Hi Tere, thanks for your comments!

It’s a lot, and there’s probably enough material here for several articles. I’ll try my best at answering your questions.

Is the dominant strategy a product of a Nash Equilibrium (in some cases)?

I would say that Nash equilibrium is a specific case where two players found optimal strategies based on their knowledge of the other player’s decision. Dominant strategy is a broader concept of game theory that describes a strategy that is strictly better than any other, independently from what other players do.

Can you please give me more intformation on the “knob” methodology for balancing (also described in previous book)?

Sadly, I’m a not familiar with this methodology nor this book.

Could you please shed me some light about the differences between balance and symmetry?

By balance, I mean that player positions have an equivalent (maybe even equal) chance of achieving victory. To me symmetry means that player position are identical.

All starting positions in a 100m dash are both symmetrical and balanced. Starting positions in Counter-Strike aren’t symmetrical, but if both teams play the same map in each role and add the results of each round, then the whole game becomes symmetrical (and also balanced). We’re really talking semantics here.

You say that chess is unbalanced.

Similarly to Counter-Strike, white has an advantage as it plays first, so the game is unbalanced. In tournament settings, players have to play both sides alternatively, which makes the whole balanced.

In the video, I use “symmetrical” for Capture the Flag, because map layout are generally completely symmetrical and teams start in the exact situation. To an extend, “symmetrical” and “balanced” can be used as synonyms. Once again, semantics.

In practice there are very few symmetrical games because the players are humans and the chances of the choices are not perfect (rock, paper, scissors is symmetric in theory, but if i tend to choose rock more than paper or scissors, then is it really not?).

I don’t agree with this notion. I believe that rock paper scissors is balanced independently from player choices. It is just a space of possibilities and you should just look at the whether or not each option has equivalent chances of success to determine if your game is balanced. The fact that one player uses more of one option doesn’t make the whole game suddenly unbalanced. It doesn’t change the nature of the game as a possibility space.

On another note, when you say that a draw in chess is a victory for black, do you mean theoretically? I believe that this dependes in the experience of the gameplay session, I have had draws with black that feel like a defeat becaue I had the upper hand during the game. So, again, for me this is balanced (because there are momentary advantages that imply risk?), jut asymmetrical.

It is the same notion here, maybe you use “balanced”/”unbalanced” to describe a give board position. “I’m about to lose the game, the situation is unbalanced”. In game theory, you just look at the game as a whole. White has an advantage, as it plays first, so even if the positions on the board are symmetrical, the whole game is unbalanced.

Of course, once again, then players switch color for the next game.

You could look at the whole situation like home and away games in sport … It is considered harder to win away, but it’s balanced because each team will play the same amount of games home and away.

If you are interested, my advice is to document yourself on these concepts in the context of game theory, the mathematical field itself.

I’m Tere, I’ve been following your blog for sometime now, congrats!:)

I liked your article a lot, I have encountered feelings about the video.

I have first a few questions about the article:

* Is the dominant strategy a product of a Nash Equilibrium (in some cases)? It is an economy concept applied to game theory concept that I’ve been struggling with for a while (read it in “Designing Games: A Guide to Engineering Experiences” by Sylvester Tynan) <a href= "http://www.amazon.com/Designing-Games-Guide-Engineering-Experiences/dp/1449337937/ref=sr_1_1?ie=UTF8&qid=1423106498&sr=8-1&keywords=designing+games+a+guide+to+engineering+experiences&quot; title= "link")

* Can you please give me more intformation on the "knob" methodology for balancing (also described in previous book)? It was accordingly used on SC2 and basically meant enhancing the difference between classes (aligned with your message of balance not being equality)

On the other hand, if possible, could you please shed me some light about the differences between balance and symmetry, I found those terms in your video and there are some things that are not aligned to previous material I've read:

+ You say that chess is unbalanced. According to what I've read, chess is balanced (understanding balance is different from equal in videogames), white starts first because it is asymmetrical. Assymetrical games can be balanced, and in practice there are very few symmetrical games because the players are humans and the chances of the choices are not perfect (rock, paper, scissors is symmetric in theory, but if i tend to choose rock more than paper or scissors, then is it really not?). These are all concepts I've come across in books, more recently, the same book I've been quoting.

+ On another note, when you say that a draw in chess is a victory for black, do you mean theoretically? I believe that this dependes in the experience of the gameplay session, I have had draws with black that feel like a defeat becaue I had the upper hand during the game. So, again, for me this is balanced (because there are momentary advantages that imply risk?), jut asymmetrical.

Thank you very much and sorry for the long post.

Tere

Thanks Clinton!

I think unless you work on a very large and complex system like a MMO, the math is rather simple, as shown with the Starcraft 2 examples. For most cases, if you really feel overwhelmed but the math, it is a good indication that the problem you are trying to solve is not clearly defined enough. Or in the terms I use in the video, your intended dynamic not precise enough.

Thank you for this video. I wonder if in the future you can delve a little deeper into the process of game balancing and with the process of designing progression mechanics?

I have a had some studio experience with game balancing and progression mechanics and yes, I naturally gravitated towards compiling numbers and clumsy formulas into a spreadsheet. As a non-mathematics person (farthest I went was basic statistics as a Psych major) it is actually the application of mathematics to these problems that both fascinates and pushes me away.

Going into such detail is usually out of the scope of most design videos or Gamasutra-style blog articles. How do the pros do it? Is there an area of advanced math that one should study to get a better handle on these skills? Or perhaps I am over-thinking this topic and most designers in the field do as I did: plotting numbers into Excel and using to playtests and critical thinking to deduce “the right balance” of things?

Sorry for the long-wind question. Please keep these great videos coming!

Hi Thomas,

I was using reports from various sources like Wikipedia, but it seems that it was actually a rumor. It got corrected in Oct 2013, I edited the conclusion and added the reference.

Thanks a lot for pointing this!

Do you have any external references for this?