# Bottom-Up Scoring

Len Stemberger is a designer in the North Houston design group. He is currently developing an area control game which features marker manipulation–placing and moving markers.  His core engagement is to keep players constantly jockeying for position in as many areas as possible at all times.  With this core engagement in mind, we began looking for the best scoring mechanism to serve it.

As we bounced various ideas around, we hit upon a mechanism which was entirely new to me and darned interesting–a system that scores both upwards and downwards.  We provisionally named it “bottom-up scoring” and decided to share it with you.  We hope it gives you an interesting tool to work with.

Bottom – Up Scoring

Area majority games generally score downwards. Awards are passed out by looking at first place, then down to second place and so on.  Bottom-up scoring does some of that.

Set collection games generally score upwards. Increasing your set increases your reward.  Bottom-up scoring does some of that too.

The first step to creating a bottom-up scoring scheme is to select a top-down scheme as you might for any other area majority game.  For our example, I’m using an exponential scheme.

 First Place 8 points Second Place 4 points Third Place 2 points

In most area-control games, the first time a player placed a marker into an area, he is considered to be in first place.  He essentially occupies the top spot.  If scoring occurred with only his marker in the region, he would receive the best possible award for the region.

Example: Danielle has a cube in the green region and it scores.  Since no other cubes are present, Danielle scores first place, 8 points.

In Len’s game, area manipulation and scoring each occur on every turn.  This is important to understanding why how we arrived at our new scheme.

Our concern centered on the massive start-player advantage that occurred when the start player placed a marker into a region on his turn and then immediately scored that region–He would get the first place prize simply for going first!  That sat well with none of us.  We needed a different plan.

In our bottom-up system, the first time markers are placed into an area, they are thought of as beginning construction in that area, only just beginning to improve and expand the area.  The player who placed these markers essentially occupies the bottom spot. When scoring occurred with only her markers in the region, she received the worst possible award for the region.

Example: Danielle has a cube in the green region and it scores.  Since no other cubes are present, Danielle scores third place, 2 points.

Massive holdings in an otherwise empty region are no better than a single cube in that region–like having the best castle in Boise, Idaho.  This is better than no award at all of course, but no longer so massive an award.

Example: Danielle has five cubes in the green region and it scores.  Since there are still no other cubes present, Danielle scores third place, 2 points.

Now in order to reach high awards, the player must work for majority in popular regions.

Example: In addition to Danielle’s five cubes, and Dean has two cubes and John has 1 cube.  When the region scores, John scores third place, 2 points. Dean scores second place, 4 points. Danielle scores first place, 8 points.

Working for majority in popular regions puts players in conflict throughout the game.  Putting players in conflict throughout the game increases player interaction.  Increasing player interaction increases engagement.  Delivering engagement is what games are all about.  We were looking at a winning scheme.

Tie Breaking The Bottom-Up Scheme

Having established the basic structure, we immediately moved on to debate the best tie-breaking scheme for Len’s core engagement.  Our best suggestions fell into three general categories.  Rather than asserting which is best, here are all three.  Each had its merits, depending on the spirit of the game and playtest data.  Len wisely decided to collect more data before making any final decision.

First in wins.  Markers placed later are considered to fall behind those placed earlier.  The only way a later player can get ahead is to exceed the previous count. This is generally best if the game has a start player disadvantage.

Last in wins.  Markers placed later fall ahead of those placed earlier.  A later player can get ahead by tieing the previous count.  This is generally best if the game has a start player advantage.

Friendly ties.  Tied players each get a full share of their position’s award.  This is generally best if there is no discernible advantage associated with the order of play.

Have you designed an area-control game? How did you award points?  How would Bottom-up scoring have changed the dynamics of your game?  Share with your fellow readers in the comments below.  And if you’re enjoying what you’re reading, create and account with WordPress and follow this blog.  If you keep reading, I’ll keep writing.

# Asymmetrical Suits in Card Games, Part 3

Our last column looked at several hypothetical cases to illuminate the proper use of asymmetric card decks.  In this column, we look at four examples which are not at all hypothetical. These are published games which feature asymmetry.  I found that each one found an interesting way to make asymmetry serve its core engagement.

Rocket Jockey

James Spurny’s Rocket Journey casts players as tramp freighter captains delivering goods from world to world within our solar system. At its heart, Rocket Jockey is a rail game in the “elaborate = better” tradition. Players make these deliveries inefficient to earn more points.

Early in the game’s development, Spurny decided that the back story of the game should center space development around Earth. For this reason, he concentrated the game cards around Earth. Earth cards are the most common.  Venus and Mars are second-most common. They drop off steadily from there.

James Spurny used asymmetry to support his game’s setting and to concentrate player focus.

Piñata

Stephen Glenn’s Piñata–first released in 2003 as Balloon Cup–uses complementary asymmetry to balance player decisions. The rarest commodity has only 5 cards but only requires that you collect three of it to score a trophy.  The most common commodity has 13 cards but requires a comparatively massive 7 cubes to score a trophy.  Piñata pushes this asymmetry further with the inclusion of 10 wild cards.

Should you collect common goods, knowing that you’ll need many of them?  Or should you focus on the rare, hoping for a quick win? Stephen Glenn used asymmetry to put players in a quandary.

Lord of the Fries

From the 1996 through 2006, James Ernest helmed Cheapass Games. CAG released a number of excellent games. One of his best was Lord of the Fries. LotF is a hand management game. Players worked with hands of ingredient cards to supply customer demand at a Friedey’s, the fast food restaurant chain in hell. Like Glenn, Ernest uses rarity to imply value.  The common and lowly 14 buns score only 1 point each while the delicious but rare 4 Berry Pies clock in at 6 points each.  Of course, Earnest also made it pretty easy to score those buns and difficult to score the berry pies.  He’s sneaky like that.

James Ernest used asymmetry to keep players looking for the most valuable options.

As an aside, Cheapass Games began releasing new titles in 2011.  Like their classic counterparts, you will be happy you checked them out.

Magic: The Gathering

It’s been more than 20 years since Richard Garfield’s idea to meld trading cards with gameplay hit store shelves.  There are many reasons for its enduring popularity. Player-controlled asymmetry is one of the best.  By allowing each player to construct her own deck, Garfield empowered players to create their own asymmetry.  Players are limited to 4 of each card which is not a basic land but even within this restriction there is plenty of room for the active deck constructor’s play. Cards that formed the backbone of your deck appeared the full 4 times.  If you wanted a certain card for emergency assistance, you might choose to include only a single copy of it.

Richard Garfield used asymmetry to empower his players.

There are a great number of ways in which asymmetry can boost your designs.  Consider the achievements of Spurny, Glenn, Ernest, and Garfield.  Then add your name to that list.

What do you think of these examples?  Do you know another which should have made this list?  Share them with your fellow designers in the comments below.  And if you’re enjoying what you’re reading, subscribe.  It makes a big difference.

We will be together again in three days to take a look at game design conferences and how to get the most from them. See you Friday!

# Ties, Damn Ties and Statistics, Part 6

Last time, we looked at schemes for scoring sets.  Each scheme has its own advantages and disadvantages.  Putting these schemes side-by-side will enable us to identify those qualities and how they can serve our core engagement.

Comparing The Schemes

It is important to understand first that these schemes tend to change character as the size of the sets increase.  Schemes which award the highest points for large sets frequently award the low points for small sets.

If players in your game only collect small sets of widgets–four or five at most–these are the numbers you’ll need to look at.  Today’s column centers on small set scoring.

If players in your game can collect small sets–sets of ten, twenty or more–you’ll need to look at those instead.  Our next column centers on larger set scoring.

A Mathematical Caveat

Designers must know when to obey the algorithm and when to diverge. Mathematical purists will notice that I’ve taken a particular liberty with two of these formulas. This was done to maintain standard scoring conventions.

An exponential doubling scheme that values a collection containing only single widget at 1 point would value an empty collection at ½ point.

Similarly, a strict Fibonacci series would value the an empty set of widgets and a set containing only a single widget both at 1 point.

Awarding points to empty sets is counterintuitive for most players. Furthermore, players should sense progress at every gain.  I therefore adjusted the numbers of these schemes so that sets with no widgets would score 0 points in all cases.

Valuing Small Sets

Here is a diagram comparing the value of the scoring schemes at low quantities of widgets.  For the linear scheme, I’ve valued each widget at 3 points each.  For the exponential scheme, I’ve chosen a doubling scheme.

This graph lets us quickly see several facts and consider their application:

A) Nonlinear schemes all start out below the linear scheme. Most catch up with or exceed it by the time the player has 5 widgets in her set.  Because each widget is worth the same as every other widget, the linear approach works best in games that make each widget no more difficult to acquire than the one before it.

B) The squaring scheme is the most explosive in the short run.  It matches the linear scheme at 3 widgets and is roughly twice as valuable as any other scheme by 5 widgets.  Because of this explosive quality, squaring schemes should be kept to games that also make it very challenging to get large sets.

C) Exponential scores are only slightly smaller than triangular scores in the short run.  If you have chosen one of these two and it isn’t quite working, consider replacing it with the other.

D) Fibonacci scoring is the slowest in the short run.  It drops behind at 3 widgets and never catches up.  This turns out to be an ideal scheme for games that have steady difficulty. The importance of gaining each new widget increases while the challenge remains steady creates excitement and competition as any game proceeds.  Fibonacci scoring increases relatively slowly; this enables you as the designer to build that player engagement while keeping scores under control.

Personal Preferences

Among all schemes, I have a particular fondness for exponential doubling.  Notice that at low quantities, it is the slowest of the growth models but it overtakes the others over time.  This delayed explosion has always intrigued me. This approach is particularly effective if the game has been designed to make each widget increasingly more difficult to acquire than the one before it.

How about you?  What is your favorite scoring scheme in the short run and why?  Please share with your fellow designers by adding it to the comments below.  And if you’re enjoying what you’re reading, subscribe to this blog.  It makes a big difference.

In four days days we compare these schemes again, this time with larger sets.  See you Tuesday!

# Ties, Damn Ties, and Statistics, Part 5

Previous articles in this series addressed games that rewarded players for their position; schemes for scoring first place, second place, etc.  Those articles supposed that scoring comes in in discrete packets which are more-or-less independent of one another. Painting the northwest section of the Chapel ceiling is worth the same 10 points regardless of what other sections you completed.  Coming in first in the 100 meter dash awards the same gold medal regardless of your performance in the relay.

To examine those games, we set aside set collection games.  Now is the time to give them our attention.  These games award points based on quantity rather than position.  In these games, the player is asked to gather sets of chapel paintings, Olympic medals, animals, gems, stocks, widgets or the like. These sets are then evaluated and the player earns points for each set.

Linear Scoring

This is the simplest scoring system for set-collection.  Under linear scoring, each object in the set is worth the same amount of any other.  The first is worth the same as the second is worth the same as the third and so on.  For example, widgets might be worth 3 points each.  If you have 6 widgets then you score 3 x 6 = 18 points.

Square Scoring

Under a square scoring system, widgets earn points equal to the square of the number in the set.  Each widget is worth more than the previous one.  The first is worth 1 but the second is worth 3 (making the total value of the set equal 4) while the third is worth 5 (9 total), the fourth is worth 7 (16 total), the fifth is worth 9 (25 total), and so on.

Triangular Scoring

Increasing the value of each widget over the previous is a good thing.  It makes player interest (and therefore competition) increase at every step.  The square scoring system can be problematic however because scores can get big quite rapidly.

For this reason, many eurogame designers employ triangular scoring instead.  Like squaring, triangular scoring values the first widget in the set at 1 but the second is worth 2 (making the total value of the set equal 3) while the third is worth 3 (6 total), the fourth is worth 4 (10 total) , the fifth is worth 5 (15 total) and so on.  Triangular scoring keeps the value of each widget increasing but at half the rate (for the mathematically curious, the slope of square scoring is 2n while the slope of triangular scoring is n + 0.5).

Exponential Scoring

Under an exponential system, each additional widget multiplies the total value of the set by a fixed value.  For example, imagine a system in which each widget doubles the value of the set.  The first widget is worth 1 and the second is also worth 1 (because the set value doubled from 1 to 2). The third widget is worth 2 (2 doubles into 4).  The fourth is worth 4 (4 doubles into 8).  The fifth is worth 8 (8 doubles into 16).

Exponential schemes can feature multiplication by any number to make their rate of growth accelerate or decelerate as needed.

Fibonacci Scoring

Every lover of mathematics knows the Fibonacci sequence.  Despite this popularity, it seldom makes an appearance in scoring systems.  Under a Fibonacci system, each quantity is worth the value of the previous two sets.  You as the designer must choose a value for the first two quantities.  The Fibonacci algorithm takes over from there.

For example, you may have set the value of one widget at 1 point and a with two widgets at 2 points. Fibonacci scoring then makes a set of three widgets is worth 1 + 2 = 3 points (the third widget is worth 1 point, the value of the first set).  A set of four widgets is worth 2 + 3 = 5 points (the fourth widget is worth 2 points, the value of the second set).  A set of five widgets is worth 3 + 5 = 8 points (the fourth widget is worth 3 points, the value of the second set) and so on.

I have seen Fibonacci scoring systems employed only occasionally by game designers.  This is a type of scoring that would benefit from further exploration, I believe.

How about you?  Do you have a favorite scoring system for set collection?  Please share it with your fellow designers by adding it to the comments below.  And if you’re enjoying what you’re reading, subscribe to this blog.  It makes a difference.

In three days we expand our examination of set collection scoring systems by comparing and contrasting each of today’s systems.  We will look for their best applications and look for opportunities to blend them in the same game.  See you Friday!