A Matter of Luck

By Richard Todd

"I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all."

Ecclesiastes 9:11

Introduction

Luck plays a significant part in many games. Indeed, some games, such as snakes and ladders, are entirely a matter of chance yet still manage to captivate their players.

One of the many decisions, therefore, that the designer of any game must make is whether or not to add an element of luck in the form of probability-based randomness.

Chance outcomes clearly do not always improve gameplay, but nor do they always necessarily hinder it.

In some circumstances, luck enriches the very forces that motivate players, whilst in other circumstances it does the exact opposite.

The nature of luck, however, is not always self-evident as the following well-known and enigmatic aphorism of Stanislaw Jerzy Lec illustrates.

"If a man who cannot count finds a four-leaf clover, is he lucky?"

Unkempt thoughts (1962)

Game developers are sometimes faced with similarly challenging decisions when contemplating whether to include some kind of deliberate randomness. For example, in the video game Unreal Tournament, when a player shoots at a target with the "enforcer" weapon, the projectile does not necessarily hit the point that is aimed at; a random deviation is added that scatters shots.

This introduces a degree of realism from an observer's perspective and no doubt gives beginners a fair chance against more experienced players, but it can also potentially frustrate skilled players.

Is it overall a good idea and, if not, could realism have been introduced in a better way?

Here in this article, with particular reference to computer games, we present a formalism through which designers across all genres and platforms may better understand not only the nature of luck, but also the effect that it has on gameplay and player motivation.

We show that luck is easily broken down into individual categories and that in doing so, a positive or negative effect on particular aspects of gameplay is observed.

First we investigate and classify the various types of luck that occur. Next we enumerate various qualities of gameplay such as motivation and learnability. We then relate the types of luck to their effects, good or bad, on these qualities.

The designer of a new game examines each proposed probabilistic feature and determines which types of luck it produces within the taxonomy. The influence of the proposed feature on each of the various qualities of gameplay is then readily calculated.


Some Examples

Consider the following examples of luck in a computer game. We number them so that we can refer back to them.

Example 1 - A player takes poor aim in a game of Unreal Tournament but random scatter causes him to hit the target despite this. (Random scatter occurs in many if not most 'First Person Shooters': weapons are programmed to fire their projectiles not directly where the crosshairs indicate, but within a given radius around the crosshairs.)

Example 2 - A player of Diablo strikes accurately at his opponent, but the opponent is saved by the automatic dodging mechanism from being hit. (The player does not need to worry about accurately aiming his strike in Diablo. Provided that the player is facing the intended target and is within range, to secure a hit the player needs merely to overcome the probability-based evasion mechanisms that automatically cause the opponent to dodge.)

Example 3 - A player of Minesweeper plays correctly but, reaching a point at which guesswork is necessary, unfortunately chooses a square that uncovers a mine. (Minesweeper is the popular logic game supplied with most versions of MS Windows.)

Example 4 - A player of World of Warcraft shoots accurately and delivers a Critical Strike. (Once a strike is successfully inflicted on an opponent within World of Warcraft, it has a probability-based chance of inflicting double damage; any such Critical Strike that occurs is reported to the player by an on-screen text message.)

Example 5 - A player of SimCity builds a magnificent city that unfortunately is destroyed spontaneously by a natural disaster. (Natural disasters occur randomly by default unless the game settings are deliberately altered.)

Some Variables

We describe any instance of luck by three variables that we list below and summarize in Table 1. Each of the four examples given above is fully classified in terms of these variables in Table 2.

Polarity - Chance is sometimes in the player's favor: we refer to this as positive luck (e.g. Example 1). On the other hand, chance is sometimes to the disadvantage of the player: we refer to this as negative luck (e.g. Example 2).

Transparency - Clearly a player may either be aware that a particular outcome was due to chance (e.g. Example 3) or he may be ignorant of that fact (e.g. Example 1). We refer to these as evident and concealed luck, respectively.

Congruity - If the chance event occurs as a direct consequence of play in accordance with the requirements of the game then we call the luck proper (e.g. Example 2). However, if the play is contrary to the requirements of the game then we refer to the luck as improper (e.g. Example 1). A third possibility is that the luck is entirely incidental: we then call it neutral (e.g. Example 5).

Table 1: Variables descriptive of luck.

Variable

Values

Polarity

Positive / Negative

Transparency

Evident / Concealed

Congruity

Proper / Improper / Neutral



Table 2: Classification of examples.

Example

Polarity

Transparency

Congruity

1

Positive

Concealed

Improper

2

Negative

Concealed

Proper

3

Negative

Evident

Proper

4

Positive

Evident

Proper

5

Negative

Evident

Neutral

In all there are 12 distinct types of luck in our classification. In general, any feature that injects randomness into a game simultaneously introduces more than one type of luck. For example, random scatter occasions improper positive luck when it causes a poor shot to hit on target (Example 1) but proper negative luck when it causes a well-aimed shot to miss.

If the player is provided with precise crosshairs, and has time to check where they are aligned at the time of pulling the trigger, any luck relating to random scatter will be evident; otherwise it is concealed.

Careful consideration like this, of each proposed probabilistic feature, allows the game designer to enumerate the types of luck that it produces. The results are helpfully displayed by laying out the twelve possibilities as a type of Karnaugh Map. For example, Table 3 summarizes the effects of random scatter from the perspective of a player taking a shot at an opponent.

Table 3: Types of luck produced by a random scatter mechanism in which during rapid exchange of shots with an opponent, the player sometimes has time to see whether the crosshairs are aligned on the intended target, but sometimes does not.

 

 

Concealed
Negative

Concealed
Positive

Evident
Positive

Evident
Negative

Proper

Yes

No

No

Yes

Neutral

No

No

No

No

Improper

No

Yes

Yes

No


Some Qualities

The game designer is of course ultimately interested in the effects of a proposed probabilistic feature on gameplay. There are various qualities to any game, each of which is important if the game is to be enjoyable and successful. We consider each of them in turn and offer our subjective impression of the relationship to luck.

Attainment - Imagine that when playing Monopoly, despite getting poor rolls of the dice, you make shrewd decisions and you win the game by a small margin. This is inevitably more satisfying than winning by the same margin by sheer good fortune in the rolls of the dice.

We refer to this as the player's sense of attainment, in other words the player's perception that his (or her) success is a true reflection of his skill of which he can be justly proud.

Clearly this is affected by luck only when the player is aware that luck has been involved; the sense of achievement is all the greater if the player knows that he has triumphed despite bad luck, and weakened if the player knows that he has been fortunate.

We define this relationship in the following table where ↑ and ↓ indicate enhancement and impediment, respectively, and '-' denotes the absence of any effect.

Table 4: Effects of luck on 'attainment'.

 

 

Concealed
Negative

Concealed
Positive

Evident
Positive

Evident
Negative

Proper

-

-

Neutral

-

-

Improper

-

-

Reward - Consider the game of Tetris. The choice of which geometrical shape appears next is entirely down to luck. If a player wants a particular shape to appear (say a straight row of four) then he (or she) will be immediately rewarded if the next piece is that shape. Reward is thus the pleasure (or displeasure) that the player associates directly with good or bad luck. All positive luck gives the player this experience of joy and all negative luck causes displeasure.

Table 5: Effects of luck on 'reward'.

 

 

Concealed
Negative

Concealed
Positive

Evident
Positive

Evident
Negative

Proper

Neutral

Improper

Control - This is the sense of government that the player has in trying to achieve his goals. Therefore all luck diminishes control, except luck which occurs as a result of the player playing poorly. For example, control is non-existent in a game of snakes and ladders because every move is entirely random.

Table 6: Effects of luck on 'control'.

 

 

Concealed
Negative

Concealed
Positive

Evident
Positive

Evident
Negative

Proper

Neutral

Improper

-

-

-

-

Accessibility - This is the ease with which beginners can enjoy the game. Positive luck of any kind enables a beginner to progress further while negative concealed luck impedes and frustrates him (or her). For example, the card game poker clearly has wide appeal for novices because even they stand a chance of winning through luck alone.

On the other hand, if they know that they have simply had bad luck, there is no reason to suppose that they will be disheartened. Similarly, if they are not playing according to the objectives of the game, any kind of luck is immaterial.

Table 7: Effects of luck on 'accessibility'.

 

 

Concealed
Negative

Concealed
Positive

Evident
Positive

Evident
Negative

Proper

-

Neutral

-

Improper

-

-

-

-

Learnability - This is the ease and speed with which the player can develop in skill and ability. This requires a clear, deterministic relationship between the player's actions and the consequent effects. Any kind of luck that confuses that dependency impedes learning. For example, the Unreal Tournament mode Instagib is easy to learn because of the clear deterministic relationship between how well a shot is aimed and its consequence.

Table 8: Effects of luck on 'learnability'.

 

 

Concealed
Negative

Concealed
Positive

Evident
Positive

Evident
Negative

Proper

-

-

-

Neutral

-

-

-

-

Improper

-

-

-


Each table can be summarized in a more concise way:

Moreover, a number of inter-relationships between the qualities are also immediately evident:

Examination of the tables in this way helps us to verify them since if any of the derived results are incorrect, so too must be at least one of the corresponding tables.

Feature Evaluation

We can now gain insight into the merits of any proposed probabilistic feature. Consider, for example, the effect of random scatter on the sense of attainment. We simply convert each cell in Table 4 to a '-' symbol if the corresponding cell in Table 3 is 'no', otherwise we leave it unaltered. We obtain the following.

Table 9: Effects of random scatter on 'attainment'.

 

 

Concealed
Negative

Concealed
Positive

Evident
Positive

Evident
Negative

Proper

-

-

-

Neutral

-

-

-

-

Improper

-

-

-

We see that there is a conflict in that through evident negative proper luck random scatter increases the sense of attainment while through evident positive improper luck, random scatter has the reverse effect.

The overall effect cannot be determined in this case by the purely qualitative model presented here; the conflict can be resolved only by subjective judgment of the relative importance of the two influences. However, repeating the process for all five gameplay qualities we obtain the results summarized in the table below.

Table 10: Effects of random scatter on all gameplay qualities.

Random Scatter Luck

Attainment

Reward

Control

Accessibility

Learnability

Concealed Negative Proper

-

Concealed Positive Improper

-

-

-

Evident Positive Improper

-

-

-

Evident Negative Proper

-

-

We see consistent effects of random scatter on three of the gameplay qualities: control, accessibility, and learnability are all decreased. This strongly suggests that random scatter is an undesirable mechanism in a first person shooter. Perhaps for this reason, the designers of some games (e.g. Call of Duty) have opted instead for random perturbation of the crosshairs.

Since the player chooses when to fire the weapon, control, accessibility, and learnability are preserved. Use of a classification such as ours thus simplifies the selection of desirable features and helps to avoid costly design errors.

For example, the oversight of inadvertently allowing enemy automata a dodge facility (concealed proper negative luck impairs reward, control, accessibility, and learnability) can be detected and eliminated early in the design process.

Discussion

We have presented here an analytical approach to classifying and understanding how luck influences gameplay for good or bad. The tables specifying the relationship between the various gameplay attributes and luck represent only our subjective impression. Opinions may of course differ and some may prefer different tables.

However, the important point is that our formalism makes it possible to consider these questions more clearly. Objective tables could no doubt be derived scientifically by psychological experiments.

Furthermore, it would be simple and straightforward to implement a computer program to edit the various tables and to perform the analysis.

Equipped with our analytical tools we return to the philosophical conjecture posed by Stanislaw Lec.

We see now that the innumerate man who finds a four-leaf clover is indeed lucky. However, although his luck is positive, it is also concealed and neutral!

To experiment with different luck conditions as described in this article, be sure to download the author's Luck Analyzer Program (HTML) by clicking here.

Interesting Reading

Acknowledgments

I am grateful to Robert Todd, Ron Todd, Carl Richards, and Martin Heffer for helpful insights in the preparation of this article, but any errors and omissions are entirely mine.

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Photos by cygnus921 and kaibara87, used under Creative Commons license.  

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