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Ruminations about “Magical Numbers” in boardgame and card game design
by Lewis Pulsipher on 03/17/14 08:30:00 am   Expert Blogs   Featured Blogs

The following blog post, unless otherwise noted, was written by a member of Gamasutra’s community.
The thoughts and opinions expressed are those of the writer and not Gamasutra or its parent company.

 

[This is a combination of two blog posts from my game design blog http://pulsiphergamedesign.blogspot.com/  While it’s about board and card games, they seem to be gaining greater notice in the video game community as video and tabletop games converge together.  It may be of use to videogame designers who design boardgame-like games.]

In the course of designing “nano-games” that have between 17 and 20 pieces for two sides and very small boards that fit on part of a postcard, I again had occasion to wonder if there is some kind of "sweet spot" or "magical number" of pieces and spaces for a boardgame (or any other kind, for that matter) where pieces occupy locations.  I’ve seen several queries from novice designers asking if there’s an ideal board size, and my immediate reaction has been “it depends”. This question could be expanded to “is there a sweet spot in the number of pieces, compared with board size, in a game that involves maneuver/placement and geospatial location.”  For games that are not about maneuver/placement and location, such as many modern boardgames and most card games, the question doesn’t apply.  For RPGs and other games where you have an avatar, a single “piece,” as in many kinds of video games, the question also doesn’t apply, although we could ask if there is some kind of sweet spot for the number of characters in an adventuring party.  But that question becomes more a matter of psychology than of game.


Let’s look first at traditional “classic” (non-copyrighted) boardgames.  Chess and checkers have 64 spaces, and (respectively) 32 (16 per side) and 24 (12 per side) pieces.  Technically the checker board is 32 spaces, since you play on only one color.   So the ratio of pieces to board locations is 1:2 in chess and 2:3 in checkers, and always goes down as pieces are captured.  In Tic-Tac-Toe the ratio is ultimately 1:1.  In the Roman Empire placement and maneuver game Nine Men’s Morris there are 24 intersections for the 18 pieces, a ratio of 3:4.  (Tic-Tac-Toe is actually a much reduced variation of Nine Men’s Morris; both are draws when played perfectly.)  Backgammon has 30 pieces and 24 locations, differing from these other games in allowing more than one piece per location.  In such instances it isn’t surprising that the ratio is 5:4.

Leaving the games of the West, in African Mancala, which is a boardgame even though it’s a board you can easily dig in the sand, there are many more pieces (stones) than there are board spaces, because any space can hold many pieces.   Oware, for example, has 12 spaces and 48 pieces (seeds). There are relatively few board spaces compared with other games I’ve mentioned.  Shogi (Japanese chess) has 40 pieces and 81 squares for a ratio close to 1:2.  Xiangqi (Chinese chess) has 32 pieces on a board of 90 intersections, for a ratio close to 1:3.  In the Asian game Go, played on the intersections of a 19 x 19 board (361 spaces), we have a situation closer to Tic-Tac-Toe where you could leave all the captured pieces on the board and fill the board up.  It may be no accident that Tic-Tac-Toe and Go are placement games rather than maneuver games.  If you can’t move from one place to another then the only way to occupy a particular place is to fill it up with a piece.

Intuitively, you might expect that fewer areas means the game is simpler to deal with, though the game may still have a great deal of gameplay depth.  You might also ask, how much are the limited numbers of pieces and spaces simply a reflection of manufacturing limitations in ancient and medieval times?  

Let’s look at some traditional commercial games for comparisons.  Many traditional commercial games such as Monopoly, the Game of Life, Clue, and Careers have just one piece per player, a kind of avatar.  Many of these games are not actually games of maneuver/placement and location; Monopoly has location but the players have no control over where they are so there’s no maneuver.  Careers and possibly Game of Life (I don’t recall) have diverging paths but most of the time there is no choice about where your avatar goes.

How about "classic" area-based wargames?  Risk has 42 areas.  Britannia has 37, plus 5 sea areas that can only be temporarily occupied and where combat cannot take place.   Vinci has 45 (by quick count). Diplomacy has 56 land regions and 19 sea regions (75 total) for 34 pieces.   History of the World and Axis and Allies have many more areas  (and original Nova Games’ A&A had a lot).

How about piece to area ratios?  The average for Britannia depends on the era, but is roughly 55 pieces for the 37 areas, about 3:2.   But as with several of these games, one area can hold more than one piece. The ratio in Vinci is something over one piece per area.  In Risk it's a lot higher, at times, as massive armies build up.  Diplomacy's ratio is much like that of chess, one piece for a little more than two areas (and no more than one piece per area).  Unlike chess and checkers, the ratios in Diplomacy don’t change much over time because the overall game economy is at first slightly positive and then stabilizes.

 

My motto in game design is "A designer knows he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away"  (Antoine de Saint-Exupery) or in another form, about Japanese gardening, "Your garden is not complete until there is nothing else that you can remove."  Consequently, nowadays I look for the smallest number of pieces and smallest board that gives the experience I have in mind.

For example, I have a couple prototypes that are vaguely Stratego-like.  One dates back about 30 years, the other is quite recent but grew out of the first.  I’ll describe the latter one below, and how I discovered I might need to reduce the number of pieces.  The older one is a space battle game played on squares, and when I first designed it I stuck with something near the typical Stratego 40 pieces per side, though on a more roomy board.  But when I resurrected it several years ago, when it was played mostly by video game students, I cut the number of pieces down to 19 and eliminated some of the special pieces - they became options that we rarely used.  The ratio of pieces to board became 38:113 or about 1 to 3.  This made for a much quicker game, as little as 15 minutes, that was just about as interesting and certainly as fun to play as the big version. The newer game is a World War II Pacific air naval battle where I found that the same ratio works quite well.

But this cutting back is harder to do when you're trying to model a particular historical situation such as a battle or war.  Going back to the “nano-games”, the postcard games, it’s quite difficult to provide an historical model with a very small number of pieces and very small board - you can focus on only a few things.  One reason why the traditional games mentioned above can have small numbers of pieces in relatively small boards is that many are abstract games rather than models of any reality.  Even Diplomacy gives the appearance of World War I but virtually none of the reality.  Risk is very far from reality. In the commercial game world we really didn’t have boardgames intended to be models of reality until Avalon Hill wargames came along in the late 1950s.  (We can probably think of isolated examples before then.)  Before then, only wargames played by the military tried to reflect a specific reality.


What about the numbers of pieces and numbers of playing spaces in relation to human comfort and human capacities?  This brings to mind the famous journal article “The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information” http://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two.  It discusses the number of things a human can keep in “working memory” at one time (barring memory tricks in specific instances).  I don’t know of other research of this kind, but I’d be willing to predict that if average human capacity has changed it has gone down, rather than up, as we live in a world of more and more distractions and more and more multi-tasking leading to more and more routine mistakes and inability to focus.  Typical human memory capacity more generally seems to continually fall, for lack of practice if nothing else.  Where people in non-literate societies had to memorize any information they needed to retain, we went to writing things down, and now to recording them digitally.  The joke used to be that old people had a disease called “CRS” (can’t remember “stuff” - or perhaps some other “s” word), but my observations of college and high school students is that they have CRS quite badly even as they usually refuse to write things down in class.

Whatever research may show, I think it’s fair to say that 21st century game players by and large prefer fewer rather than more assets to keep track of, and less rather than more memorization.  There are lots of exceptions, of course.  Yet I’m put in mind of a very intelligent freshman game player who said she didn’t like wargames because there were too many decisions, too many things to keep track of.  For her it became too much like work, no longer entertainment, though she was very capable of doing it.  I myself quit playing chess at age 15 because it was too much like work, if you wanted to be any good.

Perhaps one reason why Diplomacy has been so popular and durable is the small number of pieces for each player.  Players start with 3 or 4 pieces.  Even a winning player probably averages no more than 10 pieces over the course of a game (18 is a certain win).  And in the much more common draws (2-, 3-, or 4- way for a 7 player game) a player averages even less.  


When considering numbers of pieces we should also look at how many different kinds of pieces there are.  Most of these games have just one kind of piece, the army in Risk or Vinci or the piece in Nine Men's Morris.  Japanese chess has eight different types of pieces, Western chess six types.  In between we have Diplomacy with two types of pieces, armies and fleets.

I think the variety of pieces is sometimes almost as important as the number of pieces.  Clearly variety appeals to those who play Western and Eastern versions of chess.

One way to avoid the potential problems of using a variety of pieces is to avoid exceptions to the general rules.  Going back to Stratego and my prototype, both games have lots of different pieces, but Stratego is almost entirely hierarchical, so that there’s no difference between a “2" and a “7" (using the old numbers where the 1 is the strongest piece) other than its strength.  Only the engineers, scouts, bombs, spy, marshall, and flag are “unusual”, though many of them also participate in the hierarchy.   And each of them offers just a single exception to the rules.  There’s a hierarchy in my air naval prototype as well, but submarines and aircraft make it considerably more complex, as some ships can sink the subs, subs can sink some ship types if the sub is the attacker, and the aircraft are all over the place and may combine in attack (aircraft can move in segments, and two can move in a turn, much more complex than scout movement in Stratego.).  In other words, there are a lot more exceptions.


I saw what we might call “resistance to too many choices” in relation to this World War II naval prototype.  A casual player who loves Stratego, and played well, quickly buckled when playing my prototype.  There were too many choices, too much freedom of movement.  Stratego has lots of pieces, with a piece to board space ratio of 80:92.  The number of movement choices is very much limited by the board and setup.  In my prototype, though there were fewer pieces (25 per side at this juncture for a total of 50), there were many more hexagons (13 by 12 for 156, piece to board ratio 1:3); the length of the “border” between the two players was much longer (12 or 13 hexes instead of 6 squares); and all pieces had a choice of moving two in a straight line as well as one space.    Even the winning conditions are more complicated in my game.  In Stratego you only have to take the non-moving enemy flag.  In my game you need to get a merchant ship to the other side of the map, or wipe out all the four opposing merchant ships, which can move of course.

In both games the uncertain identity of opposing pieces helps avoid over-analysis, thus simplifying the mental task.   But my game (which is tentatively scheduled to be pbblished by Worthington Publishing) feels more like chess than it feels like Stratego.  Seeing the casual player’s reaction was quite a lesson to me, as I had thought that fewer pieces would simplify the game and bring it closer to the mass-market.  But it became clear that I’d need to reduce the number of pieces even further, given the other parameters.  (Veteran wargamers have no problem with 25 pieces per side, since they’re only moving one or two at a time.  Imagine how tough it would be on casual players if all the pieces could move at once, as in traditional hex-and-counter wargames.)

I’ve described this at some length because the heart of my inquiry has become, what do we do in designing games that makes them less like the classics, or more important,  makes them less comfortable for players?  It’s not just choice, or chess would not be as popular as it is.  It’s a combination of things.


Games with no uncertainty, such as chess and checkers, promote “analysis paralysis” as a player tries to find the very best move: because there IS a very best move, which is not true of most games with uncertainty (and which is why chess and checkers are essentially puzzles, because there’s an always-correct solution).  For most purposes you wouldn’t want to design a game today that lacks uncertainty.  (Of course, in the real world uncertainty is ever-present; games without uncertainty are usually abstract, and abstract tabletop games are hard to sell.)

(As an aside, if chess did not exist and was published today, I think it would be just another not-very-successful game, not a hit.  It promotes severe “analysis paralysis”, which is why we have chess clocks, and there’s a huge advantage to first-mover.  Moreover, it ends in a draw about a third of the time. Quite apart from the difficulty of selling abstract games. And it only accommodates two players (I know three and four player variants exist, but likely don’t work well by the nature of the game).  Doesn’t sound good, does it?)


With the above in mind, about a year ago I tried to figure out what an “ideal” introductory wargame would be like.  One of the pretty obvious characteristics was “10 to 15 pieces per side”.  And not moving all the pieces at once.  (In fact, I realize I arrived at close to the same solution as Shenandoah’s Battle of the Bulge iPad game, that only pieces from two or three areas could move in one turn.)   I also think the number of spaces must be limited, thus prohibiting the prospect of a board of hundreds of hexagons.  In other words, keep it to the kinds of parameters we see in most of the games mentioned above.     If the game can have both strategic and tactical elements it is a better introduction to the possibilities of typical wargames.  I’ve ended up with a (two part geomorphic) area board for strategic movement, and a hex board for battles.  There’s also an economy, which is what separates war games from battle games, though the economy does not dominate play.

Unfortunately I haven’t been real excited by playtest results, perhaps because the tactical element (which I adapted from a space wargame prototype where it is quite popular) isn’t yet perfected for land battles.  So I’ve set it aside for some months.


As I said in the title, these are ruminations, I have no hard-and-fast answers to my queries. So I’ll move on to “magical numbers” in cardgames.  (For a comparison of the nature of board and card games see “The Fundamental Differences between Board and Card Games and How Video Games Tend to Combine Both Functions” http://gamasutra.com/blogs/LewisPulsipher/20120219/91123/The_Fundamental_Differences_between_Board_and_Card_Games_and_How_Video_Games_Tend_to_Combine_Both_Functions.php)

I’m not a person who plays standard card games, though I have played Old Maid, Canasta, Euchre, and even Poker in the distant past, and still may play Oh Hell once a year.  I’ve never played Uno, let alone Hearts or Spades or Gin Rummy.  But lately I find myself designing games that use cards, though not the standard deck.

One of the benefits of cards is that there is a natural limit to play that does not exist in boardgames, that is, the exhaustion of the draw deck.  And card games naturally fall into relatively short sessions (one hand), though most traditional card games are played through several hands.

Hand size varies a lot in card games using the standard deck of cards.  One of the smallest hands is in Texas Hold ‘em (two cards) though more typical in poker is five cards.   Magic: the Gathering starts with seven.  I have made a brief list of hand size in some card games, and I’d judge that a hand size of five to seven cards is most common.  (I’m not counting games like Bridge and Old Maid where all the cards are dealt out.)

I like to design screwage games, which are pretty popular at the university game club I attend, and there I’ll start with somewhere between five and seven cards.  If I don’t have a strong feeling about where to start I’ll pick a larger number because that gives players more choices within the context of the usual card game limitation that there are typically fewer choices than in a boardgame. [You can read a description of what a screwage game is in “Competition, direct conflict, wargames, and screwage games” http://pulsiphergamedesign.blogspot.com/2013/10/competition-direct-conflict-wargames.html ]

When I design a boardgame that uses event cards I typically start players with five and see how it works out.  In one case, for a space wargame with three to five players, I reduced the number to four, three when there are five or more players, because the event cards had an overbearing influence on the game. In another game I reduced it to two although players can expend action points to get more.  Event cards are there for variety and uncertainty, not to dominate the game.

The number of starting cards also depends on how many cards are available in the deck and on how many people typically play.  It doesn’t take much time to work out approximately how many rounds a game will take if players are drawing one card at a time and there are a given number of cards.  Multiply the hand size times the number of players, subtract that from the number of cards available, divide the result by the number of players to get the number of rounds.

Obviously, the more cards players start with, the more options they have.  The question may be at what point are there too many options for your target audience.  One way to broaden the appeal of a game is to reduce the number of decisions players have to make.  (Another way is to reduce the number of exceptions to the rules that people must keep in mind.)  So a hand of seven cards gives more options and decisions than a hand of five cards, but the question is, is it the right number of options and decisions for your game?

As a practical aspect as well, as the hand gets bigger people have more trouble coping with handling it, with keeping track of everything, even with being able to hold it in their hand so they can see all the cards.

In many games I don’t have a set hand size, or even a size limit.  A few players like to collect lots of cards to get a big hand; but they may be less likely to win when they do this, because they’re expending actions to draw while other players are doing something potentially more productive.

I find that people so often forget to draw cards, especially in games where you occasionally use a free-to-play card that you don’t replace, that in some games I have a simple rule that if you find yourself with fewer than X cards at any time (typically five) you draw back up to X immediately.


What about deck size? I tend to stick to the old standard governed by printing capabilities of 55 cards per deck (or 110, or 165 . . .).  A standard deck is 52, plus two jokers, plus a logo card.  (I understand there is more variation now in printing machinery.)  55 is a lot of cards for many purposes, such as Event Cards.  But a game that is purely cards often demands 110 cards or more, to provide sufficient variety and versatility.


I may as well make this observation about the card game process as well.  The paradigm for standard card games is that a player plays a card, and draws a card, each turn.  But which comes first? If the player draws the card afterward then he has time to think about how to use it and what to do next before his next turn.  If the player draws to start the turn then everyone waits while the player thinks about what to do with this new card.  Moreover, if he draws before playing then the card he draws may mess up the plan he already had in mind. On the other hand, if the player feels he has a poor set of cards then he’ll be happy to draw before he plays in hopes that he’ll draw something more satisfying.  Also it may be easier for players to remember to draw before playing than to remember to draw after playing, especially if playing one card can result in some additional actions.  But it’s so important for games to be shorter nowadays that I usually choose draw-after because that speeds up the game.

Of course, you can have games that use cards yet don’t follow the standard pattern of play one and draw one.  For example as I recall, in Fluxx the number you draw varies according to cards that people have played during the game.  In other games, drawing a card is one action among many possible actions, with a player taking two or three actions per turn, so he or she may draw two or three cards, or even none.

Finally I should mention free-to-play cards, also called “interrupt” cards: cards that you can play out of turn in certain circumstances.  These are great for keeping players involved in a game even when it isn’t their turn, but can also cause a little frustration when someone notices too late that they have an interrupt card that they should have played.  They are a source of surprise (which is usually good in a game) but if used too often, can make a game feel random.  NC State Game Club members laugh because many of my card games include “Divine Intervention”, a card that cancels most other cards, as an interrupt.  But there’s only one in a deck . . .  Perhaps I’ll have more to say about interrupts when I write about Event Cards in boardgames.

***

I will be a speaker at the East Coast Game Conference, “the largest gathering of video game professionals on the East Coast,” April 23-24 in Raleigh, NC.   Exact time or day as yet unknown.  The topic will be “On the Horns of a Dilemma” (Game Design).

My online audiovisual classes about game design are now available at https://courses.pulsiphergames.com.  They are still on Udemy.com but cost more there.

 


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