[I] ZvZ Opening Probabilities - Page 4

5HITCOMBO

Japan2239 Posts

March 26 2008 20:47 GMT

#61

On March 26 2008 06:06 Chill wrote:
I was silently disagreeing with almost everything you've said in this thread, until I read "ramp". Now I agree. But on non-ramped maps I still believe 12 Pool beats out 9 Pool.

I guess the non-ramped maps of today (Blue Storm, Longinus, Tau Cross, Katrina, Ungoro, etc) just made me assume you were talking about non-ramp maps.

Oh, yes, true, definitely.

I'm not a really diverse player or observer, though

flag

United States228 Posts

March 27 2008 02:06 GMT

#62

Hippo, nice to see someone analyzing the pure math of this stuff, because I sort of skimped on the proofs (mainly because I am bad at them). So should we call it generalized equilibrium instead of Nash?

Also about 2 comments about number of viable options. Since starcraft is a complex game, when 1 build faces another its chance of winning is really some real number more precise than what we list. And for the players to have a different number of viable options, something would have to work out so two unrelated real numbers are exactly equal, the chance of this is 1/infinity so I say it's not possible. But you are correct it really is possible. I was aware of this when I posted, but really didn't want to make the post any longer/I didn't posses the ability to explain it well.

Even though you say it will "never" happen in real life, I think your original statement has useful implications for real life. Because although the actual percent chance of a build beating another is some real number to infinite precision, our ability to measure/estimate it is very low precision. So things can work out to be close enough that we can't really say which is better and call them equal. This is also where style comes into play, maybe a certain build really is very so slightly better than some other, but a player has so much time invested in a previous style that it isn't better for them. Ofcourse we are trying to be theoretical so this stuff not that important, but just nice to keep it in mind.

In your post you said even number of options is this a typo or correct?

I'm glad that you like those statements btw

hippo

France13 Posts

March 27 2008 17:37 GMT

#63

Well, the pleasure is mine. :-)
But for the "semantic" part, I was wrong : Walras equilibrium has nothing to do with game theory... it's a micro-economy concept. It's something about supply/demand equilibrium (i'm not an economist, I won't tell you more). So in the case where you allow random (or probablilist) strategies, it seems that you still call it a Nash equilibrium. Sorry I said shit (and don't know why I thought it was related :-o).

For the "real life" part, ok, then you must be careful and deal with those cases...

For the "even number" question you ask, well yes in the first sentence i meant "there is never an even number", but then in the explanation, it's correct : if n is even, then M (of size n-1) can't be invertible and we won't have a unique non-degenerated optimum.

I'll edit my post to take those 2 mistakes in consideration.

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