GDEV20-09-Outcomes And Uncertainty PDF

Outcomes and Uncertainty Predictable == Boring Lecture Time! Outcomes: Win Some, Lose Some Uncertainty: Rules = Certainty? A Detour: RNG Why are computer random number generators called pseudo-random number generators? One possible (and very simple) implementation is the linear congruential...

Outcomes and Uncertainty Predictable == Boring Lecture Time! Outcomes: Win Some, Lose Some Uncertainty: Rules = Certainty? A Detour: RNG Why are computer random number generators called pseudo-random number generators? One possible (and very simple) implementation is the linear congruential generator Linear Congruential Generator 1. Choose a nonnegative integer less than 10 2. Multiply by 31 3. Add 27 4. Mod 10 5. Remember/output the number 6. Go back to step 2 https://upload.wikimedia.org/wikipedia/commons/thumb/3/37/Dice_(PSF).png/952px-Dice_(PSF).png Linear Congruential Generator 1. Choose a nonnegative integer less than 100 2. Multiply by 41 3. Add 33 4. Mod 100 5. Remember/output the number 6. Go back to step 2 https://upload.wikimedia.org/wikipedia/commons/e/e5/Dice_(typical_role_playing_game_dice).jpg It's Fake, But Do We Care? Is there a way to predict the next number (mix and match the conditions below): Without knowing the formula? Without knowing the last number generated? Without knowing the range (minimum and maximum)? Back to our regular program... The goal of a system is to produce a measurable outcome In most games, the outcome will be unequal: there will be winner/s & loser/s Some games (and their players) use player scores as the measure of the outcome (and bragging rights) Back to our regular program... Even games without a clear end, like MMORPGs and simulations, have conditions that, if met, will result in rewards or penalties for the player/s You can also look at parts of the game instead of the entire game itself, and you will note that these subsystems produce measurable outcomes The Outcome's Outcome Result: There is competition! Does knowing beforehand who the winner will be affect your interest in a contest/etc.? https://upload.wikimedia.org/wikipedia/commons/3/3e/Archery_competition.jpg Uncertainty Uncertainty is a central feature of every game It has even been called the very essence of play However, does uncertainty (as we understand it) translate to chance and randomness? Uncertainty True or False: A game MUST incorporate dice rolls or random number generators to contain an element of uncertainty Provide examples Uncertainty Despite all the rules on shuffling, there are still “better” decks in card games like Magic: The Gathering Games like Starcraft 2 that are used for e-sports have rather rigid rules and none of those “X% chance that Y will happen” found in other games Uncertainty Most multiplayer games (especially FPS and RTS games) are games of skill, not chance But given that all the participating players are of roughly equivalent ability, how certain are you that player Z will win? Again, why are most televised sports events broadcast live? True or False? Uncertainty disempowers players, for a sense of choice and agency is removed; they feel they do not have full control Uncertainty allows players to believe their decisions have an impact on the game; they still have some control over how the game plays out True or False? Should one be true and the other false? Are both statements false? Are both statements true? True or False? Should one be true and the other false? Are both statements false? Both are true: This is the paradox that ties uncertainty to meaningful play! Decisions do have results, but there’s no meaning to the decision-making involved if you already know the “best” choice Decisions, Decisions... According to Richard Epstein, in The Theory of Gambling and Statistical Logic, there are three types of decision-outcome relationships, leading to three degrees of uncertainty: Uncertainty Risk Certainty Predictability == Boring Certainty simply means that the outcome is already known in advance A game that is completely certain is hardly a game at all, and definitely not much fun to play Predictability == Boring Calling heads or tails on a coin flip... using a two-headed coin Play Tic-Tac-Toe will always end in a draw if both players know what they're doing, even if you can't predict their exact decisions in-game Click to buy a seed, click to plant the seed, click to water, click after 4 hours to harvest, click again to get some money, repeat Risk != Uncertainty We normally associate the other two degrees with the word “uncertainty” Risk refers to a situation in which there is some uncertainty but the game's players know the nature of the uncertainty in advance In other words, math (probability, to be more specific) Risk != Uncertainty In dice rolls, roulette wheel spins, etc., there is some uncertainty but you can precisely calculate the percentage chance of the various outcomes Some games tell you exactly what % chance Juan Bigfayt has of scoring a hit against the enemy you targeted before you decide whether or not Juan should still pull the trigger 100% Uncertainty? Uncertainty describes a situation in which players have no idea about the outcome Your opponent in an online game might be selected at random – you may face a master who will most likely beat you, or a complete n00b who stands no chance against you 100% Uncertainty? Unless you know your opponent inside and out, you cannot be statistically sure of the outcome Just because a dungeon run with a group of friends today was smooth doesn't mean tomorrow's run with the same group in the same area will be just as smooth How Pure Are You? Battle Tetris usually pairs you with a similarly-ranked player You may know your friend, but when you play against each other, are you absolutely, mathematically sure about your chances of winning? Even if you gamble, your overall loss or gain for an evening of play isn’t guaranteed unless you cheat Your attack is guaranteed to do damage, but will it deal critical damage? How Pure Are You? Games of pure certainty are rare (and not that fun) Games of pure risk are also rare (except in casinos) Games of pure uncertainty are also rare (because that may imply a chaotic system where EVERYTHING is random, even the results of pressing a button) In games, we combine* all 3 degrees of uncertainty in that dynamic web we call complexity With Your Powers Combined... Certainty = information that the player knows are "guaranteed" Examples include: Actions they can perform How these actions can affect the game state Cases of guaranteed "if X then Y" With Your Powers Combined... Risk = information that the player knows with an estimated chance attached, like RNG, odds, probabilities, etc. so the player can decide if it's worth "taking a risk" Examples include: Cases of "if X then N% chance of Y" where N is either a known value or can be solved for with some testing Odds of a particular outcome given a set of possible outcomes where each is equally likely With Your Powers Combined... Uncertainty = information that the player doesn't have or is simply unreliable due to a lack of estimated odds Examples include: What other players (especially strangers) will do First-time "blind" encounters Cases of "no idea what's going on" Do You Feel Lucky? How much of a connection does uncertainty, as felt by the player, have to the actual mathematics in the game system? The feeling of randomness arises from the player's experience of the game It is possible to generate this feeling even if there is no actual chance involved Because Complexity Have you ever capitalized on a “chance” mistake by your opponent in a game of Chess or Checkers? Have you ever experienced seeing your horde of fully-upgraded, ready-to-strike infantry completely decimated by well-placed enemy artillery, because your enemy “got lucky”? Because Complexity Have you ever been hit by a “stray” rocket in an FPS? Is there really such a thing as a “guaranteed-win” strategy? In a game, the “feeling of randomness” is more important than randomness itself! Is it Good to Have One in a Game? Have you ever been hit by a “stray” rocket in an FPS? Is there really such a thing as a “guaranteed-win” strategy? In a game, the “feeling of randomness” is more important than randomness itself! Reminder You should probably start on your game design document already! Up next: OP, imba, etc.