Designing Player's Luck: Introduction (Part 1)

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(hypothetical conversation between a Game designer and me)

-What is Luck anyway? Just random chance? Well, I think fully predictable game would be completely boring. I mean this is a digital game, so why make it as obvious as Chess?
-Indeed random elements can add something to gameplay. Even Chess have something seemingly "random" as you can't perfectly predict the plays your opponent will do. But when it comes to digital games most games employ random chances affecting things like the chance to hit or miss with a sword slash or the chance to get a random reward. - I reply
-But don't Hit chances and Drop Chances feel entirely different for a player? - Insightfully points out the developer
-Yes, hit chances are related to both Probability and Immersion. The random chance adds depth to the gameplay by providing two different outcomes for attacking (hitting or missing). This makes players have to adapt dynamically (attack again or use another skill) or strategically (planning a different character or asking for someone's help). - I explain about the former
-And about Drop Chances? - asks him
-Well, drop chances have to do with Reinforcement Schedules and Character Growth. Most times we use random drops to make player repeat a specific behavior like killing monsters (or a specific monster category) or doing a stage/run. This can help to artificially prolong the game's duration (by setting overall low drop chances) but also influences a lot on the satisfaction the players experience (when they finally get that reward). - I point out about the later
-So what should I do? - Asks the designer
-Well, "stay awhile and listen" - I say as I make a reference to Diablo's quote from Deckard Cain

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   In this part I'll take a brief look at the ideas of Luck, Probability and Reinforcement Schedules and related constructs. (placeholder for part 2 part 3 and part 4)

Luck

• Refer to Luck - Wikipedia
• Prescriptive sense: Some sort of supernatural force that determines the outcome of events
• Descriptive sense:  An unlikely result (either positive or negative)
• The prescriptive sense refers to the belief that something controls the result of apparently random events. This is obviously related is related to Psychology concept of Locus of control (I'll explore it in the next section
• The descriptive sense is obviously related to the Probability of an event but also encompasses some degree of interpretation of the meaning of the result. Examples:
• "It's very unfortunate to stumble and break a leg" - An unlikely and unpleasant result is seen as bad luck
• "Lucky! I guessed the correct answer in a true or false test I needed to pass Math" - A very positive result, even if not so unlikely is considered luck
• "I received small cash instead of a note as change" - an unimportant event even tough unlikely isn't a matter of luck

Locus of control

• A theory explaining how people perceive what influences the outcome of events in their lives. There are 2 dimensions to consider:
• Internal/External
• Losing weight depends my willingness to follow a diet (Internal)
• Winning jackpot is up to the machine (External)
• Attribution of control - degree on how much a person believes an event is controllable
• Controllable: "If i study harder I'll pass the math test"
• Not controllable: "Damage caused by a natural event"
• Can be either in a specific or general:
• Karma as an explanation for good and bad events (general)
• An athlete's belief that winning or losing in their sport is due personal effort (specific)
• Now take a look at Weiner's attribution theory (Modified) as applied to student motivation scheme (image credits to Wikipedia)

	Perceived locus of control
	Internal	External
Attributions of no control	Aptitude*	Chance/luck
Attributions of control	Effort	Task difficulty

*I changed the term "ability" to aptitude because aptitude is usually understood by common sense as something you are born with, while ability could be earned with effort

   It's important to note obtaining a benefit without applying any effort (i.e. random rewards) evidently might be seen negatively by people with an internal locus of control. This could explain why so many people dislike playing Monopoly as they grow up. However you can circumvent this problem by making the random reward contingency require some sort of skill or effort. 
Here a few other examples:

• While killing monster grant some random loot, killing higher level monsters gives more/better loot - benefit proportional to the risk
• A daily random reward might increase with each day the player log in the game - benefit proportional to commitment
• A stronger attack might miss every so often - benefit with strategic risk

   It's also important to take a note about Superstitious Behavior. While this concept has been discard by modern Behaviorism due it's inherently subjective nature, it basic related to the idea of an organism behaving as if a non-true contingency was in vigor - i.e. betting the numbers corresponding to the birthdays of relatives at Lotto because that would make you win more often. In most modern games this is hardly a problem since information is plentiful with the advent of Internet.

   But every so often we can observe players systematically making choices or doing behaviors without a fully rational explanation. This can go both ways, a player can believe they can control a random event by doing something or they might not know they can control an event and act randomly to their detriment.  

Lesson: Explain the contingencies to the player so they can play the game adequately

Probability

• Can be understood as the probable Frequency of a set of events.
• "I have 50% chance to guess correctly heads or tails with a fair coin"
• Alternatively it can mean the Propensity of an outcome even when the number isn't available:
• "It's very likely to rain in the last days of autumn"
• Probability theories have been applied to several fields like Financial, Economics, Programing, most Sciences, among others.
• Even on daily basis most people deal with probabilities:
• When guessing if it'll rain, snow or be a sunny day (weather)
• When some news tells us the majority opinion about something (like voting intention during election)
• When assessing the advantages and disadvantages of a choice

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   I hope this brief text helped clearing the difference between Psychological aspect of luck (Beliefs) and the numerical chance of "random" events (Probability). Next time I'll examine some cases of using random chances in games and I'll further explore the use of Probability in games.

References:
Locus of control - Wikipedia
Luck - Wikipedia
Probability - Wikipedia