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Hey everyone, now I may be just a simple college freshman, but I love game theory in microecon. as of right now. The only real example we've encountered are Nash Equilibriums. I'll skip some background and go straight to my point. In many commentaries I see people debating whether or not to get Banshees and rush the other player in TvT. Of course the other player usually responds with Vikings. Now this made me think, hey, hard counters can be applied in a Nash Equilibrium. This is when you point out the choices made, generally by two people, and see how much benefit is possible in charts.
![[image loading]](http://i41.tinypic.com/xqb8yq.jpg)
I will now explain my pathetic chart above. Players 1 and 2 have two options, building Vikings or Banshees. I kept this as simple as possible as to try and make a point. Please do not spam me about externalities and the possibility of simply saving units, I wanted to analyze decision making in a limited but applicable environment. To work a Nash Equilibrium, you simply choose the options with the most benefit according to the other players choice. For example, Player 1 chooses Banshees, now Player 2 can either build Vikings or Banshees, I put the benefit for building Vikings against Vikings as a 1 to represent that usually both players just harass each others Vikings, no real mineral diving or anything. The 2nd choice would be he builds Banshees after seeing Vikings, this gives him 0 benefit because the Vikings generally counter Banshees quite easily. The same thought process is given to the other player and dashes are prescribed to the most optimal choice in each situation. The block that has two dashes is the Nash Equilibrium. In this case, building Vikings is the dominant strategy. This is a bit of meta-gaming so of course other factors can come into play, but when I saw KawaiiRice faceoff in the HDH tourney, I couldn't help but wonder, why would anyone build banshees in this situation? Any thoughts or comments would be nice. I really just made this because I was somewhat bored and stressed because of finals, starcraft seems to help with that. If anyone is confused about the process of choosing the best choice, I'll be happy to reiterate.
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It is nice to apply science and skills like that towards RTS and SC, but the players that do usually are not getting better when they can think about it so much more easily.
Vikings are air to air, banshees are not. Therefore whoever builds vikings first instead of banshees has an advantage and will try to maintain it. TvT is like this a lot.
I said basically all of your high science in a short little snippet. It is not good to overanalyze decisions that can be kept simple and are simple.
sometimes there is no intriguing or massive science behind why players do things.
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![[image loading]](http://img687.imageshack.us/img687/6010/312414.jpg)
hf
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On April 28 2010 05:58 avilo wrote:
It is nice to apply science and skills like that towards RTS and SC, but the players that do usually are not getting better when they can think about it so much more easily.
Vikings are air to air, banshees are not. Therefore whoever builds vikings first instead of banshees has an advantage and will try to maintain it. TvT is like this a lot.
I said basically all of your high science in a short little snippet. It is not good to overanalyze decisions that can be kept simple and are simple.
sometimes there is no intriguing or massive science behind why players do things.
This is true, I just felt like sharing.
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I read the thread title and all I could think of was John Nash doing some freaky codebreaking thing, maphacking, then pushing his desk out the window and deciding to play go instead.
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On April 28 2010 06:01 paper wrote:hf
+1
This is the true chart. Very complicated, especially when you add in ground unit choices.
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I think you have an interesting start, but there is actually a lot of analysis with randomization in game theory. Rock paper scissors, island war, or other simple randomization games would be more realistic bases for formal models about starcraft.
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Cloak and raven usually don't come until later. These tables are used for blind decisions, but I do agree that vikings will be the the standard in the matchup. I like going marauders for defense, then a viking, or more, depending on their banshee and viking count, then tanks tanks tanks. I like tanks and vikings in the end game.
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And what happens when they mass marauders that do 20 dmg vs your vikings?
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Calgary25996 Posts
This is oversimplified to the point of uselessness. It's like comparing player 2 has the option of Scourge or Mutalisks and then arguing that Player 1 should go Corsairs since they rape them both.
Like common sense and your question "Why would anyone go banshees?" should dictate that you add a column called NEITHER that bashees beat. I don't understand how you didn't consider this.
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If you start cloak the same time as you start making a banshee, it's finished what... 30 seconds after that banshee is made? Then you force your opponent to have to use scans over mules then build a raven, etc, etc.
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On April 28 2010 07:13 Creationism wrote:
And what happens when they mass marauders that do 20 dmg vs your vikings?
The viking man gets banshees to kill the rauders? 
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On April 28 2010 07:19 Chill wrote:
This is oversimplified to the point of uselessness. It's like comparing player 2 has the option of Scourge or Mutalisks and then arguing that Player 1 should go Corsairs since they rape them both.
Like common sense and your question "Why would anyone go banshees?" should dictate that you add a column called NEITHER that bashees beat. I don't understand how you didn't consider this.
Let's stay on topic please. This discussion is about the choice between rock and scissors. If you'd like to discuss paper, maybe you should start a new thread.
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Hold up. We actually do need a Neither column. I have a nice background in game theory under biological conditions which SC arguably mimics. In fact, LzGamer actually has shown this nicely in a number of his games and I would argue is why he has had solid TvT success. Without a Neither column, you can't actually generate a real equilibrium equation. The logic goes like this:
If I go Banshees and he goes no air, my Banshees increase in value.
If I go Banshees and he goes Banshees, we are at least even.
If I go Banshees and he goes Vikings, my Banshees lose value.
If I go Vikings and he goes no air, my Vikings have the same value.
If I go Vikings and he goes Banshees, my Vikings increase in value.
If I go Vikings and he goes Vikings, my Vikings have the same value.
Now this can be expanded for Cloak, Ravens, etc/ But the principle is very good. The incentive for Banshees is that it can seriously increase the chance to win the game if he chooses nothing. The incentive for Vikings is that they will never not be okay.
I'll post more later on this theory.
EDIT:
So here is what Lzgamer did to great success against CauthonLuck (I think?) a while ago. On Steppes of War, both players did a standard 10 Depot, 12 Rax, 14 Refinery, 15 Orbital + Marine and killed each others scout. So now both players are in the dark (this is before Marauders lost the innate slowing).
CL and LZ each think:
If I get a Reaper and he goes Marines, my Reaper increases in value.
If I get a Reaper and he goes Reaper, we are at least even.
If I get a Reaper and he goes Marauder, my Reaper loses in value.
If I get a Marauder and he goes Marines, my Marauder has the same value
If I get a Marauder and he goes Reaper, my Marauder increases in value.
If I get a Marauder and he goes Marauder, my Marauder has the same value.
Now, if you consider each of your opponent's responses equally likely, you just evaluate the sum of scenarios 1 and 3 for Reapers versus 2 for Marauders. CL decides to go Reapers, LZ goes Marauders, LZ comes out ahead in investment.
The players continue to tech almost identically and they reach the expanded Starport decision tree, ie Vikings vs Banshees w/o cloak vs Banshees w/ cloak vs Ravens. CL is behind because of his investment in Reapers and goes Banshees w/o cloak. LZ goes 1 Raven into Vikings, stops the Banshees and 1 tank pushes into CL's base and wins. There were only 3 skirmishes, Marauder vs Reaper, Viking vs Banshee, army vs army.
Now, the reason this is valuable is through assigning probabilities to each decision and relative point values. Then you simply do a statistical crunch via trials and what comes out is what you should do, at a given point, without any extra information. This analysis only improves with more information.
For example, if you know you are superior to your opponent in a long game, the likelihood of him going for a possibly hugely beneficial move, like fast Reapers or Banshees, probably increases. Even if that weren't the case, by taking pathways that involve less risk, you prevent any simple BO disadvantages, such as Reapers vs slow-Marauders, or Vikings vs Banshees.
Discuss.
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This comment will probably look trollish, but please, bear some thought to it.
For starters, game theory is applicable for huge processes, it will give you tools to analyze the best dominant strategy, etc...
in SC2 we are not interested in huge dominant strategies. This game doesn't have 5 years of stable meta-game, it hasn't even been released yet! What we are interested, is in individual games.
Also, to "balance a (real) game" is to make it so that applying "Game" Theory into it will give us no useful info.
the "game" in "game theory" is not the same "game" as in "video-game", so don't.
We'll get MUCH more info through empirical tests. There's WAY too much noise and game design here for game theory to bear any usefulness.
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You are dead wrong. Allow me to elaborate
The "game" in game theory refers to the use of creating simple "games" to represent phenomena. In this case, we are making a "game" in choosing tech routes. This is perfectly acceptable. In my research, we used "games" of bacteria deciding to replicate versus increase their innate defenses. They are the same scenario.
Dominant strategy only refers to, as you play an infinite number of games, what offers the best success rate. This informs current decisions by showing what should happen if you play enough. Game theory actually shows application to single instance events, ie the Prisoner's Dilemma, among 82,000 other applications that are all well-documented.
Complex game theory has successfully modeled living organisms. This is a game with a finite number of interactions, where all variables can be known and even quantified. If game theory works when we don't know everything, you are obviously wrong that is not useful here. See my example above.
If you have no idea what you are talking about, then stop.
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Thanks Sleight, I really enjoyed your responses to my post. You really discussed well on the neither option which has started some of my thinking again.
I see the point that my example could be recalled as useless, but I never told anyone to apply it to their games or their strategies. I just thought it was one example where I thought of something "cute". While that may argue that it is even more useless, I don't mind if it is, it was simply something thought in passing. Also Chill, that is not the same example because the options for Corsair vs. Scourge/Muta, is unlike Vikings and Banshees. I didn't consider a neither option because I'm generally caught up in the base of my ideas and don't think about expanding them till later.
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Those equations don't really take scouting into account. Scouting will render many of the If > then statements useless. I'd like to see common scouting opportunities worked into a comprehensive If > then tree of reasoning.. That would be awesome.
Another problem is it considers each of the 3 options marine / marauder / reaper equally likely. But in order to make a good calculation you'd have to have a massive web of reasoning describing all aspects of the matchup which you then ascertained probabilities for each action from, and that web would have to include not only unit compositions and scouting, but map features as well. Constructing such a complicated web for even one matchup would probably take like a month.
The problem with using a simple scenario is it doesn't acknowledge the actual factors which determine choices made; it merely delegates these explanations to probability. So on Desert Oasis it might be that reapers are the better choice 100 percent of the time, but you may still see them as 20 percent likely; and then you'd play 4 games on different maps and your suspicions would be confirmed.
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Starcraft is zero sum, so it doesn't make sense that in one box your payoffs are (1,1) and the other (2,2). You can't have an option that's better for both players.
Unless of course you are modeling some utility that is not chance of winning, like fun or personal improvement or something, but that doesn't seem like the case.
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On April 28 2010 08:01 Sleight wrote:
If I go Banshees and he goes no air, my Banshees increase in value.
If I go Banshees and he goes Banshees, we are at least even.
If I go Banshees and he goes Vikings, my Banshees lose value.
If I go Vikings and he goes no air, my Vikings have the same value.
If I go Vikings and he goes Banshees, my Vikings increase in value.
If I go Vikings and he goes Vikings, my Vikings have the same value.
Discuss.
Shouldn't it be:
[B1]: If I go Banshees and he goes no anti-air, my Banshees increase in value.
[B2]: If I go Banshees and he goes Banshees, we are at least even.
[B3]: If I go Banshees and he goes Vikings, my Banshees lose value.
[V1]: If I go Vikings and he goes no air, my Vikings lose value.
[V2]: If I go Vikings and he goes Banshees, my Vikings increase in value.
[V3]: If I go Vikings and he goes Vikings, my Vikings have the same value.
The next step would be quantifying the value loss-gains.
[B1] is extremely high value, since banshees with no anti-air will rape. At the very least, you might count ~50% of opponents current SCV's in this, assuming the opponent eventually gets some AA before all of his SCV's are raped. An SCV's value is 50 mins + SCV production time + lost mining time.
[B2], by definition is zero.
[B3] should be expressed in terms of the cost of both the banshees in min/gas, as well as time lost for tech lab and time lost due to banshee building.
[V1]: This is not a complete loss of the min/gas value + build time of vikings since Vikings can still land and harass and scout.
[V2]: The min/gas/time cost of opponents' expected losses should be included.
[V3]: By definition, gain-loss is zero.
In the SCV vs. mule thread, someone mentioned that we need a time-value of money calculation. We need it here, too. Looks like it's time for this to be tackled.
This analysis can be done excluding the time-lost, but it wouldn't be fully accurate. It would, however be a 60-80% complete picture, given the simple limitations of the scenario (Viking vs. Banshee).
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EPT
