Asymmetrical Suits in Card Games, Part 2

In our last column, I outlined many of the advantages of asymmetrical card decks over symmetrical ones.  No matter how good asymmetric designs can be, it is still possible to mismanage them. In this column, we look at several examples to help illuminate their proper use.

Scenario 1. Assigned Hands of Cards.

Imagine a card game with two suits, diamonds and spades. A Prize card is randomly drawn each round and some prizes are significantly better than others. Players simultaneously play one card from their hand, high number wins the prize that round. The diamonds are ranked 1-4 while the clubs are ranked 5-8. If one player is assigned the diamonds while the other player is assigned clubs, we already know how this will turn out. No fun for Mr. Diamond.

What if the distribution were altered? Diamonds are now ranked 3-6 while the clubs are ranked 1-2 and 7-8. One player is still assigned the diamonds while the other player is assigned clubs. Is this an improvement? Not really. The diamonds player now wins half of the prizes but is is clubs that is in total control. Ms. Club will decide which two prizes she takes and which two she she yields to Mr. Diamond. Mr. Diamond still isn’t having any fun.

Let’s interlace the suits even further. Diamonds are now ranked 2, 4, 5, 7. Clubs are ranked 1, 3, 6,8. Clubs now holds the highest and lowest cards but the middle cards have been interwoven with diamonds. Ms. Club is guaranteed to win one prize and to lose one. The other two are completely up for grabs. A good read on his opponent can allow Mr. Diamond to come out on top. Much better.

Scenario 2. Drafting Cards For Relative Rank.

Imagine a drafting game with two suits, diamonds and spades. Two cards will be put face up. Players will take turns drafting one card (alternating start player). Players want to get the best set in each suit. In our first case, the diamonds and clubs suits are each numbered 1-5. It is your turn to draft. In front of you are 3D and 3C. Which should you draft? It probably doesn’t matter. Each of these cards is equal in rank.

Now we change the suits. Diamonds are still numbered 1-5. Clubs have been changed to 3-7.  It is your turn to draft. In front of you are 3D and 3C. Which should you draft? 3D now stands out as the superior choice. It is in the middle of its suit while 3C is the lowest of the clubs. Even minor asymmetry creates texture in your decisions.

Scenario 3. Drafting Cards To Build Pairs.

Imagine a drafting game with two suits, diamonds and spades. Two cards will be put face up. Players will take turns drafting one card (alternating start player). Players want to build pairs–one card from each suit, both cards same rank. The diamonds and clubs suits are each numbered 1-5. It is your turn to draft. In front of you are 3D and 4D. Each of these cards is equally likely to form a pair.  Your decision is largely meaningless.

Now we change the suits. Diamonds are now numbered 1, 2, 3, 3, 4. Clubs are now 1, 2, 3, 4, 4.  It is your turn to draft. In front of you are 3D and 4D. Which should you draft? 4D is superior. There are two ways to pair your 4D but only one way to pair 3D. Asymmetry again adds texture to your decisions.

Scenario 4. Bidding in a Trick Taking Game.

Imagine a trick taking game with three suits, clubs, diamonds and spades. Similar to Bridge or Mü, players bid to determine trump suit.  In our first case, there are nine cards in each suit. This is a three-player game so you are holding a hand of nine cards.  The suits have landed equally in your hand.  You hold three of each and they are all of roughly the same rank.. You must bid trump suit. Which should you pick? You cannot tell. Each of these suits is equally strong in you hand.

Now we change the suits. There are still nine clubs but there are thirteen diamonds and five spades.  You again hold a hand of three cards from each suit.  You are holding more than half of the spades.  If you can get them to be trump, you are assured of having total control in spades.  At the same time you have an equal share of the clubs.  If clubs are trump, you are probably going to be okay this hand.  You have only a few of the diamonds so if diamonds become trump, this hand will likely not go well for you.  The asymmetry in this deck yields implications about your hand.

What do you think of these examples?  Did they clarify good uses for asymmetry?  Do you see examples that I missed?  Share them with your fellow designers in the comments below.  And if you’re enjoying what you’re reading, subscribe.  It makes this old designer happy.

I will be back in four days with some great published examples of asymmetry. See you Tuesday!

Asymmetrical Suits in Card Games, Part 1

You must walk–or so they say–before you can run.  You must similarly design from the familiar before you can find your own voice.  Freshman designers tend to begin by working with familiar things.  This means reaching for games and components already lying around.  The consequence of this is that most of us have written several card games using a regular deck of cards.  I certainly have.  In the 1990s, living the life of the cash-poor graduate student, I frequently gave these games away as birthday presents, frequently naming them after their intended recipient.

Starting with a regular deck is great.  The components are well known, readily available, and cheap.

There is a pitfall to using a standard deck, however.  This issue is subtle but important.  Mainstream card decks are completely symmetric.  Each suit is identical to every other suit, having the same number of cards and the same card ranks.  This is also true of the Scopa, Tarot, and Uno decks.  These were the decks I’d grown up with.  They were all symmetrical give or take a few special cards. It did not occur to me that decks should be any other way.

It was the flood of European games card game designs in the 1990s which revealed the power of asymmetry.

Asymmetry Serves Player Engagement

Asymmetric decks are not automatically well-known to the players.  They offer your players a puzzle.  How do these suits interact?  Which cards are now better or worse by suit? In his book A Theory of Fun for Game Designers (http://www.theoryoffun.com/), Ralph Koster notes how much our brains love to search for patterns.  Asymmetry challenges our brains to discover new patterns.

 

Asymmetry Serves Game Balance

Asymmetric decks allow the designer to balance rarity against utility.  Richard Garfield’s climbing game Dilbert: Corporate Shuffle, has one 1, two 2s, three 3s and so on up to ten 10s and a few special cards.  Low numbers beat high numbers so the most powerful cards in the game are extremely rare.  You must play the same quantity to follow another player’s lead so weak cards can defeat strong cards by outnumbering them.

Many designers prefer to make powerful cards rare.  I often find the opposite works better.  By inserting several copies of high-utility cards, you give each player a better chance of getting it.  Weaker cards and situational cards then add texture and encourage players to think laterally rather than being the majority of the hand while one lucky player draws the best card and runs away with the win.

 

Asymmetry Serves Story

Asymmetric decks are give you as the designer another tool for representing how one group is stronger, weaker, or simply different than another.

Doris and Frank’s wonderful card game Frank’s Zoo has circular card ranking.  Every card can defeat at least one other card and is in turn defeated by at least one other card.  No one card is the best.  No one card is the worst.  No player can put a card forward with impunity.  There is always a risk of it being defeated. Add that one suit contains only 4 cards while the other suits contain 11 and we see how asymmetry reinforces the game’s story.

 

Asymmetry Serves Sales

Game reviewers and the gameratti are quick to identify a game which can be played with a standard deck of cards.  Once the word spreads–and be certain that word will spread with the internet being what the internet is–many of them will throw together a set from a deck they have lying around and go straight to it rather than purchasing your game.

If you simply wish to create games for the enjoyment of others and have no interest in monetization then this is perfect.  This was certainly my intent when I created games as gifts.

You need to offer players more if you wish to sell your game.  You are asking gamers for their money.  They want to see that you earned it.  Offering an asymmetrical card deck shows them that you put some of yourself into your game.  Making it a little bit more difficult to make that home set gives them another reason to pay for your effort.

 

The best card game in the world–Tichu–uses nothing more than a standard deck of cards with 4 differentiated jokers (I games of Tichu being played in just this way at a few conventions).  That Tichu can be so excellent with a symmetric deck shows that symmetric decks still have plenty of value.  I’ve come to feel however that asymmetry should be the assumed condition over symmetry rather than the other way around.

What are your favorite asymmetric card games?  Share them with your fellow designers in the comments below.  And if you’re enjoying what you’re reading, subscribe to this blog.  It makes a big difference.

Our Friday installment will examine specific examples of asymmetry. I will attempt to pick apart compare designs with a symmetric deck against identical rule sets with asymmetrical decks.  Come back Friday and see how I do!

 

Book Report: New Rules For Classic Games

Lafayette, Louisiana is blessed with one of the best public libraries in the south. Many summers were spent raiding its shelves.  One afternoon in the early 1980s, I discovered New Rules for Classic Games by R. Wayne Schmittberger. It is without a doubt my first major influence as a designer.

In 2000, when my wife Debra convinced me to get serious about game design, my first exercise was in trying to fix broken games.  I snagged licensed property games from eBay and rewrote them.  I disassembled the structure of $2.50 garage sale games.  I sought out the games with the worst reputations.  Always in this process, I kept myself asking “how would I have written this?” and “if this were my design, how would I improve it?”

This book was inspired my approach.

Chapter 1 starts simply enough with a few simple variations any of us may have seen around our family table–simple variations on familiar games like Monopoly, Mastermind, Hearts, and the like.

The muscle of the book really gets moving in Chapters 2, 4 and 6.  This is where Schmittberger begins pushing variants to address problems and shortcomings in existing games.  The subtitles of these chapters–Fixing a Flaw, Changing the Number of Players, Handicapping–make clear his intention in writing them.  These aren’t just variants for the sake of variants.  This book is about variants with a purpose.

Chapter 7New Ways to Use Game Equipment–is filled with ideas for us game designer types.  Most of his ideas center around recycling game sets and boards but there’s still plenty of good material to be worth your time.

Middle Chapters 8 – 13 cover all the games you’d expect from a book written in this period–backgammon, checkers, chess, go, and the like.  A personal favorite of mine are his rules for simultaneous play diceless Risk.

Chapter 14 covers mechanisms for play-by-mail.  Modern readers will generally find that this section superfluous.  One dated chapter in an otherwise timeless book is hardly a mark against it however.  Particularly with the fantastic coda Schmittberger delivers in Chapter 15.

This closing chapter is where it’s at.  Chapter 15Creating Your Own Winning Variations–is the place Schmittberger completely surpasses most of his contemporaries.  Rather than simply presenting a collection of variants  extolling the variants he’d created, Schmittberger offered six solid pages of advice on creating your own variations.

In this unassumingly slim book, R. Wayne Schmittberger achieved a great deal.  He offered variations but more importantly offered the reasoning behind these variations.  As a designer, writing good variations is the first step toward learning how to improve your own designs.

New Rules For Classic Games is a great book.  Buy it.  Read it.  You won’t be sorry.

Ties, Damn Ties and Statistics, Part 7

Last time, we compared the schemes at scoring small sets.  Each scheme has its own advantages and disadvantages and comparing them enabled us to identify those qualities and how they can serve our core engagement.  Today, we move on to larger sets.

 

Comparing The Schemes

It is important to keep in mind that these schemes tend to change character as the size of the sets increase.  Schemes which awarded the least points for small sets frequently award the high points for large 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.  Our last column centered on small set scoring.

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

 

Valuing large Sets

Here is our diagram for larger quantities of widgets.

This graph reveals several new facts and again lets us consider their application:

A) All nonlinear exceed the linear scheme when sets get larger.  Mixing one of each into the same game can present your players with an engaging question.  Is it wiser to collect as many 3-point widgets as possible or is it wiser to concentrate on collecting doodads which score triangularly?  Doodads are worth more in the long run but will the game last long enough to give a return?  These are the kinds of questions that keep player attention right where it belongs–on your game.

B) The exponential scheme is the most explosive in the long run.  Like the squaring scheme, it should be kept to games that also make it very challenging to get large sets.

D) Fibonacci scoring was the slowest in the short run but triangular scoring is the slowest in the long run.  Triangular scoring is very popular among eurogame designers.  I believe this is the main reason.  The value of each widget is greater than the one before it BUT the rate of growth is smaller than in the other schemes.

A Final Word on Scoring

Always invest the extra energy to give players a scoring chart rather than asking them to calculate point values from a formula.  This is generally true no matter what scoring scheme you decide on.  Linear schemes can frequently get away with skipping a chart but the others cannot.

Providing a chart allows players to focus their mental energies on in-game decisions which is where that energy belongs.  Stopping to do calculations which could have been set beforehand breaks flow and can pull players out of the experience.

 

Scoring mechanisms can be a game’s core engagement or they can drive it.  They can be used to nudge player attention toward the best features of your game,  They can be used to drive players into direct competition.  They can build excitement.  They can offer a steady trickle of rewards.

This series on scoring mechanisms was created to put a variety of tools into your toolbox.  Now go put those tools to use!  Then come back and share your experiences with your fellow designers through the comments below.  And if you’re enjoying what you’re reading, subscribe to this blog.  It makes a big difference.

Come back in four days for a my first review of a game design book.  It was the first one I ever read and still holds a proud place on my shelf.  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!

Ties, Damn Ties, and Statistics, Part 4

One of the principles of success is the ability to prioritize challenges.  With that done, energy can be assigned appropriately.  Important challenges get priority attention while less important challenges get less attention.

Play-Driven Games

Some games are built around engaging play elements that demand its accompanying scoring system be simple and quiet.  Scoring needs to fade into the background like light dinner music and allow the main course be the star.  I would say basketball falls nicely into this category, as do many other athletic games.  So does chess.

Scoring-Driven Games

At the other end of the scale are the games which are driven by their scoring mechanism.  All other game mechanisms exist to highlight the interesting features of scoring.   Early Reiner Knizia designs like Zero, OLIX, and Taj Mahal featured his flair for gift wrapping exotic scoring mechanisms with engaging play.

Games in this category often offer different scoring options at different times or locations.  This can be immensely satisfying.  It makes our decisions feel more dynamic.  Questions of resource management, maximizing return, response to opponents’ moves, and discombobulating opponents’ plans all seem more interesting when we must also assess whether to pursue that massive 30-point score in the big region or instead try to collect several smaller regions with the same total.

Variable Scoring

And since we’re thinking about offering different scoring options within the same game, what if we allowed the scoring at each point to vary as well?  You could then include different schemes within the same overall scheme!

Dominion offers alternate scoring options through its variable kingdom setup. Cards like Farmland, Gardens, Great Hall, Harem, Island, Nobles, and Silk Road (shown here) each bring a new scoring option.  This option may not have been in the previous game and it may disappear in the next.  While it is available, it falls to us to decide how best to address each scoring option.

AEG’s Smash Up does a solid job of variable scoring within each play.   A deck of “base” cards (i.e. scoring regions) is shuffled and a few are placed face-up.  Each base card has different distribution scheme.  As soon as a base card is scored, a new one is drawn from the deck.  Scoring alone makes each area play quite differently from its neighbors.  Most regions have special rules as well but even if they didn’t, my previous statement would stand. Paul Peterson’s design is enhanced because he made variable scoring part of the core engagement.

I have experimented with variable in-game scoring a few times.  In 2004, a group of Houston designers had a friendly design contest.  My entry was about earning prize money at rodeos.  Each rodeo awarded first, second and third place prizes.  Each prize came from its own deck. The breakdown in the three decks was:

Blue Ribbons (first place) paid out $14, $17, $20, $25

Red Ribbons (second place) paid out $8, $8, $9, $10, $12

Green Ribbons (third place) paid out $3, $4, $4, $5, $7

A card for each position was drawn before each rodeo began so players could decide for themselves how hard to push at each rodeo.

More recently, I applied the same approach to an auction game. This time dice were used to set the payouts:

First place can roll $9, $10, $11, $11, $12, $15

Second place can roll $4, $5, $5, $6, $6, $7

Third place can roll $1, $2, $2, $2, $3, $3

Just as with the rodeo game, The three payout dice are rolled before the auction begins.

Note that in both cases, we decided on a system which guaranteed that first place beats second place beats third place.  We did experiment with schemes that allowed second place to occasionally beat first or that allowed third place to occasionally beat second.  Playtest data indicated that such schemes introduced more complications than engagement so we set them aside.  You may want to play with those ideas regardless.  Perhaps you can succeed where I failed.

The best games challenge the player to continuously make assessments.  Use scoring mechanisms which compliment the core engagement and your designs will do the same.

Do you have a variable scheme that’s working for you?  Please share it in the comments below.  And if you’re enjoying what you’re reading, please subscribe.  It makes a difference.

Next week, we look at scoring collections.  See you Tuesday!