# "Fairness" in game?

#### SEPKA

##### What???
In context of 2 player competitive game (excluding sport because I know nothing about these) I always find people define "fairness" as each player have an equal chances of winning. However, upon close inspection it does not seems like a good definition, since the only game would be fair by this definition are chances game (game that is totally based on chance, such as flipping a fair coin).

So let's discuss. Do you have a definition of fairness that are both intuitive and consistent even upon close scrunity? Or do we have to accept that only the game of chance can be fair?

#### Sirian

##### Redshirt
Thats funny 'cause i don't like chance games for they are basically unfair from my point of view. To me, a "Fair" game is a game where the best player will win, but in chance games its not the best player, its the most lucky. So to be fair you have to give each player the same starting conditions, and the same game mechanics, but personal skill is not an unfairness factor(for me).

#### Sugarpop

##### accepts advice on his English
Mission: Definition

Could you elaborate on this 'close inspection'?

#### SEPKA

##### What???
@ Sirian: but when you think about player skill as being better to justify why unequal chance of winning are still fairness, then you face the question of how to define what it means by "better skill"?
@ Sugarpop: let's say that you play a chess game. Then either black or white will have a sure win strategy, or both will have a sure draw strategy. In the first case, the chance of winning are not equal, and in the second case, the chance are 0. Yet it still tempt to said that chess is a fair game. It get worse with game like weiqi (a.k.a. Go!) where the rule try to make the game fair by adding point to the white player (move second), but this means that either black or white have a sure win strategy. Sure it both case people are yet to figure out such strategy, but the existence of such strategy is real. Or we can look at a FPS, and we see that given a symmetry map, each player will simply take the best weapon, choosing a hiding position that give the best expected outcome, aiming weapon ready at the angle with best expected outcome: if the player is of the same skill, then it all left to the chance of making failure, randomized calculation of bullet damage, etc.; if the player is at different skill, then obviously 1 player do not have an equal chance to win. The list can go on with many other game but I only talk about those because it encompass several type of game mechanics (simultanous vs non-simulatanous; real time vs turn based; draw allowed vs draw not allowed).

#### INTPINFP

##### Active Member
I think of games as a fun "test" for several people. Primarily, the game should be about having a good time while playing. Secondarily, it should have some sort of social or artistic aspect. Thridly, if is is a competive game (Not Solitaire) the outcome should be determined by the player with the most determination, courage, skill, hardwork and intelligience.

I don't find games where everyone wins to be fun at all. Conversely, games with only 1 winner (eg: Free for all, 1 vs. 8) I don't find fun because of the intense diificulty curve. 1v1 and Team games I find the most entertaining.

Also, certain games (ie checkers) need a random factor, because it is possible to draw the game regardless of the other person's actions. Chess, you can draw it, but there are ways the other player can prevent such a stalemate.

Also, many FPS have variable health options so that skillless players have a benefit that the other players don't, making it somewhat more fair for both parties.

#### Sugarpop

##### accepts advice on his English
I imagined that 'fair games' were made to test the human component ceteris paribus. Games are not made to produce a in-the-long-run score of 50-50, but to see which player is the best.

Sure it both case people are yet to figure out such strategy, but the existence of such strategy is real.

This is probably where my ignorance of chess - and game theory for that matter - shines through, but how do you know that such a strategy exists? And, if no one has ever found one, does it even matter?

#### SEPKA

##### What???
@ INTPINFP: I think game with everyone win is cooperative game, not competitive game, which I no little about.
@ Sugarpop:
But if you want to test human skill, you need to have a "fair" game. However to determine if a game is "fair" is not, you might have to rely on knowledge on human skill, which you don't have. This sounds like a catch-22 to me.
The existence of the strategy seems quite important to me, because that tell me that it is theoretically possible for one player to forced an outcome: if that outcome is winning, the participant of another player is pointless because no matter how skill they are, there are 0 chance to win; if the outcome is draw, then the chance of winning is equal, which is 0.

Explanation that such strategy exist:
You can actually show that such strategy exist, you use a decision tree, which is essentially a directed graph:
Each node contains all information about a particular game state (for chess it would be position of pieces, pieces still on board, king/rook moved or not, en passant available or not, number of turns since last pawn move or capture, whose turn).
Each node will have a directed edge pointing toward another node denote the state of the game which can be reach by making a valid move.
So we start by contructing the node denoting the starting state, then construct the tree from there. The rules of chess ensure that the game will terminate, and since there is a finite number of possible move from any state, the tree would be finite, albeit super huge.
Now colour those node. The node will be coloured according to what outcome can be forced from the corresponding state: white for white win; black for black win; purple for draw, and no colour if the outcome cannot be forced.
Since all the endgame state (at the leaves of the tree) are forced outcome, they will be all coloured. Because the leaves are all coloured, if there still exist a non-coloured node, at least one of them will have all children coloured. Colour that node as the same colour as the best outcome among the node (so for example if the node is at black turn and all the children are either purple or white then the node will be coloured purple). Eventually, all node will be coloured including the root.
If the root is purple, that means one player can forced a draw or even win regardless of the opponent. If the root is black, black can forced a win. If the root is white, white can forced a win.

#### Sugarpop

##### accepts advice on his English
@ Sugarpop:
But if you want to test human skill, you need to have a "fair" game. However to determine if a game is "fair" is not, you might have to rely on knowledge on human skill, which you don't have. This sounds like a catch-22 to me.

This is why your definition of fair seems a bit silly to me. If you always adjust the conditions of a game so that the scores will be even in the long run, you effectively take the element of competition out of comptetive games, thereby reducing them to coin-flipping contests.

The existence of the strategy seems quite important to me, because that tell me that it is theoretically possible for one player to forced an outcome: if that outcome is winning, the participant of another player is pointless because no matter how skill they are, there are 0 chance to win; if the outcome is draw, then the chance of winning is equal, which is 0.

Yes, in theory. However, the fact that such a strategy has yet to be found in chess tells me that, if you take human skills into consideration, we can disregard it in practise. We must either consistently consider the human factor or consistently not consider it.

I am not sure I understood your explanation. (i.e I am lazy and it is complicated.) It seems that you have attempted to describe something that could be much more comprehensible if it were illustrated.

If we insist on a theoretical approach: Is there proof of a play that can be forced by white from the initial state of the game, and that black can't counter to a win or stalemate?

------

We don't even know if we live in a universe that has room for chance anyway. As you probably realize, probability a matter of perspective. If we know the physical properties of the die, its initial state, the force with which it is thrown, the environmental factors etc, we will be able to give far more accurate predictions to a certain outcome than 1/6.

If we consider a deterministic universe and the notion of 'objective probability' (i.e considering all factors i.e an impossibility), the outcome of any game is given before it begins. Then, by your definition, all games must be unfair since no two outcomes can be equiprobable.

#### Sirian

##### Redshirt
sugarpop> I think that quantum mechanics are not deterministic but truly probabilistic. As far as we know for now, of course. It wouldnt affect a dice roll, but it means you can create non-deterministic games of luck by using a kind of "quantum dice".

SEPKA> better skill means better understanding of the game, better tactics, etc...
In a game like Quake 3, it means having better reflexes, speed, hand-eye coordination, accuracy, and also more practice. Knowing the game environment plays a big part too.

#### Artifice Orisit

##### Guest
In a FPS (Halo comes to mind) is it or is it not fair to lure people into an ambush?
For example: I'll shoot at someone nearby to get their attention, run into a building or the next room (any choke point will do) then I just stand beside the doorway and blindside them as they enter.

Isn't the whole point of being tactical not to play fair?

#### tom

@Sepka
I think you've missed the point with the concept of fairness in games. Lets take an rts as an example, if the programming means that player x always gains resources at double the rate of player y, it is not fair. If however, player x, due to better understanding of tactics, strategy and application, gains vastly more resources to player y that is still fair.
The purpose of a fair game is not for every person to have an equal chance of winning no matter what. Its purpose is to allow the player skill level to determine the outcome.

With regard to chess. I sincerely doubt that there is any strategy that is uncounterable, assuming a resisting opponent.

#### Sirian

##### Redshirt
Even if chess can be solved, humans wouldnt be able to memorize every possible positions and outcomes.

Anyway, about what is fair and what is not, i think you can compare a game to a trial. In a fair trial, each side is given the same chance to defend themselves. If it was luck determining the outcome, the trial would certainly not be fair. A game is the same in that sense : every player is given the same possibility to win, but only the best player will win. And if both players are of the same skill level, then it should either be a draw or a 50-50 chance of win.

Edit : i'm not saying that every trial IS fair, i'm just comparing a fair game to a fair trial.

#### Inappropriate Behavior

##### is peeing on the carpet
The best player doesn't always win.

However as to what is fair, it's not a matter of both sides having an equal chance to win but rather both sides having an honest chance to win. All you can ask for is that one side isn't given an inherent advantage by the game itself. Games of pure luck are a seperate issue.

#### Van

##### Member
If the game has a winner then isn't it unfair anyway? Someone has to have an advantage somewhere I think I've got this all back to front...

#### Sirian

##### Redshirt
Van > In the context of 1v1 competitive games, you expect a winner and a loser, you could say that the goal of such a game is to determine a winner. Now, the problem is that some people here take the player's own qualities into account when judging the fairness of a game. So if you consider the players as separate entities from the game, the game can be fair. If you consider the players as part of the game, then the game can only be fair if the players are perfect clones.

IB > Well sure the best player doesnt always win, but if the game is fair then you expect the best player to win most of the time.

#### SEPKA

##### What???
I think that certain quanlity of human have to be separated from judging the game fairness, while certain should be included. For example, if 2 people play chess then their chess skill should be excluded so the better one got higher chance to win but if one person is blinded then certainly the game will be unfair.
But there are still question arise:
I have never seen a game where it is explicitly intended to test a specific skill, so how do we determine which skill the game is testing the player? People can argue that dexterity is a skill that is tested in a blitz chess game, yet there will be people who disagree with it.
Another question go to IB: what do you meant by "honest chance"? If you means follow the rules, then there are still problem because a lot of time rules changed because it is unfair, so we can't judge fairness based on the rules alone (for example, offside rule are added to make soccer fair).
Also, how do you judge a game that seems fair if both player follow the rules, but cheater cannot be detected by any method?

#### Ghost1986

##### Active Member
i say a fair chance is both sides using as close to the same equipment as possible. games like World of Warcraft i find unfair due to a level 70 being able to kill a level 20 with no threat to them self. on the other hand call of duty 4 i find to be a lot more fair. a new player is mostly just restricted by skill. yes the more experienced people have nice perks and some better weapons but the advantage is not so great as to make it impossible for the new player to defeat the more advanced player.

#### Logos

##### Formerly Electric Wizard
(sorry if this is hard to follow) I find the Halo series to be incredibly "unfair" because its not always possible to survive every situation. For example if i was playing something like gears and it was me with stardard starting weapons versus the whole enemy team who had the better weapons it is still possible to win, however unlikely. Unlike in Halo when no matter how much better you are then the other people, at some point you're going to die. Like if you just spawned and a dude is facing you with rockets or a spartan laser and is moderately competant then there's nothing you can really do because of the stupid energy shields; or if two people attack you at once and you all have standard weapons once again there isn't much you can do. Then there's games like CoD:MF2 on which the maps are designed to encourage camping, and the way the game is set up, downright rewards glitchers and campers.

Which is why Super Streetfighter II Turbo HD Remix and Rainbow Six Vegas (the first one) are the two best games ever (based on pure skill)!

#### Infinite Regress

##### Active Member
However, upon close inspection it does not seems like a good definition, since the only game would be fair by this definition are chances game (game that is totally based on chance, such as flipping a fair coin).

Not always - it will depend on the odds offered
The structure of the game itself can be unfair