The focus is on game mechanisms - what makes a game exciting and why. How did the board game designer make his game fun? Components and theme are secondary. The play's the thing.

Monday, April 03, 2006

101 Ways to Score - The Art of Scoring Part 2

Printer friendly

All our talk in the first part of this article, "The Art of Scoring", has covered 3 narrowly defined ways that strategy board game designers have used to provide focused efforts with disproportionate rewards: majority bonuses, triangular scoring, squared scoring. What does a designer do when he wants to get a little creative? It's a tough problem because at first blush, there aren't a lot of choices out there, apart from just creating a table. But sometimes the above 3 ideas aren't quite what the designer wants - either because it doesn't provide the proper reward and incentives, or it's too cumbersome, or... he just wants to try something new.

After the triangle numbers (1,3,6,10) and the square numbers (1,4,9,16), the most obvious mathematical progression is exponential - especially doubling: (1,2,4,8). I'm aware of only one game that uses this: Palmyra, reissued as Buy Low, Sell High. The game was introduced in 1996, the scoring system was used in the value of contract cards, it seems to have never been used in any subsequent game, and it works poorly. At the low ends, the rewards are too slight and at the high ends the rewards are too great. Specifically, in Palmyra, there is a set of four contract cards that can generate payoffs for a given commodity. Playing the second one - half of all the cards available - only gets you one point - the same as the first one got you. The third card gives you two more points - only upping the stakes by one. Only in the unlikely event that you can get all four cards down does the payoff start reflecting the effort. But if you went to five or six cards, suddenly the payoff would explode. Indeed, in Buy Low, Sell High, Knizia caps it so that another card is never worth more than 4 incremental points per share. I've never played it the following way, but I suspect the game would have been better served if those cards had paid off in a triangle progression.


In Reef Encounter, Richard Breese took one of the simplest - and extreme - approaches possible. Subtract four; only count what's left. This obviously creates a strong (actually mandatory) incentive to only collect coral tiles when you've got at least 5, and to keep on going beyond 5 as much as possible. It also helps simplify the math because each tile scored may have a base value of from one to five points. If you had to say "a five tile group has a value of 15, times its 3 point base value equals 45", you'd find the final scoring to be that much more cumbersome. But note that, in the range of tiles that people typically take in a set (5 - 9 in my experience), it's a pretty steep curve with big benefits for collecting large sets. Collecting 6 tiles is twice as good as collecting 5. Going from 7 to 8 tiles improves your score (4/3) 33%. Even in a steep "squared" system, your value only goes up (64/49) 31%, and the relative difference is greater for the Reef Encounter scoring system at lower numbers.


Some of the consideration in choosing this method, I'm sure, was just simplicity of the calculation. But some must also be an issue of what you want to reward. In the case of Reef Encounter, the rules are implicitly saying: "any dope can feed a group of four tiles to his parrotfish." The game is about the harder effort to put together a larger group, which is going to be much more vulnerable. Indeed, the game is set up so that any player can place a cluster of up to five tiles on the board that can't be attacked (because they are all adjacent to the player's shrimp). So Breese is effectively giving players credit for a single tile, and then rewarding any tiles that go above and beyond that. The Bomb is the reward for placing *vulnerable* tiles on the board, and keeping them there for at least a turn.

In Wyatt Earp, Richard Borg and Mike Fitzgerald turned the scoring problem upside down. All players who get to share in a given outlaw's bounty share it nearly equally. The magical word here is "share". The fewer people in the bounty pool, the more you get to keep for yourself. The challenge comes in the question of whose shares count. Any player who contributed points to that outlaw within five points of what the leader contributed gets his part of the take; any player who falls behind more than that is excluded entirely. This creates lots of player interaction as any player who might be leading has an incentive to try to pull more than 5 shares ahead of as many people as possible, and everyone expecting a payoff would like to kick the others out. (Hmmm. This feels more like the sort of system that the outlaws would use to share their spoils, not good law abiding bounty hunters.) Moreover, it not only encourages players to contribute points, but it naturally turns players on each other - ultimately true to its theme and its mechanics - as they throw "take that" cards viciously at each other. Sometimes it can be a little frustrating being the leader - you expect a windfall but may only get 1 more chip than others who are in the pot. But the game absolutely does provide a bomb in providing incentives to attempt to be the last man standing in the competition to lead your opponents by at least 5 shares.

Reiner Knizia put so many different scoring mechanisms in Ra that the game could fill up an article on its own. This is a set collecting game in which players are collecting all different types of sets of tiles, each type with its own distinct scoring rules. The scoring for pharoah tiles is a traditional majority system, with the additional rule that not only rewards the majority holder, it penalizes the player who takes the fewest, and thereby discourages players from simply abaondoning the pharoahs altogether. Civilizations have their own quirkiness which shows up in some other Knizia games: I'll call it a step-wise scoring in which each new civilization is worth 5 points... except for the second one. So the value of each incremental civilization is: 5,0,5,5,5. There can be any number of variations on a system like that, say: 0,5,0,5,0,5, which would be a fully step-wise system. I don't think that this system is intended to create a bomb. After all, the first civilization is worth more than the second and as much as later ones. Rather, it is intended to enable civilizations to have different values for different players. If I have a civilization and you have none, then the one that's up for auction is worth more to you than to me - and these differing subjective values help to drive what is interesting about the game. The fact that only unlike civilization tiles score also enforces the differing subjective values. Note that the second civilization isn't totally worthless to me, because if I do take it, it enhances the value of the following civilization tile that may come up. On the other hand, the scoring for monuments is absolutely a bomb, and Knizia makes it work in two dimensions, rewarding both concentration and diversity at the same time. The value of individual matching tiles is 0,0,5,5,5 - a sudden step-wise jump. The value of collecting unique tiles is 1,1,1,1,1,1,4,5. So here is a very simple, non-formulaic pattern that rewards players for concentrating in monuments generally - but gets its intrigue from the fact that players become torn between trying to diversify or concentrate within the monument strategy.

All of the scoring systems we've looked at so far have been from the perspective of how strategy board game designers use scoring systems to create bombs - which typically force players to concentrate in an effort to get ever increasing payoffs. There is another class of scoring systems that do just the opposite. They force players to adopt mixed strategies. I think that these scoring systems have a different purpose than creating a bomb. Instead, they play into the need to create agonizing decisions for the players, especially in games where going after a single minded strategy would be very easy to execute, and therefore be boring.

Note that there is an overriding plan to some of the scoring systems in Ra. They discourage players from concentrating in some areas while entirely abandoning others. For example, if you don't compete at all in Pharoahs, you're penalized 2 points each turn. If you don't take at least one Civilization, you're penalized 5 points each turn you fail. Now you have a dilemma. You'd really like to focus on the bomb of getting oodles of monuments - but you're somewhat compelled to take at least one Civilization tile each turn or else pay a steep penalty. You can't entirely abandon Pharoahs or you're going to get dinged every turn - potentially 6 points total.

Perhaps no game beyond Ra has as many competing scoring systems all inside one box, but some do reward a balanced approach. These are systems where the whole value of several *different* things is greater than the sum of the parts. I'll call these Synergy Scoring Systems.

The most obvious examples come again from Reiner Knizia (who seems to really like using scoring systems as an essential game component) in his games Euphrates & Tigris and Ingenious. Neither is particularly like a set collecting game, but both involve scoring points in different flavors (4 different colors in E&T, 6 different colors in Ingenious.) A player's final score is based on which color he has the fewest points in. So if you end a game of Euphrates & Tigris with 15 black points, 7 red points, 7 blue points and 2 green points, your final score is: 2 points. Your two green points totally overwhelm your 15 black points. The effect here is obvious - it forces you to balance the colors of points you take. In terms of game design, it is implicitly acknowledging that it is relatively easy for a player to concentrate in one or two colors, and thereby forces him to play against his strengths to score well.


In Oasis by Alan Moon and Aaron Weissblum, the designers use multiplication to create synergies in scoring. In any given color, players play square tiles on the board, and take rectangular "scoring" tiles into their hand. The score for the color is the product of the board tiles times the scoring tiles. This means that a player must again achieve a balance within a color type to maximize his score. 10 yellow board tiles and 2 yellow hand tiles are worth 20 points, but if he instead gets 6 of each they are valued at 36 points - nearly twice as much. On the other hand, a player must concentrate within colors as much as possible. If the same player had those 12 tiles divided 3 red scoring, 3 red board tile, 3 yellow scoring, 3 yellow board tiles, his score would be 3 x 3 (red) + 3 x 3 (yellow) for a total of 18 points.

The scoring for Nile and Flood tiles in Ra (you didn't think I forgot about those, did you?), while very simple, is possibly the game's most original scheme, and another example of a Synergy Scoring System. The rule is that a player gets 1 point per Nile or Flood tile - but only if he has taken at least one Flood tile in that turn. Some players may have as many as 7 or 8 Niles by the third scoring round, and boy is there a need to get that Flood. The fun here comes from the fact that to get to that point, the player has to have made an investment in the more common Nile tiles - which will not be worth anything in each scoring round that he is unable to get a Flood (the Nile tiles carry over in each round, but the Flood tiles are discarded at the end of each round.) Each Nile tile is worth from 0 - 3 points, depending on when it's acquired and depending on whether the player gets a Flood in each round, and a Flood tile's value depends on how many Nile tiles the player has accumulated; Knizia has created a tremendous amount of ambiguity and relativeness in the value of each.

The question that I have is - how does a synergy scoring system bring fun into a game? Escalating scoring brings the tension of a bomb into the game. Majorities scoring injects player interaction as well as a potential bomb. Is a synergy scoring system more than a gimmick? Of the examples we've seen above, Euphrates & Tigris, Oasis, and the flood & Nile tiles of Ra, I think each is doing a slightly different thing. The scoring in E&T is partly just a game balancing mechanism. It acknowledges that sometimes a player can have a windfall of points, and so it doesn't want to let such a player get away with an easy victory from a single stroke of luck.

There's another element, though, that I'll call (until I come up with a better name) the Tough Nut. A player has a Tough Nut when he is challenged to play against his advantages in the game. You've got a windfall of black cubes, a solid position in red and blue cubes - and no natural assets that will enable you to get more green cubes. And you've got to cobble together a plan to get those darned green cubes. Tough Nuts keep you on your toes. They force you to solve a strategic puzzle that has emerged for you, during the course of the game, as the one that is most challenging. This is one of the great gifts of Euphrates & Tigris - the challenge that each player has to dig himself out of a hole in the color he is weakest in.

In the case of the Nile/Flood tile scoring system in Ra, I wouldn't call the Flood tiles a "bomb" because you can't work toward them. Typically, you work toward collecting the 1 point Nile tiles, and pray you can get a flood in time. If anything, I think this scoring system adds a sort of gambling element to the game. You collect Nile tiles not knowing with certainty how much, if anything, they'll ultimately be worth to you. Apart from the risky element, I'm not convinced that this scoring system adds much in terms of challenging decisions. The bomb of being able to get a flood each turn can sometimes be serendipitous - although for a player who is heavily invested in Nile tiles, the challenge of bidding on a flood certainly can raise the temperature in the room. However, I must admit that I do find these tiles to be fun, and I think that they work best as one in a suite of Ra's many scoring system, and would probably not work well in isolation.
I'm not convinced that the multiplication rule in Oasis is all that effective in the context of that game. It ends up being a hybrid between an escalating scoring rule that encourages concentration and a synergistic scoring rule that encourages diversity. The problem is that there is barely any mechanism in the game that makes it difficult for a player to concentrate in just a couple of colors, so the "bomb" aspect is not that interesting. Similarly, the two different types of tiles within each single color are just part of the same pool of assets that get auctioned. There's no conflict there either. Ultimately it's hard to figure out what challenges the designers were trying to provide for the players by using this scoring system.



Finally, let's look at Web of Power, recently reissued as China. The very original scoring system here, while simple, is in a class by itself. Michael Schacht really showed how an innovative scoring scheme can help to define the game in this terrific design. In Web of Power, there are a limited quantity of total cloisters that can be played into each region. The player with the majority will score points equal to the total cloisters - his own and all others - in the region. But all players score. Any player will get points equal to the number of cloisters held in the region by the next higher player. If there are four players participating in a region, the player with the second most cloisters gets points equal to the quantity of cloisters held by the leader. Even the player in 4th place gets points equal to the quantity held by the player in 3rd place.

This creates very erratic situations in which the most efficient move may well be to end up in last place. If a region holds 5 cloisters, and another player has placed 4 in there, I can snatch 4 points with a single cloister, while the leader gets 5 points - only one more than I got! Conversely, if a region holds 8 cloisters, and the cloisters per player are 3,2,2,1, then all the players trailing the leader will get 1 more point than the number of cloisters they put in, while the leader will get 8 points for his 3 cloister investment. It's a very dynamic system in which players must consider not only their relative positions, but also how their play may help their opponents more than themselves. Web of Power also has a very clever system of scoring "advisors" in which players must at least share the majority in *each of* two adjacent regions. Here is a synergy scoring system that really creates interesting opportunities for the players. Again, the mechanic of requiring combinations of majorities is, to my awareness, unique to this game. Each region in which a player can get a majority of advisors is worthless in itself, but creates multiple opportunities in the various adjacent provinces. The smart player can string these together in a network - but the need to at least share the majority in each of these areas makes it a challenge. When Web of Power was first released, many described it as "El Grande lite", comparing it unfavorably (I suppose that depends on your attitude to "lite") to the longer and more complex game of majorities. Had this been entirely true, I doubt that this game would have had the staying power it has shown. I think that the originality of its scoring systems - notably coupled with the unique tactical considerations that it presents to players - has helped make this game a favorite in its class.

There's a saying here where I work: "your commission plan is your business plan." That's a way of pointing out that the incentives you create for your sales people determine their behavior which in turn determines which products will sell. The same holds true for games. Your scoring design is your game design. When a designer like Michael Schacht creates a unique scoring system such as the one in Web of Power, he sets into motion a series of incentives which help to define the objectives and interactions that the players will confront for the duration of the game.

In an effort to create a little "player interaction" here at the Journal of Boardgame Design, I'd like to propose a challenge to readers. What original scoring mechanism can you envision for some unknown (or known) set collecting board game or card game which would create a distinct set of tactical or strategic considerations? What sort of game would it be best suited to? Here's an opportunity to design an original game mechanism without the messy trouble of designing and playtesting the whole darned game. I take my inspiration here from Web of Power, which showed how you could tweak the traditional majorities game and create something really fresh. What else fresh is out there? Please respond in the Comments section of this post.

25 comments:

Anonymous said...

Do any games use the Fibonacci series (1, 1, 2, 3, 5, 8, 13, 21, 34,...) for scoring?

Linnaeus said...

How about a set collection game where your score is equal to the size of all of your sets multiplied together (with a multiplier of 1/2 for each zero)?

Say there are five classes of scoring objects. At the end of the game, player one has 1, 2, 2, 4, and 5, so his score would be 1x2x2x4x5=80 points, while player two has 6, 4, 4, 0, 0 and scores 6x4x4x0.5x0.5=24 points.

The math is a bit harder than in most scoring systems, but tied to the right systems for how the scoring tokens are collected it could make for some interesting strategic decisions.

Doug Orleans said...

Sid Sackson's game Venture also uses exponential scoring: the value progression for a conglomerate is 0/0/1/3/8/20. Each new company added to the conglomerate (after the first two) more than doubles its value.

Mark Johnson said...

What do you make of the competing scoring systems in Knizia's Medici? There is majority scoring in each of the commodities, but also the "biggest boat" scoring that is orthogonal to this. And then the +10, +20 rungs on the commodity ladders . . .

Anonymous said...

I love that you've added a printer friendly link. Any chance you'll retrofit the previous post, as well?

Jonathan Degann said...

I retrofitted the three main articles with links to printer friendly pages.

The way I did this was to create a new blog, jbdgamesprintable, with identical content, but with the simplest template - no links, no columns. Any comments or suggestions on ways to improve are welcome. Smaller typeface?

Grant Miller said...

The printer friendly link is very helpful. Nice blog.

nico said...

Yes, it's a nice blog.

BionicBuddha said...

A great blog site...I also have enjoyed Clue and will try to utilize the term "alternative games" whenever a suitable occasion arises.





www.bionicbuddha.com

Anonymous said...
This comment has been removed by a blog administrator.
Click here to find the power said...
This comment has been removed by a blog administrator.
Craig C said...

Nice blog. I love the Carcassone, Settlers, Puerto Rico games... I wonder why all the good ones come from Germany?

Maybe you should concentrate on a David Hasselhof game which will sell well over there? :P

SF Photorama said...

Haven't played them for quite some time...feel like playing them now. Any one want to?

Oberon said...

......i know a game in which i always win.....nobody can beat me....it is a fair game....all things being equal.....i call it fifteen......ever heard of it?

Brightons Best Pubs said...

Backgammon uses the doubling sequence with its doubling dice....

The Celloist said...

That is one of the longest posts I have ever seen...

Fabry said...

Great!

-C said...

this is so mind numblingly, unimaginably boring.

rob said...

While I am not sure exactly what any of these games are, but I can see that you have put a lot of time and energy into this, and it seems like a pretty popular blog. Of course, it also helps that blogger considers this a worthwhile read. It is definitely a niche.

All your posts are really really long, and while I did not get through the whole thing, what I read was interesting.

Ellen said...

this is amazing@!!!!!

Raghav said...

U can predict stocks using this?

Anonymous said...

anonymous,

I don't know any games using the Fibonacci series, but you might be interested in Rythmomachia, an abstract strategy piece-taking game played in the '60's. (Not the 1960's. The 1560's. :p )
It is a piece-taking game where attacks are based on the relative positions and numerical values and shapes of the capturing and captured pieces. There are elements of checkers (the "takyng" attack of the triangle during its movement) and shogi ("When any is taken captive, he must be tourned with his conquerers collor upward & placed in the hindermost space of his victors campe, and from thens being removed must fight against his conquerours enemies, and serve him also to make his triumphe.)"

http://jducoeur.org/game-hist/fulke.html

the other anonymous

Chavat said...

cool blog! keep it up!

http://www.bewickstudios.com

HumbleAuthor said...

I was going to mention Backgammon doubling dice as well, but someone beat me to it. There's also a doubling mechanism in some scoring methods for Mah-Jong, but that's more of a tile game than a board game proper. You could make an entire book about Mah-Jong scoring though.

Game geeks of the world, Und Tschuss!

Pleader said...

I just found this blog. Thankyou for sharing. Conceptually expansive.