Guiroma 1v1 https://www.warlight.net/MultiPlayer?TemplateID=668568

Guiroma 2v2 https://www.warlight.net/MultiPlayer?TemplateID=671768

Very interesting thread! And thank you Mr Tranquilizer for an especially interesting post. I am now going to throw some further fuel into the fire. Before that let me say that the basic premise of the thread, that a good strategic game should give the better player a proportionately better chance of winning, is true.

Chess is in the end not a game of skill (nor of strategy). We have computers which have inherently no skill and no intelligence now beating world champions. So chess is a game of dedication of computing time. If a human player could spend enough time to analyze all possibilities, they would win over one who was not willing to spend that time, regardless of skill level or intelligence. The same goes for 0%SR games, they ultimately become measures of dedication rather than skill or strategy.

In human terms, we do not have time to analyze all possibilities, so at the end of our analysis range, we have to apply a judgement of how likely the resulting position is to give good results. That is skill and strategy. Lightning chess is a good measure of skill and strategy. Another example is backgammon, where you cannot know what moves you will be able to make. You have to place your pieces so as to get the best chance of getting good subsequent outcomes. Skill and strategy. But also possibility of upsets.

Another factor is whether a game is interesting and enjoyable. Basically, if you want worse players to continue playing, they must have a chance to win and at least feel good for a large part of the game. Even chimpanzees can work this out, if nobody plays you can never win.

Yet another factor to take into account is that "100% luck" in warlight does not make it a lottery game. You still have the basic attack/defence probabilities and a bigger force will have a bigger chance to beat a smaller one. So the skill is making your bigger force appear at the best place. Perfect example of strategy.

So I propose the following with regard to strategicality of settings:
- luck percentage doesn't matter, it just changes what you have to account for, and 0% is more likely to reward time spent than actual skill.
- Same for SR versus WR
- A small upset should not leave you screwed. E.g. opponent is lucky and gains a bonus first move and you do not. In a good strategic game, you should be able to recover from this and your greater skill be able to compensate for a bit of bad luck.

One final unrelated thought on team games: a team is not just the sum of the skills of the players, there are other things that come into play.

Like teamwork.

"""
IMO there's nothing more strategic in 16% SR than there is in 0% SR and vice versa
its just that you have to make few adjustments in your attacks(IF NEEDED) to account for luck

with the new updates warlight has made in the analyze attack column its much easier to calculate now and those who were unaware of how it worked earlier can access it with much more ease :)
"""


I(and others) meant 0%WR over 0%SR. 16% SR over 0%SR isn't that much of a difference other than a few differences at attacks with higher armies as you've stated.




"""so basically those who are ignorant have high chances of losing in 16% SR than those(top players) who are not which is an important thing to note because this is somehow misunderstood to be a part of strategy(which i don't like when pro players say it)"""

I fear you make an assumption here that you have enough income to always play the perfect move. The "strategy" comes into play when you do not have sufficient income and must decide how to balance risk vs reward.
i.e, not every move is worth attempting with a 4v2, but some absolutely have to be. You must decide carefully, how you attempt expansion/exploration etc.


P.S - This is actually a good research area. If you have free time, check this article (https://en.wikipedia.org/wiki/Multi-armed_bandit)

@ Corvus5

"""
there is ways to measure that error e.g. "Binomial test"
lets make a simple calculation based on your numbers
the expected value for tails in your example is 5000 and the mean average error is 50
That means inside the intervall [5050,4950] -times Tails we have an accumulated prabability of 68.3%
and in intervall [5100,4900] -times Tails we have an accumulated prabability of 95.4%
and in intervall [5150,4850] -times Tails we have an accumulated prabability of 99.7%
so if you get outsides these intervalls (especially the last one) the probabillty that your coin was biased gets bigger all the time since its very improbable that you got soch a big deviation from the expected value
"""


I see. But in this case,what is my expected value for a player(is it the Elo rating?.. and if so how do I use the Elo rating to measure the error, as well as use to it determine the deviation from the expected value(so as to determine the "strategicness")).

I'm a bit confused now, as I feel we're starting out with a statement and using it to prove that it is correct.

@MOTD:

Your expected value here would be the overdog win % derived from the Elo difference. Your actual value would be the actual % of the time that the overdog wins. So you can figure out how far the actual value is from the expected value in terms of standard deviation/standard error in order to figure out how likely it is that you would've gotten this actual value had the expected value been accurate for the template. So if the actual win % is a certain distance away from the expected value and the probability of your getting that win % is, say, <5%, then you can be reasonably certain that your expected values don't describe the template's actual results- i.e., the template is "unstrategic."

What Corvus pointed out is that it's rather odd to use the Elo scores to derive expected values since they themselves would be affected by a flawed template.

Which made me realize that I flipped the test- the expected value should instead be the actual win rate. The measured value is the Elo score- what we need to be measuring is how accurate the Elo score resulting from a flawed template is going to be in terms of matching up with the expectations set by the actual win rate. (See my post before this).


However, where I'm stumped here is how to get the standard deviation- which sample are we calculating the stdev./stderr. for?

So how do I go about quantifying the improbability of results?

I mean, I can't just straight up multiply the odds of getting the results I did end up getting- that would lead to some odd results (try multiplying (.5)^2000 to represent the probability of getting any certain set of flips from a coin). And I can't just use combinatorics to sort that out since there's too many players for me to just reorder things and sort them out that way.

All I really want to calculate is P(I got the results I got|the theoretical model I'm using here is valid) to get something really useful. But I have no idea how to do that.

Edited 6/19/2015 05:33:17

New idea: Literally just calculate the probability of getting the results you got.

This needs to be modified to calculate cumulative probabilities of getting the # of overdog wins you got or more overdog wins- ie, to measure how far you're deviating from the center

So we have the probability that the average overdog beats the average underdog.

Since Elo probabilites are based on the difference in rating, we also have the average difference in rating (or, in this case, we take the difference in the average rating- which should be the same as the # of overdogs is the same as the # of underdogs, so the average rating difference is the same as the difference in average rating). We end up using this to calculate the average probability that an overdog beats an underdog (which, in my understanding, is the exact same as the probability that the average overdog beats the average underdog- once again, because in this case the average rating difference is the same as the difference in average rating).

Now, once you know P(overdog win) and P(underdog win), you can start treating it like heads and tails and use combinatorics. So you end up using the formula:

P(my results|the Elo predictions made based on the template are accurate) = 
P(overdog win) ** (# of overdog wins) * P(underdog win) ** (# of underdog wins) 
* C(# of games, # of overdog wins)

This gives you the probability that you would've gotten the exact # of overdog and underdog wins that you did end up getting, based on the template.

Main assumptions here:

A strategic template would yield reliable Elo ratings.

Over a set of games, you can accurately model the probability that an overdog wins each game and the probability that an underdog wins each game based on the average probability of overdog/underdog wins across all the games. In other words, if you know that the overdog, on average, wins 60% of the time across all the games, then you can accurately model the games by saying that each time the overdog has a 60% chance of winning. I don't think this is a farfetched assumption- if, over 1000 biased coin flips, you have a 90% chance of flipping heads on average, you can treat that as saying that, for each coin flip, you have a 90% chance of flipping heads.

So if your Elo ratings are bad, your resulting P-value should be low (e.g., your Elo ratings predict that the overdog will win 90% of the time but in reality the overdog only wins 60% of the time, so your template is bad and has led to inaccurate Elo ratings and a low P-value)

Edited 6/19/2015 06:49:29

Pure skill setting is enough to obtain an equal game.

Derp. Figured it out and ended up doing just what Corvus hinted at (calculate the probability of getting results that are x # of standard deviations from the mean). I'll apply this to ladder data at some point, I promise.

It's implemented in CSL, at least, for now.

Edited 6/19/2015 10:18:08

Pure skill setting is enough to obtain an equal game.

It may be an equal game in some perspective, but equal does in no way mean strategic. A lottery game, albeit pure skill settings, is still not a strategic template. The question here is wether it is possible to measure how strategic a certain template is.

hmmm you're right
If you want an equal game use symmetric maps with symmetric (=simular starting places) and the game will be very strategic. pure skill setting but fix the starting position to the symmetrical places
some symmetrical maps which could be suitable
https://www.warlight.net/Map/5319-Fractal-War
https://www.warlight.net/Map/8447-Round-Round
https://www.warlight.net/Map/6084-Sierpinski-Triangle
https://www.warlight.net/Map/6084-Sierpinski-Triangle

I played this one in a toernament, but I quit because it was really to boring
https://www.warlight.net/Map/7670-Road-Utopia

It is great to determine your skill in these games but be aware that these games could be boring

Symmetrical maps are not required for equal games. What is required is manual distribution: with manual starting picks, all things are equal, because the skill of the players' picks will determine the equality of the position he is given.

Edited 6/19/2015 21:01:46

Not even that- an extreme example would be a map that has 1-2 "good" picks (think of the poorly disguised lotteries where one bonus has 10000 armies). So the map itself has to be well-designed enough that luck in picking order doesn't matter.

Do something better with your time. :O

It's hard to find a better use of my time than programming + statistics.

I am still convinced that

     strategicness ~ width of ratings distribution in a population

and that this approach blows away all others on the basis of work involved vs. insight gained, and that it works especially well for templates used in seasonal ladder, because seasonal ladders are short.

Granted, I have not carefully read all of the other posts, mostly because I fail to see why you would do anything else, at least for the 1st iteration.

Well, it's a great method but it's also limited in that your width is going to be affected by other factors (like # of games). I've come to prefer the two-tailed binomial test since I definitely want to use it on more than just ladders.

Semice, I'll explain it later. Thanks to JSA, I now know what Warlight's API call results are formatted like, so I'm working on a piece of software (hopefully with a graphical interface, but I get lazy sometimes) and I'll explain all the analytic stuff in the documentation there.

But both the bias rating (now hidden) and the (two-tailed) p-value are calculated live on the CSL spreadsheet so you can see what the data looks like here: http://tinyurl.com/csldata. "CSL Czech Republic 1v1" might have some 'splainin' to do.

This thread (especially Corvus, MOTD, TeddyFSB, and JSA's contributions) I especially appreciate as it allows me to figure out what methods to use.

Also, there's an edit button under your username on a forum post. Use it if you want to make updates.

Edited 6/20/2015 07:17:01

bump. Very nice thread

I am really confused about the way this thread went. I am baffled so many people are interested in this topic overall and at the same time I am very suspicious about many, many posts here.

First, regarding the general idea about template numerical "strategicness measurement" based on over/underdog elo ratings does not make much sense to me since the elo ratings you're using are based on games that were played on that template already. If you had access to some magical real values of some general warlight skill elo, that'd be possible. On that topic I'd heavily support Teddy's post, if you'd ever want to really test strategicness of many templates, you'd need multiple ladders for a big enough sample with the same elo settings, the bigger the rating gap between first and last would be, the more strategy there'd be. Warlight atm does not have nearly enough players nor ladders to consitute such an experient.

Ok, now off to some more weird posts:

Even hundreds of years later opinions differ still in matter if chess is strategic or psychological game. One should not dvelve into quantitative and qualitative analysis without eliminating first its prejudice.

Please tell me, who atm thinks that chess is not strategic.

There is probably no universal definition of strategy

Please look up game theory for definitions of strategies and strategic games. Warlight is indeed a strategic game and you can very effectively incorporate existing models to help you improve your Warlight understanding. Also it'll show you that you breaking up strategy into 2 segments is not necessary, it'll all fall under the same thing.

is EU 4x5 0% WR just as good as EU 4x4 0% SR?

No, but almost.

Is Rise of Rome too big to be a good 1v1 map?Is it a good 2v2 map then?

Yes and no.

Chess is in the end not a game of skill (nor of strategy). We have computers which have inherently no skill and no intelligence now beating world champions.

Please explain to me the reasoning behind this, I do not follow the trail of logic here.

The same goes for 0%SR games, they ultimately become measures of dedication rather than skill or strategy.

If you have no fog and no picking stage it might be true, however as a general statement it is far from true.

So I propose the following with regard to strategicality of settings:
- luck percentage doesn't matter, it just changes what you have to account for, and 0% is more likely to reward time spent than actual skill.
- Same for SR versus WR
- A small upset should not leave you screwed. E.g. opponent is lucky and gains a bonus first move and you do not. In a good strategic game, you should be able to recover from this and your greater skill be able to compensate for a bit of bad luck.

That shows a great deal of misunderstanding of how settings affect the game. In general it has been agreed by most good players that 0% vs other % discussion is long over and 0% is superior in all aspects. That is mostly, because in practical terms, regardless of luck % almost all the time, the same move will be optimal, because settings like 16%, 20% etc. will turn some attacks like 7vs4 from 100% to 90% and it is very, very rare that it's optimal to change your deployment just for that extra x%, not to mention games can be decided by luck factor alone (bad net income when ou're attacking the enemy for example). SR vs WR is an entirely different thing, because it really changes how strategy works. SR has been becoming more and more popular, because sometimes games in wr were only decided on 3v2 rolls, but very often those were the cases when it was not an optimal move and a player was forced to go for risky expansion route, which in long run will show. When it comes to luck% it is literally like throwing a coin every turn to see who'll get a free edge/disadvantage. If we're going for comparisons, we could analyse some 16% wr games since we have a decent sample for that and compare win rate with cumulative luck at the end of the game. With a big enough sample I'm interested in seeing a study like that.



Now, to comment on the fundamental question of the topic:

I'll repeat, if you ever want a numerical study, go for Teddy's suggestion, but I doubt you'll ever have any kind of relevant data for that anytime soon. Still, I don't think it is necessary to make such a high-level theoretical study for sth that can be broken down to a few key and more easy to understand components that have been already discussed before on the forum:
1) use 0% luck, there is no downside, try not to use other things than normal fog unless you have a good reason for it
2) get good at warlight so you understand the game mechanics regardless of template
3) have a basic idea for the template (1v1 or team game/map/1-2 cards at most if any)
4) check if your idea makes sense (map size in comparison to team size, some cards are game-breaking (again, back to point 2))
5) try to find a balance for the picking stage
6) test it out with good players
7) repeat points 5 and 6 untill you're satisfied with how you can control the game each time

That is basically it, so far for me it has worked well, I don't think I'll be changing that formula. So you get 2 short answers for the question at hand, the "real" answer is what Teddy said, the perfect strategic template would be the one that'd give the biggest rating range in the population, but in practical terms, it just means the level of game control you have. For me personally I like templates, where I can literally always trace my losses back to either a mistake I made or some sort of luck involvement during the picking stage, but that's mostly a personal preference. The better you are as a player, the better feel for the game you'll have and the easier it'll be for you to find balance for templates that you want to be strategic.