use your pieces together, the game is more interesting even during the period where the winning player is clinching it.
Option #2 would not be so much fun. Sure, sometimes you will have a close game that’s decided at the very end, and that’s fine, but I’d like for victory to be some reflection of cumulative game play, as otherwise it’s meaningless.
Sometimes this isn’t so important. In Scrabble, for example, the play itself is enjoyable. The competition can also be good—it’s fun to be in a tight game where you’re counting the letters, blocking out the other player, and strategizing to get that final word on the board—but even if you’re way behind, you can still try to get the most out of your rack.
In some other games, though, once you’re behind and you don’t have a chance to win, it’s just a chore to keep playing. Monopoly and Risk handle this by creating a positive incentive for players to wipe out weak opponents, so that once you’re down, you’ll soon be out.
And yet another approach is to have cumulative scoring. In poker it’s all about the money. Whether you’re ahead or behind for the night, you’re still motivated to improve your bankroll.
One thing I don’t have a good grip on regarding game design is how to get that balance between all these possibilities, so that how you play matters throughout the game, while at the same time keeping the possibility of winning for as long as is feasibly possible.
I remember my dad saying that he preferred tennis scoring (each game is played to 4 points, each set is 6 games, you need to win 2 or 3 sets) as compared to old-style ping-pong scoring (whoever reaches 21 points first, wins), because in tennis, even if you’re way behind, you always have a chance to come back. Which makes sense, and is related to Costikyan’s point about uncertainty, but is hard for me to formalize.
A key idea here, I think, is that the relative skill of the players during the course of a match is a nonstationary process. For example, if player A is winning, perhaps up 2 sets to 0 and up 5 games to 2 in the third set, but then player B comes from behind to catch up and then maybe win in the fifth set, yes, this is an instance of uncertainty in action, but it won’t be happening at random. What will happen is that A gets tired, or B figures out a new plan of action, or some other factor that affects the relative balance of skill. And that itself is part of the game.
In summary, we’d like the game to balance three aspects:
1. Some positive feedback mechanism so that when you’re ahead you can use this advantage to increase your lead.
2. Some responsiveness to changes in effort and skill during the game, so that by pushing really hard or coming up with a clever new strategy you can come back from behind.
3. Uncertainty, as emphasized by Costikyan.
I’m sure that game designers have thought systematically about such things; I just don’t know where to look.
Generally modern board games with scoring have negative, rather than positive, feedback (“catch-up mechanism” is the standard term in game design). Of course you don’t want the negative feedback to be so great that it is actually better to be behind than ahead! But you can soften the impact of being behind, so that maybe you have a 30% chance of still winning rather than 10%, say.
An example mechanic like this in a multiplayer turn-based game is to have the players take turns in increasing order of their score every round, so the players in back have a chance to pick up better resources or what have you.
Dan:
I guess it depends on the game. In a game like chess or Monopoly, game play is fun when the game is close, or if you’re slightly behind and you want to catch up, or if you’re slightly ahead and you want to win. But it’s not so much fun when the game’s not close.
Then there is Othello, where you can apparently be winning all along, and the board flips to a loss at the end!
From my understanding, the idea of rich-getting-richer is largely considered bad design in board games with many players (Monopoly isn’t great, even without house-rules). No one likes being knocked out and having to wait, or finishing a game with a forgone conclusion. Resigning let’s it work in 2-player games like chess. And it works in the context of online video games, where you can just start a new game with a new group of strangers the moment you’ve lost.
Kj:
Let me put it this way, then. It’s good to have a mechanism where, once someone is far enough ahead that others don’t have a chance, the game ends quickly. At the same time, we don’t want it to be too easy for others to gang up on the leader, in which case the game play seems pointless.
This is similar to decisions involving the regular season and the playoffs in sports leagues. If you go old-style MLB and it’s just the top team from each league playing in the World Series, then the second half of the regular season becomes pointless for most teams. But if everyone gets into the playoffs, then the regular season doesn’t matter. And then there are compromises involving seeding, byes, home-field advantage, etc.
The other thing, really the most important, is that the game should be fun to play even if you’re not winning (or, for a spectator sport, fun to watch even if your team is not winning). I brought up Scrabble as an example, but this is also the case with sports. Your team might be in the middle or bottom of the pack in the late season, but if the players are still trying hard, the game can still be watchable. So that’s a tradeoff too: the balance between having fun and trying to win. If it’s a competitive game, you want to enjoy it but it’s also important to have some motivation to win and not lose.
There are also games where the rules are endogenous. For me, golf is a game I only play against myself. I may start with the goal (win) of scoring less than X (I’m too embarrassed to tell you what X is). After a bad hole, X may not longer be achievable, so I adopt the goal of X/2 for the second nine holes. When things really go south, my goal may be to count the number of pars I get. Sometimes it may be to minimize my score on the last 3 holes.
Multiplayer games also can have endogenous rules. You can be far enough behind your opponent(s) that you adopt a goal other than beating them (such as being the spoiler you mention above). To some extent, the game you invent need not achieve the perfect balance since the players can adopt their own rules in reaction to shortcomings in what you designed. I would think that a bit of user testing would reveal some of this and allow you to modify your design when common reactions become evident.
Scoring systems can make all the difference – as in tennis discussed above where the fantastic scoring system is a large part of its appeal.
Golf-wise Stableford scoring is pretty good since it allows you to play a round without completely torpedoing your attempt at a good score by having a disastrous hole or two. You can still play against yourself but your aim would be a high Stableford score (you need to acquire or invent a handicap tho).
I’m in a similar situation as you I think. My aim, every time I set out on a round, is to break 90 and I never, ever manage this even if I sometimes shoot a low (for me) score on one of the 9 holes (eg 42 or 43).
Yeah – the danger of scoring well on the last few holes is that it gives you a false encouragement that the next round is going to be pretty good!
In an educational setting, I wonder how much these principles apply to grading? To be clear, I don’t think of education as a game, but it seems to me that an important pedagogical reason for having grades is to provide an incentive structure that motivates students to learn, which is similar to a game design objective.
Principle #2 would seem to apply pretty directly to grading—we want it to be possible for students to “come from behind” if they realize their mistakes or put in additional effort.
Principle #1 may not apply, since grading is not competitive in most cases. That said, it may be related to some notion of “scaffolding”, whereby the feedback a student receives helps to guide their subsequent efforts in the class (e.g., recognizing that a particular situation calls for a particular solution attempt that they can then generalize to future problems) or encourage them to go beyond the coursework (e.g., to get them excited about doing research or applying course concepts outside of class).
Principle #3 I thought might not apply at first, but then I changed my mind. True, we want students to be graded “fairly”, meaning there should not be randomness inserted into the grading process itself. But students also should not be able to predict everything about the course, since then they will simply “learn to the test”. If students are to learn concepts/skills that generalize to the world outside the class (which is, by definition, uncertain) then there should be some uncertainty in what students will be graded on.
gec –
I know this is an offshoot, but…
> but it seems to me that an important pedagogical reason for having grades is to provide an incentive structure that motivates students to learn.
Ostensibly, sure. But I’m skeptical. I think of grades as actually functioning primarily to rank students (and perpetuate status quo). To the extent that they motivate students, it’s mostly among those who regularly get good grades. For others they can certainly tend to be demoralizing not motivating. Either way, grading can have an effect of creating passive learners who pass over responsibility for assessment to others.
> Principle #1 may not apply, since grading is not competitive in most cases.
Hmmm. I see grading as highly competitive. First, in most grading an individual’s score is based on how well they did relative to others. Grading is inherently linked to tanning students.
Second, students are often very focused on how well they did relative to other students. If a student gets a B but finds out that everyone else got no higher than a C they would in most cases be satisfied.
What you describe matches my own experience with how grades are used and how students typically view grades. Personally, I love giving feedback but I hate giving grades—I only give grades because I have to.
My interest in relating the original post to grading was to consider how the motivational factors involved in good game design might help grades to better serve an important pedagogical function of providing an incentive structure to reward learning. It may be that grading cannot serve that function very well, if at all! My own prior beliefs lean against it, but given that we have to do it anyway, I’d like to see how to use grades more effectively.
Finally, regarding “competitive”, what I meant was “zero-sum”. I agree that students are often competitive with one another regarding grades, but it is not generally the case (except when doing things like grading on a curve) that one student receiving a high grade entails another student getting a low grade.
gec –
Thanks. Not that it really matters, “tanning” was supposed to be “ranking.”
So is grading (except of a curve) zero sum? Maybe not in a direct sense, but maybe yes indirectly, sometimes? A certain number of slots for whatever are reserved for students who get top grades. That’s then zero sum indirectly?
One student getting an A doesn’t mean another student getting an A in the most direct sense, but I do think there’s a complicated psychological aspect for graders. It’s generally considered sub-standard if too many students get A’s.
Now that I think about that, an idea occurs to me about “grade inflation” which is generally considered inherently as something really bad. If grade inflation is linked (causally) to poor learning outcomes, then that makes sense. But without proof of that (controlling for other variables? How likely is that?), maybe grade inflation is a good thing. More students are motivated by getting good grades and maybe it means more students are learning more if you assume that grades actually measure achievement. What if they don’t measure achievement, and only reflect on ranking? Hmmm. Then the reason why “grade inflation” is bad would only be because their function of ranking students is diminished – not anything else of importance? So then “grade inflation” just means using education to rank students shouldn’t be the goal as demonstrated by revealed preference?
GEC, Joshua:
For incentive structure in a course, having the final exam count for a high proportion of the grade allows students to make up for past mistakes and is an incentive for them to up their game. It definitely works as an incentive, especially if the instructor steps up with some additional help for the students – by providing a pre-exam study session with the instructor present where they can work together and ask questions; or additional study materials that help them prep for the exam. This kind of chipping in from the instructor both gives them extra materials, extra work, and a sense of confidence that the instructor is on their side.
I’ve never done it as an instructor but in undergrad and grad courses I had some profs:
1) let students keep their existing grade and skip the final (incentive to work hard during the class so you don’t have to take the final)
2) let students choose to have their grade on the final be their grade for the course (incentive to work hard for the final if they dropped the ball during the class).
Actually it’s interesting to think about the similarities and differences between success in education and success in a game.
The biggest similarity is obviously that both have scoring. However, games typically have a substantial element of chance – rolling dice, drawing cards, or just the shap of a football which makes it bounce wierd – while having an element of chance in grading in a course would be a very strong demotivator for students.
Also games are often refined and tested extensively to craft the best response for the general conditions of the game. The rules and outcomes have to be understandable to the players. But an academic course may or may not be well crafted. Some are terrible, some are excellent. It depends entirely on the prof / instructor. So an academic course with clear guidelines on what’s necessary to succede, followed up by organized presentation and supporting materials that allow the students to achieve as much as they’re willing to work for, would yield the highest level of grade-driven motivation. IOW, if lectures are garbled, the relevance of the supporting materials is unclear, and test questions seem to come out of the blue, the motivation to achieve will be low. You’d probably expect the same level of motivation to win a game if the game was poorly designed and how to win wasn’t clear.
@chipmunk. A football is spherical. Why would its shape make it bounce weird?
chipmunk –
One of the issues I have with grading a that it rests in a belief that students should be resonating to extrinsic reward systems.
I think the best learning takes place in pursuit of intrinsic reward. By structuring the system based on extrinsic rewards, we’re counterproductively substituting extrinsic rewards and for many students, stunting their growth as self-actualized learners. We’re curcumnavigating they’re meta-cognitive development as executives of their own learning. It’s a system that nets many passive learners as a product.
I do think there’s a better model for grading – criterion based (not norm based): Establish a taxonomy of mastery of a topic. One level equals an A, another a B, etc. Allow students basically as much time as they want to get to whichever level they desire. Be there to help them achieve that level of mastery. Allow them to take tests or submit papers multiple times.
Of course, that’s a logistically complicated model. But what is the point of using a less logistically complicated model that we feel is producing inadequate results.
It’s like that Woody Allen joke, roughly, “The food here is terrible, and the portions are so small.”
Responding to, not resonating to.
@Robin: not if yernamercan!!
Joshua:
Those are fine ideals. Reality is that learning has two functions: 1) the growth you describe; 2) preparation for the working world. It would be nice if all of us could spend our lives in pursuit of personal growth but biology requires us to produce something in return for food and shelter (it’s not a social requirement – with no society to support people they’d still have to find food and shelter). And to that end we have to limit the time that people have to become educated enough to obtain good enough work to pay their own way.
The system we have suffices to achieve that when people use it for that purpose.
BTW, some other thoughts on the “game” aspect of education:
The instructor in a course really is equivalent to the whole game:
1) The instructor makes the rules.
2) The instructor creates the board (syllubus, lectures, labs, study materials).
3) The instructor is the score keeper
(3) is critical: unlike in most games, the scoring in a course and in education in general often doesn’t have reliable rules. In any game where the score is an incentive, the scoring rules have to be reliable.
Becuase the instructor is basically the entire game, experience in one round of the game (a course taught by “Dr X”) doesn’t necessarily translate to the next round of the game (a course taught by “Dr Y”). Students often feel that Drs. X, Y, Z, A, B, C did a crap job on all of 1-3, so at the outset of any course they’re generally disinclined to be incentivized by grades because their experience is that the rules change, the board is shitty and the scoring is unpredictable. So if you want people to respond to the scoring mechanism, you have to demonstrate to them that the scoring is fair. In my experience, if you do that, they respond.
I feel like as an instructor I was able to accomplish that for the most part. And under those circumstances, the outcome for the individual student is up to them. If they want to work hard, they’ll do well. If they have other priorities, they probably won’t do that well. Whatever the case, I offered a system where success is in their hands. Unlike GEC, i didn’t dislike grading for any reason other than it was a chore. I didn’t “give” grades. I just graded the work according to the rules. The grades were what the student achieved.
Personally I think it’s unfortunate that so many people in academics and education have lost sight of the fact that education is a functional necessity. The foo foo growth thing can come a long as a free benefit but when it becomes the purpose of education it will lead to a declining society, not an improving one. The primary thing people have to do is produce at least what they consume. Sorry, any living entity has to do that, humans are no exeception. To the extent educators are selling students on “growth” they’re harming them, not helping them.
Chipmunk
Thank you for explaining to me how the real world works, oh wise small rodent of the forest.
But you misunderstand. My critique of our educational model is based on its failure to function well in preparation for the working world.
You see, if you weren’t so busy collecting acorns, you would have noticed that the working world has changed. Schooling no longer has a function of creating workers for an industrial workplace where following instructions dutifully is the primary skill necessary. Now society and the workplace both need independent thought and initiative is a critical skill.
I’m talking about how the educational model can help students to learn better about how to be lifelong learners. There’s a fairly solid literature on the importance of metacognition. It actually helps people to learn more content in the long run, as well as help them to be better learners.
> The system we have suffices to achieve that when people use it for that purpose.
I have to say it’s impressive to find someone these days who thinks that our educational system suffices.
> Personally I think it’s unfortunate that so many people in academics and education have lost sight of the fact that education is a functional necessity.
This is what it’s always about for you. Pretty much every comment is about your agenda, trying to disabuse lubrulz, egghead academics, etc. of their silly ideas about “how the world works.”
> The foo foo growth thing can come a long as a free benefit but when it becomes the purpose of education it will lead to a declining society, not an improving one. The primary thing people have to do is produce at least what they consume. Sorry, any living entity has to do that, humans are no exeception. To the extent educators are selling students on “growth” they’re harming them, not helping them.
Pick up a book, and read about what’s out there in the literature on educational psychology and epistemology. It’s an imperfect literature but it’s a place to start in understanding this stuff. It’s not enough to just have a political grudge and an agenda and then reverse engineer reality from that starting point. It’s like you’re tying to fit 10 lbs. of shit into a 5 lb. bag. It doesn’t work.
Competition exists whenever there is not enough of something to give it to everybody who wants it. The method of settling that competition may be based on some kind of merit or quasi-merit based ranking. It could also be settled by a lottery.
There are not enough desirable jobs or spots in graduate and professional schools to go around. If schools do not provide usable information about how the applicants perform, there are consequences. I once served on a committee to select the incoming class of resident physicians for a hospital department I worked in. This was back in the late 1970’s when many medical schools had changed their grading to pass-fail (and almost nobody ever fails). Most of those medical schools compensated for this by using coded language in their deans’ letters of recommendation–this coded language happened to have enough gradations to be similar to a traditional letter-grade system. Some medical schools, however, did not do that. You might try to read the tea-leaves of their letters of recommendation to get an idea of how that applicant had performed, but it was difficult at best. At our hospital, the graduates of such schools weren’t given serious consideration unless they had actually done an elective rotation with us–in which case we had our direct observation to rely on.
My point is that some kind of ranking and selection is inevitable, and it is best to do it with the best information available.
So we should try to develop better grading systems, systems that are more valid assessments of what students know and can do. Grading on a curve, or any other kind of norm-referenced system, on its face, and in fact, fails to accomplish that. Criterion based grading is the way to go. If everybody in the course has truly mastered the material, there is no reason not to give everybody an A. And if nobody has, there is no reason to give anybody an A.
Of course, for many things, criterion based grading is difficult to do. When faculty make up their own exams, they generally lack the skills to assure the proper validity and calibration of those instruments. Even when the faculty have those skills, often the sample of students they assess is too small to carry out a decent psychometric assessment of the test. It would really be helpful to have validated and calibrated tests for courses that many students take, professionally curated and maintained. We have that now in medical education: core courses use “shelf exams” developed by the National Board of Medical Examiners. Not to mention Steps 1 and 2 of the US Medical Licensing Examination that are taken in the middle and near the end of medical school to provide a uniform, criterion-based assessment of performance.
It would be nice if something like this were available in more educational areas.
Clyde –
I wrote an overlapping comment that posted just one minute after yours did!
> My point is that some kind of ranking and selection is inevitable, and it is best to do it with the best information available.
Sure. But “ranking” needn’t be the engine that drives our educational model.
I once got a job at a brand new high school that was part of the “Coalition of Essential Schools” system – dedicated to educational reform.
The idea was to implement a radically different model. I’ll never forget the first day of planning meetings, before the first day of school. We were discussing all these cool ideas about how to organize a new model. And it quickly became apparent that essentially everyone else in the room just assumed that a standard method of norm-based grading was a critical part of the program. My heart sank, because as I said in think norm-based grading is the engine that drives a more conventional model. Much of the other changes, while the looked very different, were really more or less window dressing in comparison.
For situations where ranking is critical to the goal, rank. But don’t make ranking the goal of the educational model.
Then there’s Monopoly, which was designed so that the first mover eventually grinds everyone to death under the burden of Ricardian rents… https://en.wikipedia.org/wiki/History_of_Monopoly
Then there’s academia where you can win by cheating, making up data, plagiarizing, knowing the right people, going to the right schools, ignoring criticism, tormenting executioners, and sometimes by merit.
You’re doing it wrong – in academia you execute your tormentors.
This issue is actually being studied by games makers. On a flight I sat next to a guy, a PhD in psychology, who works for a game making company and looks at the design elements that make game situations exciting and compelling. The flight was 150 minutes long, and he drank three bloody marys in the mid afternoon. I figured that he was drinking to overcome the fact that he uses science to make screen games more addictive for teenaged boys.
Badminton used to have the best[*] scoring system (until they ruined it in the name of unnecessary modernity). Games to 15 points, points won on serve, except if you tied at 14-all there was an option to reset to win at 17. This meant a good player could always overcome an early run of bad luck, and even at 0-14 you could still come all the way back and win as long as you avoided losing two points in a row. Now they just count points regardless of who serves, the winning threshold is 21 (but must win by 2 or be the first to reach 30). So if someone gets ahead by a few early, say 8-2, that’s pretty much the ballgame, because you would need a better than DiMaggio level statistical improbability to come back from 0-20, and quite often the games get less interesting as they progress.
[*: I might be a tad biased]
I’ve never thought of that as a tactic in Scrabble, but why not – “if you’ve got it flaunt it” – can imagine it could be quite a distraction for your opponent.
The original Mario Kart gave better weapons to whoever is behind. The internet calls it “rubber-banding”.
“Bell says the idea is a lot like the way that Mario Kart gives players falling behind in the race the best power-ups, designed to bump them towards the front of the pack and keep them in the race. Meanwhile, faster players in the front don’t get these same boosts, and instead typically get weaker powers, such as banana peels to trip up a racer behind them or an ink splat to disrupt the other players’ screens. This boosting principle is called “rubber banding,” and it’s what keeps the game fun and interesting, Bell says, since there is always a chance for you to get ahead.”
https://www.bu.edu/articles/2021/could-mario-kart-teach-us-how-to-reduce-world-poverty-and-improve-sustainability/
n.b. – No. No Mario Kart cannot teach us how to reduce world poverty. Still fun though (Mario Kart, not poverty).
Not really rubber-banding, but an element of randomness in the game can help.
Playing chess against someone who is better than you is thankless. You’re going to lose every time.
Playing backgammon against someone who is better than you is still interesting. On average you’re going to lose, but on any given game you might get lucky.
Some games, like Go or Golf, also lend themselves to handicapping to keep things even. That can greatly increase the distribution of (relative) opponent quality that maintains a fun game. Thought that is not exactly the kind of thing Andrew is talking about here, which is more about incentives to keep playing within-game once the balance swings, and not to re-balance the game from the start.
Robin:
You say, “Playing chess against someone who is better than you is thankless. You’re going to lose every time.” That’s not true! Sure, if I play chess against E. J., I’ll lose every time. But against Phil, I’ll win one game in four.
I will say, though, that playing chess against someone who’s a bit better than me feels different than playing against someone who’s a bit worse, even if the moves of the game end up being the same. Expectations matter.
Consider a multi-player game that has the following two properties: i) some possible actions target/penalize specific other players (e.g., placing the robber in Settlers of Catan, attacking somebody in Risk), ii) progress towards victory is public. This combination should automatically lead to some degree of catch-up, since trailing players are incentivised to target leading ones. If this is combined with a positive feedback mechanism for progress towards victory (as in engine-building games), then there is a nice basis for satisfying games involving both crushing victories and dramatic comebacks (though it always depends on a careful balancing of the elements).
Some games (Jaipur) do the tennis scoring where you play best 2 out of 3 or whatnot. But that really only works for short games.
Other games (District Noir, 7 Wonders Duel) go with multiple win-conditions. For example, they might have a point system where the most points wins at the end of the game, but also say that a player instantly wins if they collect 3 copies of a special card. So even if you feel you’re hopelessly losing by points, you can still often go after an alternate win. Chess kind of does this since even when you’re down pieces, you can often keep looking for some clever mate.
While I feel this is easier to design in 2-player games, some other examples would be QE and Warewords.
In QE, spending money earns points, but the player who spent the most money by the end auto-loses, and spending is mostly private information. In Warewords, the team that wins at the main task of guessing the word usually wins, but the losing side is still given a single last chance to win.
As others have said, most games include rubber-banding, where those who are behind are given some advantage to help them catch up. But like you said Andrew, it risks taking the fun out of the game if good play is not adequately rewarded. I think this is where the time-consuming task of play-testing and balancing come in.
One mechanic that can work well to endogenously deal with this is social stuff like trading or choosing who to attack. Players can go after who is winning or choose not to cooperate with them. However, I find this can backfire if the mechanic is too powerful and there’s no incentive to be a runner-up. Perhaps my least favorite game, munchkin, can last forever as everyone just saves up to kill whoever is about to win.
Also, most board games are POMDPs. Designers get to play with both how much the world can shift with time, and how much players know about the current state of the world There’s a significant difference between not knowing whether you’ll maintain your lead and not knowing if you’re even in the lead.
I think there needs to be some element of randomness and multiple paths to win. I think that is why fantasy sports are so popular.
Hmm, how about a game where you as you progress you win spaces on a Roulette wheel. At the end of the game the wheel is spun* to determine the winner. Incentives remain constant throughout the game independent of whether you’re ahead or not.
*Better would be a final battle which is not entirely luck-based.
“From Games, Gods and Gambling ISBN 978-0-85264-171-2 by F. N. David:
“In ancient times there were games played using astragali, or Talus bone. The Pottery of ancient Greece was evidence to show that there was a circle drawn on the floor and the astragali were tossed into this circle, much like playing marbles. In Egypt, excavators of tombs found a game they called “Hounds and Jackals”, which closely resembles the modern game “Snakes and Ladders”. It seems that this is the early stages of the creation of dice.The first dice game mentioned in literature of the Christian era was called Hazard. Played with 2 or 3 dice. Thought to have been brought to Europe by the knights returning from the Crusades.Dante Alighieri (1265-1321) mentions this game. A commentor of Dante puts further thought into this game: the thought was that with three dice, the lowest number you can get is three, an ace for every die. Achieving a four can be done with three dice by having a two on one die and aces on the other two dice.[2]: 293–4
…
…”the same problem as Cardano’s, Galileo had said that certain numbers have the ability to be thrown because there are more ways to create that number.[2]: 302 ”
https://en.wikipedia.org/wiki/History_of_probability
Code.
Play hazard online (free and open source).
https://mrieppel.github.io/hazard/
> I remember my dad saying that he preferred tennis scoring (each game is
> played to 4 points, each set is 6 games, you need to win 2 or 3 sets) as
> compared to old-style ping-pong scoring (whoever reaches 21 points first,
> wins), because in tennis, even if you’re way behind, you always have a
> chance to come back.
Table tennis used to be best-of-five games or best-of-three games with each game to 21. You could come back in a game, even if you were far behind. And, I’ve lost a lot of matches where I won the first game. Some years ago, they changed it to 11 points. (Serve alternates every two points instead of every five.) I think this was because they felt that the end of a game was more exciting than the beginning or middle. Now, we play best-of-seven games or best-of-five games. They also added a rule that lets players call a time-out. In the old days, we’d say this was to give more commercial breaks.
Back when they changed the rules, I wrote a little article comparing the various match formats: https://www.davidmarcus.com/Eleven.php
A lot of “worker management” games are incredibly boring cause the scoring is so convoluted I can’t even track who’s winning, especially after a few beers. I like simple win conditions like in Risk. Ticket to Ride has scoring with possible come from behind which I think is about the maximum scoring complexity that is still fun.
Timers are a good way to add excitement like in sports. Tends to work better with party game genre though.
I’ve always said I love games because of probability and I love probability because of games. If there’s not some element of probability in the game, it’s just not as fun to me. Collectible card games are the best. Star Wars Destiny being my favorite
Yeah, Ticket to Ride is great like that. Misdirection of your opponents is key. My favourite game.
Expanding this beyond games, this is a relevant issue for seasons too. A Major League Baseball team plays 162 games in a season; the players get two days off per month during the season. A team can be pretty much hopelessly out of contention after 120 games, but the players still have to get out there for another 42 games and put in a professional effort. Supposedly it can be pretty hard to get psyched up to play out the string.
On the one hand, there’s quite a bit of randomness in a baseball game, so it can take a lot of games to separate the teams. That argues for a long season, if you want a high chance that the better team comes out on top. On the other hand, in recent decades that long season has led into short playoff series in which there’s a good chance the better team won’t win. From a sporting perspective that doesn’t make a lot of sense: they should shorten the regular season, and play longer series in the playoffs. But I guess that doesn’t make sense financially: all the non-playoff teams would only be selling home tickets for 70 games (or whatever) instead of 81.
I know someone else will mention these words if I don’t, so here they are: “Miracle Mets.”
Marvelous Marv Throneberry
The randomness occurred every time a ball neared first base (where he played). Too much randomness if you were a fan – except when a team loses 120 games in a season, you need some excitement.
They could also go with relegation along with shorter regular seasons and longer playoff series’, but would prolly be too radical. Although they did make big changes recently.
Basketball has an even bigger structural problem that way, with so many game played and so many injuries that result and keep the players that people want to watch out of many games. Shorter seasons would work but no one wants to give up the revenue. The in-season tournament was a good innovation but doesn’t address the long season problem.
Sports betting is so huge now. I find it troubling given the problem of gambling addition, but it’s hard to fathom just how influential it is. I’d have to imagine somehow that influence will become more evident in how issues like this are addressed.
Sports betting… yeah, it’s huge now. I guess that’s one more type of transaction the internet has facilitated. I certainly understand the appeal of the occasional friendly wager, I’ve made them myself, but regularly betting on a whole bunch of games is something I don’t get, the same way I don’t get the appeal of monster trucks or playing golf every day or lots of other things. Different people like different things, sure, but usually I can understand why someone might like a thing, even if it’s something I don’t like myself. In this case I’m a bit baffled.
I think the primary reason for differing numbers of games/matches in a season is not statistical convergence but rather the recovery time for different sports. In (American…I see you, Robin!) football, you spend about 30 minutes beating up your opponent, so you need to wait a week to do it again. Basketball and many other games mostly involve running around intensely for a while, with recovery time of a couple of days, depending on the length and intensity of running. Then there’s baseball, which consists mostly of standing around, with some optional chewing. As Ernie Banks used to say, “Let’s play two!”
A novel which, for me, captures the feeling of game-playing as a competitive obsession is “The Player of Games” by the great Iain Banks (RIP).
It may be interesting to look at the earliest known game. The rules have been reconstructed from tablets dated 2k+ years after the first gameboards have been dated, but here is what people came up with:
https://en.wikipedia.org/wiki/Royal_Game_of_Ur#Play
From that it sounds like early games were close to your second extreme:
So I’d guess the asymptotic solution is start from randomness then work towards a deterministic outcome (depending only on initial conditions), repeat until a balance is achieved that is enjoyable for the most people.
Another thing is apparently “reduction of choice”. Ie, the choices offered to the player should decrease as the game progresses. This actually sounds a lot like the above idea of how to develop a game: Random -> deterministic.
I was actually talking with a friend about this the other day, but can’t find whatever their source was for this concept at the moment.
Then there’s Go, which is altogether another kettle of fish entirely.
Unlike the “board games”, whose interest lies in the complexity of the rules, Go can be described, correctly, with three rules.
But since counting at the end is a pain, there are a multiplicity of methods to make that easier, and all of them end up requiring large numbers of additional clauses. And since the player who moves first has an advantage, said player is required to win by a certain amount. And that adds more clasues. And more arguments about what’s the “right” fudge factor.
Anyway, Go is different from Chess in that there’s a handicapping system that really works (in that one is still dealing with the same openings and strategies; it’s still Go.). The weaker player starts out with an advantage and desperately tries to avoid getting snookered, and the stronger player gets to show off his snookering abilities.
The current round of Go programs are very good at estimating how the game will turn out assuming ridiculously good play on both parties’ parts. So playing a handicap game with a program is depressing, as it’ll tell you how much your lead is decreasing at every move…
Just to comment on the very basics of this:
> Consider two extremes:
> 1. One player gets ahead early and then can relentlessly exploit the advantage to get a certain win.
> 2. Nobody is ever ahead by much; there’s a very equal balance, and the winner is decided only at the very end by some random event.
Alternatively, the winner may be decided at the end by an event that is not so random, i.e., one can get themselves in a good or not so good position for the final event, and also it may require much skill and not luck, but still it would be open for a long time who wins because things that happen earlier have a rather small impact, at least as far as openly measured/counted.
And the current position may depend to a large extent on hidden information, i.e., players may know what counts for themselves but not for the others, so that even though the game may in principle be decided early, players only see this at the end. (Of course if there is no random element some players may analyse well enough to understand what happens even if not open.)
The old complex tabletop game Dune had different player roles with different abilities and also some had different winning conditions (this kind of thing is still around), and the Bene Gesserit could write down in the beginning a prediction which other player would win in what round, and if this happened, actually the Bene Gesserit themselves would win. Genius idea (it also meant that if somebody else was going to win, and you were predicted by Bene Gesserit, they would suddenly help you big time, and sometimes you could win one round earlier or later than predicted by them, so taking the profit yourself)!
Game designer/researcher/teacher here 👋.
The standing term for what you are looking for is “game balancing”.
Some good resources:
1. Ian Schreiber & Brenda Romero’s Game Balance (https://www.routledge.com/Game-Balance/Schreiber-Romero/p/book/9781498799577).
2. George Scaff Elias, Richard Garfield (creator of Magic: The Gathering), and K Robert Gutschera’s “Characteristics of Games”, especially chapters 4 (Games and Systems) an 5 (Indeterminacy): https://mitpress.mit.edu/9780262542692/characteristics-of-games/
For inspiration, chapters 5 and 6 of “Building Blocks of Tabletop Game Design: An Encyclopedia of Mechanisms” may also be a worth a look.
One design ideal/practice in many “eurostyle” board games where you build an economic system (think Settlers of Catan) is to identify and tune positive/negative feedback loops in resource accumulation: you want to give people the good feeling of progress and being able to do/grow more and more, but you also don’t want runaway leaders/laggards due to early luck/decisions.
Mechanics to fix that include resource sinks, nonlinear price curves and/or catch-up mechanics (“Hare & Tortoise” is famous for those). Another thing to balance is the lumpiness/impact of individual game choices and resultant volatility/”swinginess” of gameplay: if actions have a chance to produce a very large effect relative to the average score spread between players, that means even a very far behind laggard has some chance to catch a lucky break and catch up again. Make it too swingy/volatile, however, and that undermines the perceived value of strategy/skill in building up a lead.
Tooting my own horn, we tried to reconstruct a plausible predictive processing/prediction error reduction account of why uncertainty is engaging: https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2022.924953/full
Much of the discussion here seems to imply that there is some optimal position-time-payoff probability space for a game but really it all depends on the experience the game is trying to elicit.
Most games want players to feel like they have meaningful choices which is why it is popularly considered bad balance to have a winner decided too arbitrarily (due to chance) or too early (due to a runaway cumulative advantage). That said, there are games that violate this balance principle yet succeed in creating enjoyable experiences. Tales of the Arabian Nights (https://boardgamegeek.com/boardgame/34119/tales-arabian-nights) approaches Candy Land levels of arbitrariness but delights many players with the absurdist stories it spins.
The (in)famously brutal Agricola (https://boardgamegeek.com/boardgame/31260/agricola) is about subsistence farming, has no catch-up mechanisms at all, allows players to have essentially 0% chance of victory by the midgame, yet captivates players by allowing them to build adorable bespoke farms that belie the oppressive conditions the players had to overcome.
You might enjoy this design diary about victory conditions from a respected contemporary designer, Cole Wehrle: https://boardgamegeek.com/thread/2335197/designer-diary-8-destinations-and-paths-victory-pa
It argues that carefully designing the relationship between uncertainty, advantage, and victory is a powerful way to achieve a specific tone. The Napoleonic Wars for instance, is a complex, calculative war game yet its ending is determined by a simple die roll which evokes “the absolute the terrifying sense of political uncertainty… associate[d] with the Romantic Era and Napoleon in general”.
One of my favorite ways of meeting the design goals you enumerated at the bottom of your post is to allow for a moderate level of player interaction in the form of resource sharing, trading, and temporary alliances. In games with more than two players, this allows the losing players to try and innovate cooperative deals to reel the leaders back in. If cooperation is too easy however, you run the risk of “bash the leader” dynamics which are often unpopular among contemporary board gamers. Here is a great design article on positional balance with more details in this vein: https://www.gamesprecipice.com/positional-balance/
(You may well find other articles on that site useful.)
Another important consideration could be “mercy rules” that keep your game from dragging. If a player plays well and consequently gets a big lead, sometimes that’s just the story of the game and not a problem to be fixed. But its often good to ensure the game ends quickly after this position has been established
I would be interested to hear more about this game in the future!
“but really it all depends on the experience the game is trying to elicit”
This got me thinking that there is a lot more than balancing uncertainty and motivation, and more than the experience a game is trying to elicit. More generally, what is the purpose of the game? Some games are designed for entertainment/enjoyment, and most of the comments here seem focused on that. But sometimes games are designed to educate or transform users. Sometimes there is a conflict between what users would enjoy and what the game designer wants to achieve. Many of the violent video games may be quite enjoyed by users, but (arguably) can promote violence. I have used games/simulations a lot in teaching. In business courses, there are many that emphasize competition, not as many emphasizing cooperation. The objective of the experience should (in my mind) aim for a balance between the 2. Quite possibly, the resulting game may be less enjoyable for students than one that purely sticks to one goal.
Many of the comments raise complex issues about game design – and these arise even if the goal is the “simple” one of maximizing the users’ enjoyment of the game. Once we expand the goal to include the game’s impact on the evolution of the users themselves, then it becomes even more complex. The same might be said for any educational endeavor – designing courses for example (suggested in the above comments regarding evaluation of students).