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Subject: How strong a first-player advantage breaks a game for you? rss

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J. Alan Henning
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I have a two-player card game that plays in 5 to 15 minutes. Right now, the first player has a modest advantage (looking across 48 logged plays with stable rules and card makeup).

It's an instant-win game, so some first-player advantage is to be expected. I'm testing a minor rules change to mitigate this (different starting hand sizes, different starting cards), but as I test these I'm looking for a target to shoot for. (I'm most likely not going to hit 50%, which is of course the ideal target.)

Poll
A 2-player game has a known first-player advantage. What percentage of wins for the first player would make you regard the game as "broken"?
51%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
      87 answers
Poll created by Jeffrey Henning

 
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Paul DeStefano
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If it's a game where you replay on switched sides, then I'm OK with it.
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Philip Becker
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So my first thought was that anything other than 50% is broken. And then I remembered hearing that white had an advantage in chess and started wondering if chess is broken. Which lead me to this interesting article:
http://en.wikipedia.org/wiki/First-move_advantage_in_chess
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J. Alan Henning
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Wow, Philip, that's an eye-opener. I would have guessed White won 51% of the time, not 52-55%.
 
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Kent Reuber
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Scarab Lords has some similar issues. The starting player can only execute 2 of the 4 possible phases during his first turn.

Also, SL uses the criteria that you have to have the winning condition at the *start* of your turn, which means that your opponent is always allowed a last turn to counter your potentially game-winning play.
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Bryan McNeely
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Are we talking abstracts here? If so, then surely going first would have some advantage, but I'm not going to quibble over a percentage point or two. One fantastic move will negate that.

If we're talking strategy games with turn order tracks, then it is certainly important to go first each round. That's why it's there.
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Blorb Plorbst
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Jeffrey Henning wrote:
Wow, Philip, that's an eye-opener. I would have guessed White won 51% of the time, not 52-55%.


Well, in chess, there are 3 options: Win, Lose, Draw

SO looking at the numbers, White might win 5-10 percentage points (pp) more often than black.

Whereas with only win/lose, a win % of 55% means that 1st player will win 10pp more than their opponent and at 60%, you're talking a 20pp advantage!

Much more significant than chess.

More over, chess is a game of pure skill where even a marginally better player can play black and win consistently. In a card game with inherent luck, I would get frustrated knowing that my odds of winning just got chopped in half if I went 2nd.

One balancing factor is to have a "score" and players would take turns playing first. Without the score, there would be little value to taking turns since it would likely end up with each player winning once.

Another way to balance player 1 advantage in a card game is to limit hand size. Hand size = options, less options for player one shifts control to player 2.
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Jeremy Lennert
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I suspect that the people voting 51% are overestimating their ability to even detect a difference at that level. I could count on one hand the number of 2-player games that I've ever played 50+ times against the same opponent, and I doubt any of them came within 1 game of a 50/50 win split.

On the other hand, I think I voted 65% mostly for the psychological reason that it's close to a simple fraction...

It also probably depends on the setting. First-player advantage in Chess is already big enough that tournaments spend a lot of time worrying about it (though it clearly doesn't "break" the game to the point that people no longer bother to hold tournaments at all), but it's small enough that casual players can largely ignore it.

I'm always amused when people bring up Chess in a discussion about game balance, because they usually use it as an example of a game that is not only balanced, but obviously guaranteed to be balanced, by virtue of symmetry--which is of course completely wrong, because the first-player advantage renders it asymmetric. Contrariwise, real-time computer games like StarCraft or Smash Brothers are often perfectly symmetric (if you consider race/character selection to be part of the game), so people often offer definitions of game balance that guarantee them to be 100% perfectly balanced without realizing it...
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Jeremy Lennert
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Occupy Boardwalk wrote:
Are we talking abstracts here? If so, then surely going first would have some advantage

Not so--abstract games with a first-player disadvantage are less common but definitely exist.

In fact, adding together 2 copies of any impartial game following the normal play condition always produces a game where the second player can easily force a win.
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J. Alan Henning
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Antistone wrote:
I suspect that the people voting 51% are overestimating their ability to even detect a difference at that level.

The psychology of this is fascinating. I had never noticed the bias until I reviewed the log. (Thankfully I kept the log!) The first player wins at 65%. That's a big enough difference, to me, to be broken, and seems like a large enough difference to be noticeable. As you said, it's almost a simple fraction: the first player wins 2 out of 3 times. Yet we'd never recognized it.

And of course there are streaks: quite a few occasions where the second player won 3 or 4 games in a row, or the reverse.

And testing is a challenge. We reduced the first player's starting hand by one card and they won 6 games in a row. Obviously, having a smaller hand doesn't improve the ability to win! But there's the data. We reduced it one more card and they lost 4 in a row.

The lesson, I guess, beware small sample sizes. And even if you've played a game 10 times, when you talk about it, your information is anecdotal.
 
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Steve Zagieboylo
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It depends somewhat on how subtle the skill is, and how much of an advantage skill is over luck.

Note that the chess statistics are misleading, and I'm surprised that the article didn't point it out. It says that of tournament games in which there is a winner, 52-56% of them are won by white. This doesn't seem like much, and would probably be perfectly acceptable for your game.

However, consider how much chess is a game of skill. I would estimate that at least 80% of chess games in tournaments are really decided before they start. That is, one opponent is enough better than the other that he's going to win no matter what.

So that means that the ~5% edge overall (making a 10% swing) is really coming from just 20% of the games! This means it is a 25% edge, or a 50% swing! Of course, a lot of this could be attributed to the psychological effect of going second, but that's an edge, too. And since you see the edge in computer vs. computer games, it clearly isn't purely psychological.

Back to your game -- I think it is somewhat a matter of perception. If the game has an instant win that possibly could happen on the first player's first turn, even if the chances are under, say, 2% of that happening, I still think it's broken. I don't want to play a game where I might already have lost before I even get a turn.

In fact, any early instant win should have to be telegraphed and interruptible. For instance, suppose we were to add to Rummy an instant win that if you lay down three sets in a row of ascending value, you win instantly (i.e. a set of 5's, followed by a set of 6's, followed by a set of 7's). One could argue that this would be an interesting twist to the game, making a strategy of keeping lots of cards in hand more viable. However, I'd still say that the rule is broken unless you have to do it over three turns, and that the opponent has some play option that breaks up the streak (possibly costing him a lot of points -- that would be ok.)

OK. I've rambled enough. I hope I gave you some food for thought. Or just ignore me.
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Only 100% would be broken because then there would be no point in playing the game. Otherwise it's all fine as long as the advantage is known and accounted for. Not all games need to be perfectly symmetric.
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Jeremy Lennert
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Zag24 wrote:
Note that the chess statistics are misleading, and I'm surprised that the article didn't point it out. It says that of tournament games in which there is a winner, 52-56% of them are won by white. This doesn't seem like much, and would probably be perfectly acceptable for your game.

However, consider how much chess is a game of skill. I would estimate that at least 80% of chess games in tournaments are really decided before they start. That is, one opponent is enough better than the other that he's going to win no matter what.

I doubt it's as high as 80%. Tournaments generally take place between players of roughly equal skill; they don't pit grandmasters against novices. There are probably some tournament matches with very little chance of an upset, but I can't imagine it's as high as half, let alone 80%; if most of the matches are foregone conclusions, then the tournament's not very interesting.

In any case, if a computer program playing against itself has the same win rate for white, then that's the real win rate, no matter how tournaments work.
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Tommy Occhipinti
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Antistone wrote:
In any case, if a computer program playing against itself has the same win rate for white, then that's the real win rate, no matter how tournaments work.


I don't think it is that black and white, depending on what you mean by "real win rate." Since there is no randomness in chess, with perfect skill, on of three statements is true:

A) White will always win
B) Black will always win
C) The game will always lead to a draw

There is a great deal of debate which of these is true (people certainly think it is A or C), and we probably won't know for another century [citation needed]. If A is true, though, as an AI becomes more and more advanced, its win rate versus itself as white should converge towards 100%. On the other hand, a very unskilled AI couldn't exploit the first player advantage, and might well have a win rate closer to 50-50.
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Jeremy Lennert
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delirimouse wrote:
Antistone wrote:
In any case, if a computer program playing against itself has the same win rate for white, then that's the real win rate, no matter how tournaments work.


I don't think it is that black and white, depending on what you mean by "real win rate."
...
If A is true, though, as an AI becomes more and more advanced, its win rate versus itself as white should converge towards 100%. On the other hand, a very unskilled AI couldn't exploit the first player advantage, and might well have a win rate closer to 50-50.

Fair enough. My intended point was just that the advantage is not being artificially compressed towards 50% due to games that are decided by a vast difference in player skill, because when a computer plays against itself there is no difference in player skill.

Though it's not necessarily true that higher skill will "converge" towards the perfect play win rate, or at least not smoothly. There's a guy on chessvariants.org who performs experiments with different handicaps by having his AI play against itself, and he's commented that he tends to get the same result whether he uses long time controls or short ones--that is, giving one side an extra knight (or whatever) has about the same effect on that side's overall win rate whether the AI has a long time to think about each move or is forced to play quickly, as long as he uses the same rules for both sides (if he gives extra thinking time to only one side then that side gains an advantage). That suggests that there's some "skill" range over which player advantage is relatively constant.

To understand why this might be, imagine a hypothetical game position in a game of no chance. In this hypothetical position, there are lots of moves that are obviously bad, several moves that a skilled player could figure out are bad using various tricks, and 3 moves that all look like very good options. It turns out that eventually (dozens or hundreds of moves later), 2 of those moves will eventually win you the game while the third one will cause you to lose. With theoretical perfect play, you'd win 100% of the time; nonetheless, if there is no practical way to tell in advance which of those 3 moves is the loser, then your odds are 2/3 for all "realistic" skill levels--whether you're grandmaster, or merely OK, or anything in between.

It's entirely possible that white winning (say) 55% of the time is a more "real" measure of white's advantage in Chess than the theoretical perfect-game outcome, even across a wide range of skill levels. There's no a priori guarantee that improving your skill from "good" to "amazing" is going to change that number in any way.
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50% win percentage for first player in a two player game is balanced perfectly.
50% win percentage for the first player in a four player game is outrageous.
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The Dave
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One possible solution is use some metric alongside the instant win condition. Then a "game" consists of two plays with each player having a chance to be first player. Then the winner is the person with the most/least of that metric across both games.
 
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Jeremy Lennert
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frumpish wrote:
50% win percentage for first player in a two player game is balanced perfectly.
50% win percentage for the first player in a four player game is outrageous.

...which is presumably why the OP asked specifically about two-player games.
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Michael Iachini
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An important issue to weigh here is play length. If the game takes 5 minutes to play, it's okay if it's tilted toward the first player because people will play best 3 out of 5 or something like that, alternating who goes first. If it takes an hour or more to play, it's more important that it be closer to 50/50 since players are unlikely to play a series of games.

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If the game is really played over a series of smaller games (like tennis and serve advantage) then it's part of the game and so long as the series of smaller games is repeated often enough it doesn't matter. But if it's a six year monster war game, then...
 
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monchi
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I have an issue with calling it broken. It is an advantage, it doesn't mean it is "broken" as per say. The greater concern I would think is that if the first player has that great of an advantage they why would it be a game people would want to play? Personally I know that I like to know that starting a game I have as good a chance as anyone to win. If a game is so skewed to the first player I takes a lot out of the game as I would suspect that one would start to feel like you are just going through the motions.

My question to you would be why or what is the reason for this advantage? Is it that there is just something that the first player gets to do that gives them such an advantage that they are stupid not to do that move every time they play? In two player games it really is critical to have as balanced a game as possible as there aren't other people that can change the course of the game. If the first player basically sets the tone for the game it takes a lot of fun out of the game.
 
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Jeremy Lennert
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monchichi wrote:
I have an issue with calling it broken. It is an advantage, it doesn't mean it is "broken" as per say. The greater concern I would think is that if the first player has that great of an advantage they why would it be a game people would want to play? Personally I know that I like to know that starting a game I have as good a chance as anyone to win. If a game is so skewed to the first player I takes a lot out of the game as I would suspect that one would start to feel like you are just going through the motions.

I'm curious what qualifies as a "broken" game in your mind, if a game where you "feel like you are just going through the motions" does not.
 
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Antistone wrote:
monchichi wrote:
I have an issue with calling it broken. It is an advantage, it doesn't mean it is "broken" as per say. The greater concern I would think is that if the first player has that great of an advantage they why would it be a game people would want to play? Personally I know that I like to know that starting a game I have as good a chance as anyone to win. If a game is so skewed to the first player I takes a lot out of the game as I would suspect that one would start to feel like you are just going through the motions.

I'm curious what qualifies as a "broken" game in your mind, if a game where you "feel like you are just going through the motions" does not.


I think I have a different opinion as to what is "broken" Sometimes what people think is broken really isn't broken, it is just that way. I find that "broken" is thrown around a lot and isn't always merited. If the first player in a game has a distinct advantage like this in a game means it is "broken" there are a ton of broken games out there. This is kind of why I asked about what makes this so. I don't think it can be ruled as broken until you know this. For me broken means it is totally unfixable. I only see a game as truly broken if you can't make it playable. If you can alter something or add/subtract something and make it work is was just a flaw in the design.

I guess the best way to describe how I see it is that if I say chip a cup I can still use it. It holds water, just doesn't look pretty. Now if I drop that cup and smash it into pieces it is now broken. I may be able to try and glue it back together but it will break again.

The thing is there is an optimum way of playing most games. So in this case is it that the first player always wins when they adopt a certain opening strategy or does the first player always win just because? Or does the first player win because the winner is the first person to reach a certain vp number and it is the first person that crossed the line that wins?

If you step back and look at most games from an "optimum" play stand point you can "break" a lot of games. But this is what makes games so awesome. It is the human factor. You can never account for what people will do and why they do it. This adds a layer of randomness to everything.
 
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monchi
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I should note that it could very well turn out to be "broken" but based on what he has said sounds like it is tweakable.
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J. Alan Henning
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Thanks to everyone for their feedback. This has been very helpful. We will continue testing our tweak to the card count until we get a win percentage in the range of 45% to 55% for the first player. According to the poll, that will satisfy 80% of you.

And if 52-55% is good enough for chess, I think is certainly acceptable for a card game.
 
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