The Games Journal | A Magazine About Boardgames

Dice Fest

Dave Shapiro

June, 2005

The best throw of the dice is to throw them away.

English Proverb

This article will attempt to address an issue frequently debated in gaming circles: randomness and in particular, the randomness generated by dice. No gamer is ambivalent; merely mention the cubes and the wagons circle and someone makes the inevitable "dice fest" comment.

The majority of non-abstract games include some mechanic for generating random results or events. The intent is to prevent the game from becoming predictable or repetitive by presenting the players with the challenges of the unknown or unexpected. In some games the random element enhances the gaming experience but could, conceivably, be removed. For example, the various civilization attributes could be removed from Vinci and the game remains playable; diminished but playable. Other games rely more heavily on the random element. Consider a game of Cosmic Encounter without any alien powers.

There are a variety of mechanics for introducing random elements into games; the four most common are dice, cards, tiles and spinners. Each of these methods exhibits certain advantages over the others and the designer's decision to implement one over another determines the influence of the random element. Bruno Faidutti is often harangued for developing chaotic games, Citadels being a common citation. In Citadels, players select a character to play each turn, each granting special powers. That exact same statement could be used to describe Puerto Rico, a game usually touted as being devoid of luck.

Citadels presents the player with eight characters from which to choose while Puerto Rico offers only seven; not a significant difference. However, it is with the intensity of the character powers that the perception of chaos arises. The player powers in Puerto Rico are significantly weaker than those in Citadels and the powers in Puerto Rico are shared while those in Citadels are individual. Consider the reaction to Puerto Rico if the Mayor received all the colonists, only the Captain was allowed to ship goods, or if the Prospector nabbed his booty from another player.

Perception is not necessarily reality. Classic Risk is regularly described as a dice fest; often this appears as some form of declaration as if Moses had brought this information down from the mountain. But is it accurate? Is Risk more inherently random than Battle Cry or Memoir '44? Is the luck factor greater in Risk or Tigris and Euphrates with its multitude of tile draws? Which incorporates the greater random factor, classic Risk or some of the old Avalon Hill and SPI war games? Baruch Spinoza one wrote: "A thing appears random only through the incompleteness of our knowledge."

These are areas that should be addressed as there is evidence of substantial misinformation and misconception. It is impossible to properly examine randomness and dice without the inclusion of some statistics and probability. For our purposes, I will reduce the inclusion of these factors to a minimum.

The Fine Line

God does not play dice with the universe.

Albert Einstein

Before proceeding with an examination of dice, we need to clarify two terms. There is a significant difference between randomness and chaos and the two are often confused. Chaos is a measure of a player's control in a game. Chess and Through the Desert are both games with perfect knowledge. A two player game of Through the Desert is similar in chaotic composition to that of a Chess game; players enjoy a tremendous amount of control in either. Chaotic elements are introduced by play alone. Now invite additional players into the game. Through the Desert loses the Chess-like feel, the total control—it has a greater degree of chaos. The control a player exerts is inversely proportional to the number of players in a given game; more players equals more chaos and less control. Yet it remains a game of perfect knowledge.

Knightmare Chess cardCompare this with the introduction of cards to a Chess game as Faidutti did with Knightmare Chess. The inclusion of cards introduces a random element to the game, an element over which the players have no control. In this event there is a little chaos, players still have complete control over their units but have no control over the cards. Randomness is a complete lack of control concerning a specific event or mechanic. The random or luck factor must be mitigated by external applications such as probabilities or simply accepted as "the luck of the draw".

Many players incorrectly assume that a game with dice has a greater "luck factor" (i.e. more randomness) than one without. In many games, including those with dice, the random element is minor or even disguised. Often games are thought to be lacking a random element when, in fact, there may be a more critical random factor. Puerto Rico is one of these type of games. Consider a five player game and the difference in the opportunities available to the first player in turn order and the last player. The first player has the entire seven character set from which to select. Each player thereafter has one less character from which to choose. The last player in turn order has but three. He has no control over which characters will be available when it is his turn to select and there are no tools available for predicting or influencing which characters will remain. As the players shift positions in turn order the amount of randomness they must confront will vary. The subtle inclusion of this bit of randomization forces the players to contend with a possibly less than optimal choice while improving the freshness and challenge of the game.

One of the most potent tools available to game players, a tool that allows a player to consider viable alternatives based on incomplete information, is the theory of probability. (Don't become alarmed, you won't need a calculator.) Depending on one's particular involvement with a specific game there are very powerful techniques available for analysis. Professional gamers (Chess, Poker, Backgammon, etc.) employ these techniques continuously. But the purpose of playing games, at least for most of us, is to have fun. I am not suggesting that you enter a program for a degree in combinatorial mathematics, just to use a little common sense.

Acrylic Polyhedrons

Clergymen and Bishops are fond of dice playing.

Vitalis (1075-1143)

Dice are the oldest gaming implement known to man and they have made several appearances throughout recorded history. The oldest surviving die is on display in the National Archeological Museum in Athens, Greece. It is believed that the first dice rolled nearly 5000 years ago. Archeologists have uncovered numerous references to dice in ancient texts from around the world. There are several references in the Bible, the most striking has the Roman legionnaires "casting lots" for the robes of Jesus. Ancient Egyptians believed that the dead played dice games in the underworld. Several texts from antiquity address the issue of loaded dice! Dice are an integral part of human history; one of the first toys of man.

Originally dice were two sided (heads or tails). With technological advances, the knuckle bone of certain animals substituted for the base and the number of faces doubled to four sides.6-sided dice The early Greeks used the ankle bone of sheep for the foundation material and the number of faces rose to the now familiar six (d6). Upon discovering dice games, the Romans became so enamored that "dicing tables" have been uncovered etched into portions of the Forum, the Coliseum, the Temple of Venus and the House of the Vestals.  Of course as the popularity of dice games traveled throughout the Empire, unscrupulous characters participated more often. In order to alleviate a growing problem, dice towers were introduced. Though there are numerous tales concerning dice and the Roman Empire, the most familiar is the statement of Julius Caesar as he ordered his troops across the Rubicon, attacking Rome itself. As the troops began to cross he is quoted as saying: "Jacta alea est" (The die is cast).

Long after the Roman Empire had faded, the popularity of dice and dice games continued and flourished throughout Europe. There is the legend of the Olafs. In 1020 C.E. King Olaf of Norway and King Olaf of Sweden agreed to decide the status of a disputed area (Hising) by rolling dice. As the story unfolds, Olaf of Sweden rolled first and produced boxcars (6-6). Olaf of Norway matched these so another roll was required. Once again Olaf of Sweden rolled doubles sixes. Olaf of Norway rolled the first die—a six. The second die spilt when it hit the table and the faces showed a six and a one. The legend concludes that they agreed that Olaf of Norway was the victor and they parted amicably.

Less idyllic while demonstrating the continued growth in "dicing", early casinos known as Dice Dens arose and by the 17th century every Dice Den in England employed one person who was assigned the task of swallowing the cubes should the "coppers" appear. It was in this period that two young men began corresponding about a particular dice game resulting in a new branch of Applied Mathematics.

For hundreds of years the basic structure of dice remained unchanged; dice were six sided cubes with pips on each face and the total of the pips on opposite faces always totaled seven. However, in the latter part of the 20th century new forms began to surface. The familiar cube was joined by 3, 4, 8, 10, 12, 20 and even 100 sided dice. Play shifted from being dice-centered to dice becoming simply a tool in the game. The traditional dice-only games remained but waned in popularity. Several attempts to re-introduce dice-only games, even with altered faces, have met with minimal success. Recent examples include Dragon Dice, Rolled Bones, Doom Cubes and a game where the faces of each cube depict a couple engaged in... suffice it to say that, though anxious, I have yet to try this game.

Another recent development in dice has been tactile in nature. Where the originals were carved from bone, then wood, followed by molded acrylic; today the material ranges from sponge to precious stones and finally (returning somewhat to their origins) dinosaur bone. Common production sizes today range from 5mm to 50mm with specialty dice being produced with faces that exceed one foot! (The world's largest collection can be viewed at www.dicecollector.com.)

The advent of the 10-side die (d10) opened a new venue for dice. For years scientists and mathematicians investigated a variety of methods for generating random numbers, eventually publishing tables of these numbers several pages long. Years later it was discovered that these numbers were not truly random, that there was a bias toward certain digits. Computers appeared to be the solution but even the random numbers generated by computers were flawed. Internal cycling caused certain patterns to appear; the random numbers were not actually random. In addition to this problem, early computers were far from portable and so long tables of random numbers were still published with regularity.

Then in the 1970s, probability and statistics professors discovered that a popular game among their students offered a solution. Borrowing the d10 from Dungeons and Dragons, the professors had discovered perfect, portable random number generators. Though computers have, once again, returned to this task, there remains nothing more efficient than rolling five d10s to generate a random number.

Genius and Vision

There are three kinds of lies—lies, damned lies and statistics.

Disraeli (Re-quoted by Mark Twain)

Several hundred years ago a young man, while enjoying an evening of gambling, began to wonder about the possibility of his winning a particular dice game. Now, by any standard, this young man, Blaise Pascal, was a mathematical genius. By the age of 16 he had published a paper on conics and followed this with an invention—a rudimentary calculating machine. He developed what is today known as the Pascal Triangle, the barometer, the hydraulic press and had invented the syringe. But that night he was troubled by his lack of understanding for the dice game he played. Beginning the following day, he corresponded with a pal (Pierre de Fermat) expressing his frustration. This led to the development of Probability Theory.

So what is Probability Theory? Short answer—a tool for making decisions based on incomplete or unknowable information. It is more than a feeling but less than a certainty. Basic probability theory is a matter of logic and common sense; it is applied, real world mathematics, much of which, most people perform intuitively on a daily basis. For example, there are two lines in a grocery store. One line has several customers with only one item each while the shorter line has a single customer with a cart filled to the brim. Which line should you choose? Or on a slightly more complex level, comparing two phone plans with differing free minutes and overage charges. One plan offers more free minutes per month but charges double the amount for overages. Which do you choose?

Dig deep enough into probability theory and you will encounter distributions, sequences, confidence levels, series and a supermarket of other mathematical tools. Does the average gamer require this amount of knowledge to play a game? How much analysis is too much? Isn't this supposed to be fun?

My introduction to statistical methods was by an ageing professor from Poland. Whenever a student approached him with a particularly difficult problem the professor was fond of replying: "If you take 10,000 coins and throw them in the air, roughly half will land heads and half will land tails... the rest is details." He continuously promoted a common sense approach to probability.

For gaming purposes, all that is required is a smattering of the basics and a bit of common sense. Determining the basic probabilities will provide the player with an improved understanding of the particular game, the underlying mechanics at work and improve the decision process resulting in more competitive play.

Traditional Dice Games

When God rolls, the dice are loaded.

Greek Proverb

In the past decade, criticism of dice games parallels the rise in popularity of the Eurogame. It appears that many gamers were deceived into believing that a game with dice is inherently more random, and therefore inferior, to a game without. Unfortunately this concept has propagated to where the mere mention of dice in a review is often presented as a warning to the gamer. To be clear on this, the exclusion of dice does not guarantee that a game is less random than a game that includes them. The inclusion of dice as a game mechanic often requires the gamer to consider additional possibilities that may entail minor calculations. Is Venezia (dual spinners) or Ticket to Ride (multiple card draws) less random than Fortress Europa or Monopoly simply because there are no dice? (Note: I am not suggesting that Eurogames are inferior, I am however, suggesting that there is a bias concerning games with dice that is inaccurate.)

In order to understand the influence of dice it is important to differentiate the three types or categories of dice games: traditional, custom dice and games with a dice mechanic. Each of these types presents the player with a different degree of randomness. To lump all dice games together is as foolish as suggesting that all games played with cards are similar. (Consider Mamma Mia versus Bridge.) The following is an overview of these distinct types.

Traditional

Traditional dice games can be separated into those where the player has some influence and those that simply involve tossing the bones. It is this latter group that strategy gamers find so distasteful. One very common version of this type of game is the Put 'n Take game. Each player begins with a few chips or coins and on his turn rolls a die. With an odd number roll, the player contributes that number of chips/coins to the pot. An even result permits the player to retrieve the number rolled from the pot. (There are many variations of this game including the recently popular LCR.)

Though only an example of this "non-decision" type of game, it is included to demonstrate the absence of any control in these games. In the proper arena (such as a dark, loud bar) these games serve their purpose but seldom find a place in a gamers collection. These are completely random games; the player has no control over any events in the game. Surprisingly, Knizia , when discussing dice games of pure luck wrote: "Even though you have no tactical influence, these games provide great entertainment. It's like watching a good movie. You cannot change the course of the action but you join in the excitement."

The second group of the traditional type of dice games allows the player some influence over the course of the game. Yahtzee and Craps are probably the most familiar of these types of games. The choices afforded the player reduce some of the random element. In these games a player can benefit significantly from an analysis of the various statistical probabilities. One can determine the probability of rolling triples or a full house and, armed with this information, determine their best course of action. Most of the games in this group involve bluffing (Liars Dice), gambling (Craps) or "pushing-the-envelope" (Cosmic Wimpout).

Craps is often used to demonstrate the advantage of understanding a smattering of probability theory. Distilled to the basics, a player rolls two dice and if he rolls a 7 or 11, he wins. Otherwise the number he rolled becomes his point number (X). Wagers are placed on whether he can roll his point number (X) again, before rolling a 7 or 11 (which now becomes the kiss of death). So how do you place your bet? It is relatively simple to construct a table that displays all 36 possible results of the roll of two dice. (Note: These results are universal to every game in which two d6 are rolled. Every gamer should be familiar with this table.)

Number Possible Rolls # of Hits % Chance
2 1-1 1 2.8%
3 1-2, 2-1 2 5.6%
4 1-3, 3-1, 2-2 3 8.3%
5 1-4, 4-1, 2-3, 3-2 4 11%
6 1-5, 5-1, 2-4, 4-2, 3-3 5 13.9%
7 1-6, 6-1, 2-5, 5-2, 3-4, 4-3 6 16.7%
8 2-6, 6-2, 3-5, 5-3, 4-4 5 13.9%
9 3-6, 6-3, 4-5, 5-4 4 11%
10 4-6, 6-4, 5-5 3 8.3%
11 5-6, 6-5 2 5.6%
12 6-6 1 2.8%

There is a tremendous amount of information in this table. If in our imaginary game of Craps the player rolled an 8 with his first roll; there are only 5 out of 36 possible methods for "making the point". However, from the table it is obvious that rolling another 8 is almost five times more likely than rolling boxcars. In short, bet with the player on an 8 and against the player with a 12.

This table can be used for any game employing two d6—the optimum choices for placing the starting houses in Settlers of Catan; the likelihood of landing on a given property in Monopoly; the Combat Results Table (CRT) in a war game and so on.

Custom Dice Games

Statistics can be made to prove anything—even the truth.

Anonymous

Custom dice games form the second major category of pure dice games and these are relatively rare. Games such as Dragon Dice, Rolled Bones, Dicemaster - Doom Cubes and the Star Trek The Next Generation Collectible Dice Game met with minor success. These games are unusual as they share more with strategy board games than with typical dice games. In these games the dice are the components—the board, the units and the conflict resolution devices. In order to determine a viable strategy, each of the dice in the game must be examined. Analysis of the different races in Dragon Dice allows the player to determine which races function better at the various levels of the game. This, in turn, permits the player to assemble an army mix that should maximize his opportunities. Similar to Magic: the Gathering, competence in this type of game requires dedication as it is a substantial effort. As these games are nearly unique, this is not the venue to address any particular one in depth.

Games With Dice

Shake, rattle and roll.

Bill Haley and the Comets

The third major group of dice games are those games where the dice are one of several components in the game. In some instances the dice generate a minor random element while in others, especially war games, the die rolls become a critical element. The most familiar of the first group, the group in which the dice add an element of randomness or surprise, is Monopoly. Dice are rolled to randomize the movement but from that point on it is player action/strategy that determines success or failure. (The cards have a minor affect on play and will not be considered here for the sake of simplicity.) Randomizing the movement of the players prevents the game from degenerating into a solvable puzzle. Assuming the random element were removed then given sufficient analysis, a perfect solution, or at a minimum, a solution to maximize opportunities could be determined. The game would become predictable, programmed and dull. The random element is required to create conflicting goals among the players.

The same is true of Settlers of Catan or Carolus Magnus where dice are used to generate player resources. If players were simply allowed to select a specific good (Settlers) or the desired color (Carolus Magnus), the games would lose their elegance, becoming multiplayer puzzles. Repetitive openings, mid-game and end-game strategies could be developed that would eliminate the dynamics present with the uncertainty of the die rolls. Certainly the luster of Settlers is derived from the need to trade for resources; removing that destroys the game. (Note: the same concept applies to many of the card or tile driven games. Consider the damage to Tigris and Euphrates if a player could simply select the desired tile every turn.)

Reviewing the earlier discussion on the probabilities for rolling two d6 and the table created, the obvious choices for selecting starting positions in Settlers is, in decreasing order, tiles numbered 6 or 8, 5 or 9, 4 or 10, 3 or 11 and finally, 2 or 12. Of course this will not guarantee a victory but it will increase a player's chances. This is fundamental. A player who chooses to ignore this information does so at his own peril. A good card player will unconsciously count cards, recognize patterns and so on. Whether it is Poker, Gang of Four, Rummy or Wizard, the player considers what he has been dealt and develops a strategy based on the reality of his hand and what has been played. This is just as valid for board games; the dice add a random factor that forces players to evaluate their position and possible strategies.

Is it possible that "bad rolls" will cost you a victory in a game of Settlers? Certainly, however if you have positioned yourself properly during the set up phase (starting on #6 and #8 tiles) then the probability that you will receive resources is greater than if you had started on #4 or #10 tiles. From this point on we would be entering the realm of situational probabilities which is not appropriate for our purposes here. Gamers must play with what fate deals (or draws or rolls) them, attempting to maximize their position as often as is possible. Though we may wish to blame the bones, most often it is our own, ineffectual strategies that precipitate a loss.

Conflict Games

Then there is the man who drowned crossing the stream with an average depth of six inches.

W.I.E. Gates

Among historical simulations (wargames) it was common for dice to be combined with a Combat Results Table (CRT) for the resolution of battles. Some of the early CRTs were grossly flawed. A player would roll a single six sided die (d6) and reference the CRT, the chart, that ranged from a defender being eliminated on a roll of "6" to the attacker being eliminated on a roll of "1"! Soon the CRTs were modified to reflect the relative strengths of the opposing sides. As these games evolved, additional modifiers were considered including, terrain, supply, time, leadership and many, many other factors often requiring fairly detailed calculations to determine the correct table or modifier to employ.

A typical Combat Results Table

Attacker Odds
Die Roll 1:4 1:3 1:2 1:1 2:1 3:1 4:1 5:1
1 AE AE AE AE AE EX EX DE
2 AE AE AE AE EX EX DE DE
3 AE AE AE EX EX DE DE DE
4 AE AE EX EX DE DE DE DE
5 AE EX EX DE DE DE DE DE
6 EX EX DE DE DE DE DE DE
  • AE - Attacker eliminated

  • DE - Defender eliminated

  • EX - Exchange

All of this served to simply change the odds, the probability that a particular result would occur. Though far less dramatic, substituting a d20, d50 or even a d100 and setting variable ranges would have been more efficient, reducing these calculations and chart references to a single die roll on a single CRT. For most, the time and energy required to properly analyze the probabilities of success given the multitude of possible situations, is not worth the effort; for many this was not gaming, it was accounting. (Note: replacing the die/dice with cards will not necessarily improve the situation as the number and distribution of the cards must be considered.) These were heavy games, monster games.

At the opposite end of this spectrum are the very light war games such as Battle Cry, Memoir '44, Axis & Allies, Heroscape and the Risk family of games. There are three basic systems used to resolve combat in these light war games: cards, unique dice and standard dice. It is only these latter two groups with which we are concerned. These game systems attempt to reduce the calculations required to the barest minimum.

Of the first group (Battle Cry, Memoir '44, etc.) Heroscape is the simplest system (and is very similar to the system adopted for Clash of the Gladiators). The attack and defense dice are unique to the game with special icons printed on some sides of a standard d6. Any player can easily examine the sides of the attack and defense dice, noting the number of "hits" or "shields". The probabilities for the dice can easily be calculated. For example: the attack dice in Heroscape have "hits" marked on three sides. As these are six sided dice, there is a 50% chance for a hit with each roll. The defense dice have "shields" on two of the six sides rendering a shield, a miss 33% of the time. Armed with no more information than that, a player knows that this is a game where the attacker has the advantage. (Note: This is very simplified, I am aware that there are other factors involved and that creatures roll differing numbers of dice. This is not intended as an analysis of Heroscape, rather a demonstration of the type of analysis available.)

Memoir '44 diceSystems such as Battle Cry and Memoir '44 are slightly more sophisticated. Hit results are not universal. There are unique icons for infantry, cavalry and artillery as well as other special modifiers. Unlike the Heroscape system, the "miss" results are built into the attack die. The faces of a Memoir '44 die are as follows: 2 infantry, 1 each of grenade, armor, a flag (retreat) and a star. The only difficulty in calculating the probability of rolling a successful event (a hit) is recognizing that the grenade is wild; they are infantry, armor and artillery for purposes of the calculation. With this information a player enhances his ability to play competently without reducing the experience to a battle of numbers.

It is only when one begins calculating these probabilities for Memoir '44 that you can appreciate the revolutionary brilliance of the system. Varying numbers of dice are rolled depending on the distance from the attacker to the target. Effectually this is a different CRT for each hex and this is all incorporated into the dice! The economics of the system is absolutely amazing.

All of the games and systems mentioned above are static; a hit is a hit whenever the proper face is rolled. The next step in this ladder is the Risk family. Risk-type games employ a dynamic system where the range of the attacker's success is a function of the domain of the defender's roll. There is no specific face of the die that guarantees a hit. What renders this just that much more engaging is the stipulation (rule) that ties are won by the defender. Though the Risk bashers may find this difficult to believe, mathematicians have been studying the Risk combat system for years. There are "real world" applications to discovering the proper solution to this type of problem. Two significant questions that arise are:

  1. What is the probability that an event (attack) will be successful?
  2. What is the expected potential cost (loss of units) of the event?

Baris Tan (Koc University, Istanbul) published his results in Mathematics Magazine (December 1997). Using Markov chains, he concluded that given equal armies, the attacker will succeed less than 50% of the time. Additionally, he determined that a 2 to 1 attack would be successful 80% of the time. Unfortunately, as is the case with so much of probability theory, the same data can produce a different result based on the methods used for analysis. Jason Osborn (North Carolina University - Raleigh) disagreed with the findings suggesting that Tan had assumed that each die roll was an independent event. Though seemingly a minor difference, Osborn concluded that the attacker had a better than 50% chance of success with equal armies if the number engaged on each side had a minimum of 5 armies. These are examples of the analysis being done, to date there has been no definitive solution to the problem.

So what does this mean for gamers? Is this type of analysis actually required to play the game? Am I even serious about this... after all, it's only Risk? Reality check—when we gather to play a game, say Clash of the Gladiators, no one whips out a graphing calculator prior to or during play. However the purpose of the cursory analysis presented above is to demonstrate the methods available when examining the apparent randomness of a dice game. These games may be "dice fests" but it is not accurate to describe them as luck fests.

Games with dice are often easier to analyze than games with cards or tiles. With Risk for example, minimal calculations are required to establish a "best result" table. A "best result" table is basically a projection of the probability of success. Consider the following two "best result" tables for imaginary games involving a coin toss. In the first game a single coin is tossed and the results are applied. As the only possible results are Heads (H) or Tails (T) the probability for success is .50 (a 50% chance of obtaining either result). The second imaginary game requires two tosses to secure a result. In this case each of the second tosses of the coin are related to the first result and the table becomes:

H-H H-T T-H T-T

Assuming that the order of the toss is not significant then it is apparent that our most probable result is a mix of Heads and Tails with two possible results out of the set of four. If we were seeking a toss that resulted in dual Heads, there is only one in four, a 25% chance that we would be successful. The actual formula requires that you multiply the probability of the individual events ( .50*.50 = .25) but it is often just as easy to recognize that there is one acceptable result out of four possible results.

Blue Moon or Magic: the Gathering are exponentially more complex as the interplay of the actions/events introduces a range of results far greater, less predictable than the possible rolls of two d6. Does this mean that Blue Moon is more random than Risk? Of course not, complexity and randomness are not directly proportional. From a non-gaming view point the complex relationships in Blue Moon are amazing and the fact that there are no glitches, no lock-ups is impressive.

The Others

Not only does God play dice with the Universe, He throws where they cannot be seen.

Niels Bohr

We would be remiss if we failed to conduct an even cursory examination of competing forms of random event generation. There are three other common methods for generating random events: spinners, cards and tiles.

Entdecker spinnerSpinners - It's all in the pie cut. Spinner construction can be tailored to maximize or minimize the amount of randomization that is introduced into a game. Most common spinners have pie cuts that sweep out equal areas; every event has an equal probability of occurrence. This is identical to the probabilities generated by rolling a single die with faces equal to the number of pie wedges. Very often some method to compensate for this is introduced. For example, Venezia (two spinners!) allows the player some movement to alleviate the randomization.
Nuclear War spinnerAn alternate method that significantly reduces the randomization is a spinner constructed with variable area wedges. As a thought experiment, imagine a spinner with only three wedges constructed on the face of a clock. We can ensure a 50% probability of a specific event by delineating one wedge that encompasses half the face (12 to 6). We can offer a 42% probability for a second event with a wedge that stretches from 6 to 11 and an 8% event with a third wedge from 11 to 12 on the clock face. Additional wedges would produce varying probabilities and all of this is controlled with a spinner. For some reason, these types of spinners are rare.

Cards - One can not possibly examine all of the varieties of card games and the associated probabilities in a few paragraphs though some generalizations can be observed. Card games are usually more difficult to analyze than dice games due to the size of the initial domain (52 cards in a standard deck), their possible combinations and whether there is any form of re-shuffle allowed. The possibilities and analysis can be staggering. For example, there are in excess of 2.5 million possible hand combinations in a game of Five Card Stud (Poker). Compare this with the 36 possible results of rolling two d6. It would be futile to attempt to persuade someone that most traditional card games do not border on the extreme edge of randomization.

Non-traditional card games, even those with reduced decks, can also be extremely difficult to analyze. Games such as Magic: the Gathering or Blue Moon employ systems where the interrelationships between cards is intricately complex and often have variable values based on these relationships. A specific card played at one point in the game is worth X where if played at another time may be worth a completely and substantially different value. (Consider the "Gangs" in Blue Moon.)

Tiles - For our purposes we can segregate tile games into two general categories: those games that share card game mechanics and those that have unique mechanics. Some of the tile games found in the first group are little more than card games printed on thicker stock. Of course the draw pile is the equivalent to the draw deck in a card game and the game mechanics will determine the suitability of using a card game format and techniques for analysis. There may be fewer tiles than there are cards in a standard deck but the same formulae would apply and the calculations are identical. Games of this type include King's Gate, Kingdoms and Carcassonne.

The second group of tile games, the unique games, must be considered individually as they can be as different as one boardgame to another. Through the Desert includes no random element following the initial, pre-game placements. Most of the "heavy" tile games (Mexica, Java, Tikal, etc.) have minimal if any randomization; certainly substantially less than any dice game and this appears to be typical of games in this genre.

Conclusion

Einstein: "God does not play dice with the universe."
Bohr: "Einstein, stop telling God what to do."

The degree of randomness in games, in particular, games with dice, is often a matter of perception or lack of knowledge. Removal of all random events from a game invites the possibility of reducing the game to a mere puzzle; something solvable such as Tic-Tac Toe. It is natural to fear the unknown; to fear that which we don't understand; to be wary of the surprise. So games with a significant degree of random development or games where the random element is difficult to analyze become anathema; condemned and labeled with the infamous tag "dice fest" or "luck fest".

Too often we curse the randomness without acknowledging its contribution to the game itself. Understanding the degree of randomness and the possible ramifications allows a player to develop counter strategies, even gaining an advantage over the random factor. This knowledge can be as critical as strategic planning itself. Ignoring the random element of a game while concentrating on map or resource analysis is as ineffectual as using only one foot to pedal a bike. At the macro level, it is random events that render life so interesting. At the micro level, it is often randomness that elevates the challenge in a game, resulting in a far more interesting experience.

- Dave Shapiro

Horizontal line

About | Link to Archives | Links | Search | Contributors | Home

All content © 2000-2006 the respective authors or The Games Journal unless otherwise noted.

http://www.thegamesjournal.com/