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What are the probabilities of each opening build beating each other build? If this question can be answered then you can calculate with which percentage you should choose each build. This method can be used for any match up, any game or anything where opponents choose something blindly and the result of those choices can be calculated (does not have to be mirror match either). This is not exactly useful for playing random people on iccup, because there you can do the same thing every time, and your opponent will have no idea that you do this. This is more important for people trying to play unpredictably in repeat matches. Although the results here should still be useful for iccup users because certain builds should never be used and this will identify them.
I chose zerg versus zerg because they have the widest range of viable openings. I'm not a zerg player so figuring out these percentages is difficult. I would really appreciate if a top level zerg can give their own estimation of the probabilities. But for now I'll give my own estimations. Thanks goes out to saarto for helping me test some stuff like 6 pool versus 12 pool.
(for python, assuming both players pro level)
(PS anyone know how to post stuff using monospace font?)
Given these percentages, the optimal choice of strategy is 26.6% of the time choosing overpool, 66.6% 12 pool, 6.6% 12 hatch, and 0% for all others. Obviously this does not apply when players at 12/3 and 6/9 as you can see what each other are doing.
Note, I did not include builds such as extractor before pool, 9 hatch and stuff. If anyone feels those builds are viable, please estimate the probabilities v each build and I will include it in the chart and update calculations.
I was surprised by the result that you should never 4-9 pool, the reason for this is because the overpool strat still has good rushing potential and isn't so screwed against 12 pool. I doubt that more accurate values will bring back the 4-8 pool, so please put most emphasis on estimating 9 pool - 12 hatch @ natural please.
One non obvious implication of this method is that no player ever has more or less number of viable options than their opponent (even in non mirror matches). It is hard to explain why, but if you think about it should be clear. I can explain more if needed.
Edit: another non obvious implication is that in mirror matches, there is never an even number of viable builds.
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United States24755 Posts
Why don't you retype your chart using other software and then paste in an image of it... I'm having trouble reading it.
Edit: I'll think about it more mathematically at that point because it's an interesting idea.
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System font is what you're looking for.
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Updated chart, thanks for the idea micronesia. 5hitcombo, is there way to do that in post directly?
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It makes sense from a macro stand point. I think it would help your different bo's tremendously. Thanks for writing it out like that. More intricate tables would be awesome for other races and mid game strats, but the probabilities are endless...
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Its funny because the most powerful build in ZvZ might be 9 pool speed, which according to your mathcraft should be never done.
Starcraft > Mathcraft
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Belgium9950 Posts
hmm I dont know what to make of this.
If you do your suggestion vs a player that always 12hatches, you'll be behind in 73% of the cases, and be able to do small damage in 26.6% of the cases. If you do it vs someone that always 12pools, you'll be behind in 26.6% of the cases, even in 66.6% of the cases, and ahead in 6.6% of the cases.
Why is this a bad statistical analysis? The 4pool, 5pool, 6pool etc weigh in as much as 9pool 12 pool and 12hatch, eventhough they're barely used. So your statistics will prefer safe builds, while in the end (ofcourse incorporating the map layout and distances, which will prefer certain build), it will remain more or less RPS.
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Calgary25993 Posts
On March 21 2008 03:59 FieryBalrog wrote:
Its funny because the most powerful build in ZvZ might be 9 pool speed, which according to your mathcraft should be never done.
Starcraft > Mathcraft
My thoughts exactly. In theory you should be able to apply percentages to the builds and solve for an optimal build. I'm not sure where you got your percentages from, but something is wrong. For example, how does 4 Pool beat 5 Pool 10% of the time?
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Calgary25993 Posts
On March 21 2008 04:02 RaGe wrote:
hmm I dont know what to make of this.
If you do your suggestion vs a player that always 12hatches, you'll be behind in 73% of the cases, and be able to do small damage in 26.6% of the cases. If you do it vs someone that always 12pools, you'll be behind in 26.6% of the cases, even in 66.6% of the cases, and ahead in 6.6% of the cases.
Why is this a bad statistical analysis? The 4pool, 5pool, 6pool etc weigh in as much as 9pool 12 pool and 12hatch, eventhough they're barely used. So your statistics will prefer safe builds, while in the end (ofcourse incorporating the map layout and distances, which will prefer certain build), it will remain more or less RPS.
Very true, it needs to be iterative, right? You need to attach a "probably of opponent doing build" matrix as well.
So in case 2, the chance of every build is 1/n.
Case 2, the chance is equal to the probability of winning from Case 1.
Run it to infinity and see what comes out.
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On March 21 2008 03:59 FieryBalrog wrote:
Its funny because the most powerful build in ZvZ might be 9 pool speed, which according to your mathcraft should be never done.
Starcraft > Mathcraft
"Given these percentages, the optimal choice of strategy is..." I never claim to be a zerg expert. If 9 pool speed is the most powerful, or even viable, its because I have underestimated its chances against other builds, or overestimated other builds that fulfill the same niche. I really want help from more knowledgeable zergs with this estimation, if you have any suggestions please make them. I think the most likely cause of error right now is bad estimation of overpool versus 12 hatch, I haven't tested that match up yet and it has a large impact on the results, is 70% too high an estimation for the overpool there?
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On March 21 2008 04:02 RaGe wrote:
hmm I dont know what to make of this.
If you do your suggestion vs a player that always 12hatches, you'll be behind in 73% of the cases, and be able to do small damage in 26.6% of the cases. If you do it vs someone that always 12pools, you'll be behind in 26.6% of the cases, even in 66.6% of the cases, and ahead in 6.6% of the cases.
Why is this a bad statistical analysis? The 4pool, 5pool, 6pool etc weigh in as much as 9pool 12 pool and 12hatch, eventhough they're barely used. So your statistics will prefer safe builds, while in the end (ofcourse incorporating the map layout and distances, which will prefer certain build), it will remain more or less RPS.
If you know what they are doing already, don't use this method, choose the counter instead. But if they always do 12 hatch and you use this method, on average you will have a 50% chance of beating them. Because even though you are behind 73% of the time its not nearly as far behind as you are ahead when you do the overpool.
This is not bad statistical analysis, the 4pool, 5pool, etc do not weigh in as much as the 9pool 12 pool and 12 hatch. Infact they do not way in at all since they are inferior. The method I used to calculate the result, assumes that they are also choosing builds based on their goodness. It is standard game theory stuff. I can post the program used to calculate the results after I clean it up some.
On March 21 2008 04:04 Chill wrote:Show nested quote +On March 21 2008 04:02 RaGe wrote:
hmm I dont know what to make of this.
If you do your suggestion vs a player that always 12hatches, you'll be behind in 73% of the cases, and be able to do small damage in 26.6% of the cases. If you do it vs someone that always 12pools, you'll be behind in 26.6% of the cases, even in 66.6% of the cases, and ahead in 6.6% of the cases.
Why is this a bad statistical analysis? The 4pool, 5pool, 6pool etc weigh in as much as 9pool 12 pool and 12hatch, eventhough they're barely used. So your statistics will prefer safe builds, while in the end (ofcourse incorporating the map layout and distances, which will prefer certain build), it will remain more or less RPS. Very true, it needs to be iterative, right? You need to attach a "probably of opponent doing build" matrix as well. So in case 2, the chance of every build is 1/n. Case 2, the chance is equal to the probability of winning from Case 1. Run it to infinity and see what comes out.
I already do this...
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Calgary25993 Posts
Oh, okay. You didn't mention in your post weighting anything based on chance they use it.
Edit: I must not be reading this properly, I don't see how you can come to the conclusion that you should do different builds. I'll have to reread it later. :X
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On March 21 2008 04:02 Chill wrote:
how does 4 Pool beat 5 Pool 10% of the time?
Well this is an estimation, the 4 pool is behind by about 2 drones, but random stuff can happen on the way to their base since you are heading into the dark some of the time since you can't have scouted everywhere yet. I think this number is reasonable, but please instead of saying hey that's a bad estimation, just give a better one and I'll update. I didn't explain all my estimations because I expect a better zerg to come through and give better estimations making all mine irrelevant anyways. Also note since it turned out neither of these builds are used, it doesn't actually effect the results in any way what the chance of 4 pool beating 5 pool is.
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Calgary25993 Posts
On March 21 2008 04:20 flag wrote:Show nested quote +On March 21 2008 04:02 Chill wrote:
how does 4 Pool beat 5 Pool 10% of the time? Well this is an estimation, the 4 pool is behind by about 2 drones, but random stuff can happen on the way to their base since you are heading into the dark some of the time since you can't have scouted everywhere yet. I think this number is reasonable, but please instead of saying hey that's a bad estimation, just give a better one and I'll update. I didn't explain all my estimations because I expect a better zerg to come through and give better estimations making all mine irrelevant anyways. Also note since it turned out neither of these builds are used, it doesn't actually effect the results in any way what the chance of 4 pool beating 5 pool is.
I mean, what kind of variability do you want? If I 7 Pool against a 5 Pool, there's a small chance I move out with my Zerglings and he comes in at the same time and kills my Spawning Pool / Drones. Are we giving credit to things like that? If neither playing makes a mistake, 4 Pool loses to 5 Pool every time. Do you want to apply a random "chance of mistake" factor?
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On March 21 2008 04:19 Chill wrote:
Oh, okay. You didn't mention in your post weighting anything based on chance they use it.
Edit: I must not be reading this properly, I don't see how you can come to the conclusion that you should do different builds. I'll have to reread it later. :X
Ah yeah I should have mentioned the method used instead of assuming people would trust me. Basically it assumes the opponent knows what percentage you choose each strat, and you know what percentage they choose each. Your chance of winning is the sum of each strat's chance of winning times the probability of the two of you choosing the respective strategies. This method will give you optimal choice of strategies, but will not exploit inferior players tendencies. Although if you know their tendencies, you can choose a strategy that is optimal for defeating just them, and it might even be a strategy that my method says not to use at all. However if they know you will do this... (and so it repeats).
Sorry for the multiple post, hard to keep up with all the things being said in one post.
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On March 21 2008 04:23 Chill wrote:Show nested quote +On March 21 2008 04:20 flag wrote:On March 21 2008 04:02 Chill wrote:
how does 4 Pool beat 5 Pool 10% of the time? Well this is an estimation, the 4 pool is behind by about 2 drones, but random stuff can happen on the way to their base since you are heading into the dark some of the time since you can't have scouted everywhere yet. I think this number is reasonable, but please instead of saying hey that's a bad estimation, just give a better one and I'll update. I didn't explain all my estimations because I expect a better zerg to come through and give better estimations making all mine irrelevant anyways. Also note since it turned out neither of these builds are used, it doesn't actually effect the results in any way what the chance of 4 pool beating 5 pool is. I mean, what kind of variability do you want? If I 7 Pool against a 5 Pool, there's a small chance I move out with my Zerglings and he comes in at the same time and kills my Spawning Pool / Drones. Are we giving credit to things like that? If neither playing makes a mistake, 4 Pool loses to 5 Pool every time. Do you want to apply a random "chance of mistake" factor?
It is hard to measure chance of an inferior build beating a superior one. The main important factor to keep things accurate, is that we are consistent. To ensure consistency, assume that the players are "pro level" and make about the same amount of mistakes as pro. I know this isn't an exact science, but luckily these crazy things like 5 pool versus 7, don't effect the results much. What effect the results more are stuff like 9 pool versus 12 pool. This is alot more common and good zergs probably know what their chances of winning in that situation are. In looking at previous ZvZ topics, people mentioned at least 2 instances where a pro using 9 pool beat one using 12.
And in that example you described I think the 7 pool build didn't make any "mistakes" they just got unlucky, so it would be good to say the 5 pool has at least a chance v 7 pool. (same true probably for 4 pool versus 5).
Also one other thing I never mentioned is, if positions are 12/3 or 6/9 then 4/5 pool builds are screwed, but a 6 pool build that builds 8 drones and cancels last 2 if they don't see an overlord coming can adapt with no penalty. So really the 4/5 pool builds need to multiply chance of win v overpool by 1/3 and chance of win v build in question by 2/3 to get real value and add them together. (I did this already in computation but didn't list in chart for simplicity purposes)
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How many people overpool?
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Guys, how often are zvz games at the pro level decided off of the build?
It's honestly more about adaptation. Every zvz is different.
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no one really cares about the zvz match up its basically you overpool or 9 pool or your pretty much dead after taht its just your choice of agression fest lings, muta, sourge, devoirers. When i play zvz i think very little of my build after the 9 pool i just do what come naturally which is fast lair to zerg air when i play
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