03 April 2011

[Literature] Game Balance ch5 - The human-side of probabilities

My notes from course 5 of the Game Balance class of Summer 2010, by Ian Schreiber.

The more randomness in a game, the more casual it is: there are fewer strategic choices. Less randomness means more of the fate of the game lies in the player’s choices. That’s not always the case, though. Ex: TicTacToe has no randomness, but is not about skill. Other counter-example: a Poker hand is random, but there are skilled Poker players.
Skill dominates (over luck) if the player is rewarded for predicting and/or responding to the randomness. Ex: one can base his decision on probabilities in Poker, but not in Black Jack.
There is no skill in executing a difficult pattern that you’ve practiced (eg counting your hand or memorizing cards in BlackJack). Skill appears in planned, successful and unexpected decisions.
Luck can be carefully increased to even the playing field. Ex: headshots make it possible for weaker players to sometimes luckily kill better players. Head shooting is also a high-level skill. How much luck or skill a game should have depends on the target population: social games and kid games = luck, hardcore games = skill.
How to transform skill into luck:

  • replace player choices by dice rolls
  • throw less dices (so that there is no law of large numbers, hence less prediction)
  • increase the impact of random events on the game state
  • increase the range of randomness (like changing a d6 roll to a d20 roll)

Human biases

Humans tend to remember things that happen the least often, or forget those who are unpleasant (eg match loss), hence they tend to overestimate their level. Humans have a flawed understanding of probabilities, hence showing the actual probabilities will actually make them feel like something is wrong/broken. Here are a bunch of biases humans are subject to:

selection bias improbable but memorable events are seen as more likely than they really are
self-serving bias "unlikely" (5%) is interpreted as "nearly impossible" (0.01%) when the odds are in your favor. However, "unlikely" (5%) is interpreted as "possible" (30%) when the odds are not in your favor.
attribution bias positive random result is assumed to be because of a player’s skill, negative random result is assumed to be bad luck/cheating
anchoring over-evaluation of the first/biggest number seen. Ex: losing 2/3 of the trials is not as bad as losing 20/10 of the trials. Consequence: small base dmg but high bonus dmg = player likely to underestimate.
gambler's fallacy assumption that a string of identical results reduces the chance the string will continue
hot-hand fallacy assumption that a string of identical results increases the chance the string will continue


Dishonest game design = make the players believe they are very likely to win. It increases excitement and anticipation of hitting a jackpot. Hence it keeps them engaged. Ex: dishonest car dealership: show VERY big prices first to anchor the customer, then show "normal" big prices: they look like small prices.
Honest game design = tell the player one thing, but actually do something else. Examples:

  • If the player has 75% chance of winning, under the hood roll the number as if it were 95%.
  • If the player gets a failure, make the next failure less likely, and the one after that even less likely (= avoid long streaks)
  • Hot-hand streaks should happen in a positive feedback loop, to counteract the greater chance of a miss after a string of hits (ie give bonuses when series of wins)

But also, stay ethical as much as possible. Display wins, losses and various stats to enable players to grasp their actual skill and to "prove" the game is not unfair/imbalanced or that the AI is not cheating.


In a game where the player can save anywhere at any time, players are likely to save just before an important roll, and keep reloading until their roll succeeds.

  • Naive solution: do not re-generate the random number each time they reload => new problem: players can now anticipate future rolls (the seed has not changed).
  • Alternate solution: the player can save anywhere, but the total number of saves is limited (cf the original Tomb Raider) => new problem: players need to know how far apart they should save on average so that in the end of the game, they still can save.

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