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Someone Make a Bonus Algorithm Plox: 2/4/2016 02:23:19


Semicedevine
Level 59
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I spent my whole day on this

http://js.do/Semicedevine/82017

(don't round the number, cut out the decimal places directly instead for the estimated income)

and it was a FAIL...



I am willing to pay a 5,000(xp) Grant to anyone who finally figures out a forumla for determining incomes for bonuses... no matter how many variables are involved...

and no don't you dare give me a sht switzerland forumla (https://www.warlight.net/Map/13883-Switzerland-Big)
Someone Make a Bonus Algorithm Plox: 2/4/2016 02:24:46


Fleecemaster 
Level 59
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I'm not really understanding this properly, but are you talking about something that analyses bonuses, like my map analysing tool? Or, something else...?
Someone Make a Bonus Algorithm Plox: 2/4/2016 02:24:47


Semicedevine
Level 59
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but do a little something more interested then "income = number of territories inside bonus - 1"

really im just fasinated with how they designed that one version of the china map that people still use for ladder

Edited 2/4/2016 02:25:28
Someone Make a Bonus Algorithm Plox: 2/4/2016 02:27:11


Semicedevine
Level 59
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basically I just want some accurate way of determining what a bonuses' income should be (since a lot of time, manually assigning incomes lead the risk of biasing a map)

Edited 2/4/2016 02:27:29
Someone Make a Bonus Algorithm Plox: 2/4/2016 02:29:02


Semicedevine
Level 59
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take this map for instance

https://www.warlight.net/MultiPlayer?GameID=10324105

at first it looks unbalanced, but somehow... its not...
Someone Make a Bonus Algorithm Plox: 2/4/2016 02:31:42


Fleecemaster 
Level 59
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So like, you have a bonus of say, 10, and it has 5 territories, and you have an income of 2 per territory. That's like, your basic.

Are you talking about taking into account time to take it and troops needed, etc? Cos that's what my tool does, you just need to tell it neutrals per territory and kill rate (though I normally just run it as standard) also it depends on if it's the starting turn, if you're starting in that territory, and if not then the neutrals in picks that aren't taken.

Or... Are you asking about something else? Honestly, I'm so confuse...
Someone Make a Bonus Algorithm Plox: 2/4/2016 02:32:37


Fleecemaster 
Level 59
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That China map isn't balanced, but maps don't need to be, if you want symmentrical maps then you will upset the "Strat" players who need something artitary to argue over...
Someone Make a Bonus Algorithm Plox: 2/4/2016 10:06:19


Incaman
Level 55
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Interesting...

I don't think you can set a fixed bonus algorithm. Every map is very different and so much depends on what are you trying to achieve with it. Consequently every territory is different depending on placement, role etc.

I think the best thing you can do is try to make the map as consistent as possible throughout. So if you decide to use the territory-1=bonus then try to keep that rule throughout the whole map.

From what I can tell you tried to take into account the number of territories bordering that bonus. Hm, I don't think it's that important, unless it's really a choke point. But then again I'm not a top player so maybe you should take this discussion to them hoping they will provide better judgement ;)
Someone Make a Bonus Algorithm Plox: 2/4/2016 10:24:24


Fleecemaster 
Level 59
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My system takes into account he value of bordering bonuses and how easy they are to take, as that it important for expansion and identifies key areas to contest over. Whilt sometimes it's good to have "safe" income, most of the time I would rather have good contol over the important areas of a map. Maybe it's down to preference, I'm not sure...
Someone Make a Bonus Algorithm Plox: 2/4/2016 11:53:37


Semicedevine
Level 59
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So like, you have a bonus of say, 10, and it has 5 territories, and you have an income of 2 per territory. That's like, your basic.

yep, precisely what im talking about

fleece, is there by chance, a map you've made with bonuses that are completely dependent upon that analysing tool?
Someone Make a Bonus Algorithm Plox: 2/4/2016 11:54:08


Semicedevine
Level 59
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I would greatly appreciate sort of an "example map" to get the main idea
Someone Make a Bonus Algorithm Plox: 2/5/2016 04:53:56

wct
Level 56
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Semice, if you can tabulate the details of a map that you think is well-balanced, e.g. that China map, then I can do a bit of math and give you some hopefully useful results. Here's what I need: A table, with all the bonuses listed, one per row, and each bonus has all the variables you think are relevant recorded into each row.

For example, if we go by your previous attempts, the variables you think are relevant would have been:
var a = 5; //number of territories total
var b = 2; //number of exposed territories
var c = 3; //number of bordering outside territories
var d = 4; //number of territory links within bonus
... plus the additional variable of ...
var e = 3; //Bonus Value
So, I'll give you the first couple entries in the table (Hainan and Taiwan, since they are easy), each variable separated by a comma (the first row is just the variable names for reference):
a,b,c,d,e,name
4,1,2,5,3,Hainan
5,2,2,8,4,Taiwan
(...add the rest of the rows here...)
Here's the neat thing: You can include as many variables as you want, but you have to provide me data for every variable, for each bonus. The more variables you include, the more information I can give back to you, but the more tedious it will be for you to collect all the data in all the rows of the table.

[Strictly speaking, the 'name' variable is not required, but it might help you to keep the table organized and make it easier for you to double-check your data.]

There is only one problem with that China map, and that is that it has overlapping bonuses, especially those +1 bonuses which are embedded within larger bonuses. I'm not quite sure how to handle those. So, maybe it would be better if we start with a map that doesn't have overlapping bonuses. Pick your favourite one, make a complete table for it, post it here, and I'll get back to you with some results.

What you'll get back will be a kind of 'rough' formula for how to calculate bonuses *similar* to how your chosen map is balanced. It won't be perfect, but it will be pretty good, and give you more insight than your previous attempt with your Javascript code. For example, you'll be able to see which of the variables you recorded were the most important ones for determining the value of the bonus.

One super-nice feature of this technique I'll be using is that it is based on real data from real maps, which will help to figure out what the formula should be, rather than starting from an arbitrary formula and generating possible bonus values which may have no connection to being well-balanced in reality.

Finally, we should probably start small, perhaps with a smallish map, and with only a few variables that you think would be most important/interesting. That way we can get some basic results quickly, and we can expand it to a bigger map or more variables later, once you've got the hang of the whole thing.

[PS: You could (probably should) use a spreadsheet for collecting the data. In any case, you don't *need* to use commas to separate them. You could use spaces or tabs or any other separator, as long as it's consistently used.]

Edited 2/5/2016 16:19:19
Someone Make a Bonus Algorithm Plox: 2/5/2016 16:06:04


Fleecemaster 
Level 59
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Semi, do you want me to run that map through my program? Maybe that will help explain...

I've not made an example map, the main problem is how do you give value to arbitary things like "expansion potential" and "defensibility" ?

I mean, I can calculate everything in relative terms, but if you want to know what the single best pick on the board is for example, then I just have to put in my own weights for how important a factor is...

Edited 2/5/2016 16:08:11
Someone Make a Bonus Algorithm Plox: 2/5/2016 16:21:26

wct
Level 56
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I would also be interested to see the output of your analyzer, Fleecemaster. Sounds cool.
Someone Make a Bonus Algorithm Plox: 2/5/2016 18:07:35


Min34 
Level 58
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I`m accually also working on one for my next map. So far it look a bit like this:

V = T/2 + 0.05*B + 0.2*DBO + -0.2*DBW

In this formula
V = Bonus value
T = Amount of territories within that bonus
B = Amount of territories that border the bonus
DBO = Double Borders from other boni
DBW = Double borders within the bonus

The territories divided by 2 is my personal standard. It can be set to anything else.
T*(2/3) is also a good possibility for example. You`ll have to alter it to your liking.

0.05*B because I think it is important to note that boni on the edge on the map are usually easier to defend. They have less sides they can be countered from. The amount of territories that borders a bonus makes a difference for flanking and possible routes of attack. A bonus that has more "enemy" territories around it, should be worth more than another bonus. This could make some boni very overpowered (like a 2 territory bonus in the middle of a map. It can gain quite some extra value if its territories are big). It is limited to 0.05*B and not 0.1*B or something like that to avoid boni getting to powerfull.

0.2*DBO (Double Borders Outside) because I think that if there is a territory that double borders your bonus, it should be accounted for. Double borders make a bonus harder to defend. Double borders can make such a difference that a bonus sometimes becomes unpickable. To counter this these boni get a bonus.

-0.2*DBW (Double Borders Within). If the opposite of the DBO is happening and your bonus double borders another bonus, it should be accounted for aswell. In this case your bonus becomes worth less, as it is easier to take out connected boni if they have about the same value.

After that the bonusvalues work very easily:
Values between 0.50 and 1.49 are rounded to a value of 1. and so on for every other number.

NOTES:
1. Double borders are only double borders if they belong to the same bonus. If a territory connects to two territories that aren`t from the same bonus it obviously isn`t a double border.

2. Superboni and such do not count for this formula, nor are double borders from superboni included.

3. If a territory has multiple double borders it counts for multiple double borders (as an example: Congo on the ME map double borders both South Africa and East Africa. So it counts as two DBW.
--------------------------------------------------------------------------------------
The formula has not been tested yet, and is also not finished yet. I`m not completely happy with some values (like 0.2 for DBO and DBW, it means a bonus with a double border has a difference of 0.4 with a connecting bonus).
I also haven`t thought about territories that border 3+ territories of an enemy bonus yet. That should be taken into account as well.
Also exposed and safe territories still needs to be added to the formula. As they also make a big difference.

The biggest fear I have is that this formula neutralizes the advantages gained from bottlenecks and double borders too much. With that it would kill a part of the strategic value of this game. As I said it hasn`t been tested yet, but if it would seem to be the case then the formula needs to be altered.

Edited 2/5/2016 18:12:45
Someone Make a Bonus Algorithm Plox: 2/6/2016 02:53:37


Fleecemaster 
Level 59
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That's interesting Min34, I think it's so hard to balance the worth of things, that's a good take on it you have though. Do you calculate all this from the API call, you don't put everything in by hand do you?
Someone Make a Bonus Algorithm Plox: 2/6/2016 19:38:37


Min34 
Level 58
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I accually don`t, but that is my own stubbornness. I also draw everything by hand, I don`t use one of the fancy ways to create borders. I like it when everything is done by me, but that is just me. I would advice everybody else to not do that ;)

For Exposed and Safe territories I was thinking of something like this:
0.1*(E-S)

With E being Exposed territories and S being Safe territories. I don`t know how balanced this will be. It could give a lot of an advantage if a bonus has only exposed territory.

Maybe something like 0.05*E - 0.1*S might be better. I think this is one of the harder parts to decided on.

Edited 2/6/2016 19:44:42
Someone Make a Bonus Algorithm Plox: 2/6/2016 21:34:30


Timinator 
Level 62
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how do you handle triple(or beyond)-borders Min?
Someone Make a Bonus Algorithm Plox: 2/7/2016 01:49:35


Red Λrmy 
Level 56
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This is very interesting. Could I bother anyone for an example? Maybe a bonus or two the from Rise of Rome map? I just want to make sure I understand the terms like double borders and exposed territories, etc.

I suggest RoR, because I also wonder, would super-bonuses follow the same rule with respect to all other super-bonuses? It'd also be interesting to compare the resulting values with what the map set bonus values are. Any example will do though.
Someone Make a Bonus Algorithm Plox: 2/7/2016 04:01:23


Traintown 
Level 56
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I used a formula similar to Min34's for my Large Skyrim map. I don't remember exactly what it was, but it included the number of territories in the bonus, the number of territories from other bonuses that bordered it, the total number of connections in and out of the bonus, and the ratio of "unsafe" territories to the total number of territories. I also used it for the contiguous superbonuses. The only parts I didn't balance that way were the scattered superbonuses, like the farms.

I'm not suggesting the map is at all balanced, but I just wanted to provide my input.
Someone Make a Bonus Algorithm Plox: 2/7/2016 13:32:52


Min34 
Level 58
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how do you handle triple(or beyond)-borders Min?


I honestly don`t know yet. If you have a suggestion I would gladly hear it!

would super-bonuses follow the same rule with respect to all other super-bonuses?

A superbonus is not going to follow my formula (I accually don`t know what the values would be, because of the massive amount of safe territories it might be OK to do). You could make a formula for superboni as well. I don`t like superboni to much, so I usually try to avoid them, but I understand they are often used. My one map which has superboni was just filled in based on feeling and size of the superbonus. A formula would be usefull though, but might be even harder to make balanced.

Maybe a bonus or two the from Rise of Rome map?


Sure! ( https://www.warlight.net/Play?PreviewMap=16114 )
If we look at the Magna Italia bonus we see, just above Rome, the boni Italia Superior, Liguria and Raetia

If we use the formula:
V = T/2 + 0.05*B + 0.2*DBO + -0.2*DBW + (0.05*E - 0.1*S)

Italia Superior:
Current Value: 2

V = 3/2 + 0.05*6 + 0.2*2 + -0.2*2 + (0.05*3 - 0.1*0)
V = 1.5 + 0.3 + 0.4 + -0.4 + 0.15 = 1.95

Bonus Value after formula = 2



Liguria (This bonus has a territory that triple borders Narbonensis to the left. Triple borders are not yet taken into account):
Current Value = 3

V = 4/2 + 0.05*10 + 0.2*4 + -0.2*4 + (0.05*4 - 0.1*0)
V = 2.0 + 0.5 + 0.8 - 0.8 + 0.2 = 2.7
Bonus Value after formula = 3



Raetia (Also tripleborders a bonus):
Current Value = 4

V = 5/2 + 0.05*12 + 0.2*5 + -0.2*5 + (0.05*5 - 0.1*0)
V = 2.5 + 0.6 + 1.0 - 1.0 + 0.25 = 3.35
Bonus Value after formula = 3

So this value would be different, mainly because of the T/2, were as RoR has a very high income:territory ratio.

To test for superboni:
Magna Italia Current Value: 10

V = T/2 + 0.05*B + 0.2*DBO + -0.2*DBW + (0.05*E - 0.1*S)
V = 29/2 + 0.05*19 + 0.2*8 - 0.2*6 + (0.05*14 - 0.1*15)
V = 14.5 + 0.95 + 1.6 - 1.2 + 0.7 - 1.5 = 15.05
Bonus Value after formula: 15
There were a couple of triple borders, they have not been taken into account



Compared to the superbonus Gallia:
Current Value: 10

V = T/2 + 0.05*B + 0.2*DBO + -0.2*DBW + (0.05*E - 0.1*S)
V = 31/2 + 0.05*13 + 0.2*8 - 0.2*5 + (0.05*17 - 0.1*14)
V = 15.5 + 0.65 + 1.6 - 1.0 + 0.85 - 1.4 = 16.2
Bonus Value after formula: 16
There were a couple of triple borders, they have not been taken into account

So on superboni Gallia would be worth more than Italia. If I look at the boni, this doesn`t seem off. The value is what troubles me though, 15 and 16 are quite big numbers, and it is a superbonus. Superboni are meant as a little extra, not as a full bonus.
A solution would be to cut the value in half for superboni. That seems much better. Once again, I`m not a pro at the superbonus stuff, so you guys can think about that.
----------------------------------------------------------------------------------------

- I/We need to find a way to use the triple border into account. maybe something like 0.2*DBW for double bonus, 0.3*TB for triple and so on?

- Still not sure if I`m happy with the Safe and Exposed territory thing.... Maybe it is because RoR has barely any safe territories in it (seriously, it`s surprising how few there accually are).
Someone Make a Bonus Algorithm Plox: 2/7/2016 13:39:57


Min34 
Level 58
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Ctesiphon (1-bonus in Partha) is also interesting:

V = T/2 + 0.05*B + 0.2*DBO + -0.2*DBW + (0.05*E - 0.1*S)
V = 1/2 + 6*0.05 + 0.2*0 -0.2*3 + 0.05*1
V = 0.5 + 0.3 - 0.6 + 0.05 = 0.25

So the value should be set at 0 rather than 1

If we look at Rome:

V = T/2 + 0.05*B + 0.2*DBO + -0.2*DBW + (0.05*E - 0.1*S)
V = 1/2 + 0.05*3 + 0.2*0 + -0.2*1 + 0.05
V = 0.5 + 0.15 - 0.2 + 0.05 = 0.5

So Rome would be worth 1.

What do you guys think? I understand that the strategic value of Ctesiphon is higher because of the relatively high amount of double borders. It seems kinda hard to keep safe though, should it be worth 0 while Rome is worth 1? Cause if I weren`t using a formula and had to fill everything in out of my head, I`d do the exact opposite (make Rome worth 0 and Ctesphon worth 1).
Someone Make a Bonus Algorithm Plox: 2/7/2016 19:18:37


Semicedevine
Level 59
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After scrolling through a few maps, I've realised that there is actually a pattern that's beginning to appear more and more frequent now.

Maps can go one of two ways:
1) Become a FFA map where center bonuses are worth more than isolated bonuses (the ones near the edges of maps) since the center bonuses are the areas where most of the action will take place
2) Become a strategic 1v1 map where center bonuses are actually worth less than isolated bonuses, primarily because taking a center bonus would equalate to more rapid expansion as it borders more territories than more isolated ones where you're pretty much taking only about 2 territories a turn
Someone Make a Bonus Algorithm Plox: 2/7/2016 20:27:58


Semicedevine
Level 59
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I've not made an example map, the main problem is how do you give value to arbitary things like "expansion potential" and "defensibility" ?

umm... er... very difficult problem I ran into along the way lol

Right now I'm mostly leaning towards the concept that bonuses with huge territories that border lots of other territories should be worth less, since they are extremely easy to defend while also easy to use for expansion
Someone Make a Bonus Algorithm Plox: 2/7/2016 20:31:55


Semicedevine
Level 59
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@wct so where do you want me to start?

Collect data from just any map that I find balanced so that way we can try and find the hidden mechanics in them?
Someone Make a Bonus Algorithm Plox: 2/8/2016 13:22:21


Red Λrmy 
Level 56
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@Min34. Thanks for the examples. Just to check I've understood it:
  • Double Border from Other bonus (DBO) is when one territory in a bordering bonus has two distinct connections into the bonus we're assessing?
  • Double Border Within bonus (DBW) is when one territory in the assessed bonus has two distinct connections into a bordering bonus?
Sorry, distinguishing these terms seems to confuse me more than it should... I drew a diagram if it helps.

If this is correct you could treat triple, quadruple, etc, borders as just combinations of double borders. (I've shown this in yellow on my diagram.)

3C2=3!/[2!(3-2)!]=6/(2*1)=3 i.e. a triple border can be treated as 3 double borders; 0.2*3=0.6
4C2=4!/[2!(4-2)!]=24/(2*2)=6 i.e a quadruple border can be treated as 6 double borders; 0.2*6=1.2

Currently I think your formula essentially treats them as a one 'double border' since in the Liguria example I'm using, you arrived at 4 for DBOs and DBWs. Each one affects the bonus value by 0.2 just like the other double bonuses. The above however could take into account the strength/weakness of triple border positions.

Alternatively, you could introduce a new constant for triple borders that has a weaker effect than the above calculations give. For example, 0.4*TB would skew bonus values by 0.4 as opposed to 0.2 or 0.6. Lowering the constants would be probably be better than taking the double bonus combinations value; it would not have as heavy handed an effect as the above calculations which look at every double border combination.

All in all, I'm very glad to have an alternative approach to 'number of territories in bonus, minus one' to consider lol. This is a good way to bring the other factors into play.

Edited 2/8/2016 13:26:45
Someone Make a Bonus Algorithm Plox: 2/8/2016 13:37:14


Min34 
Level 58
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-Double Border from Other bonus (DBO) is when one territory in a bordering bonus has two distinct connections into the bonus we're assessing?
-Double Border Within bonus (DBW) is when one territory in the assessed bonus has two distinct connections into a bordering bonus?


You got it :)


If this is correct you could treat triple, quadruple, etc, borders as just combinations of double borders.


Yeah, as I said it is difficult to put a value on them. I`m still not sure whether 0.3*TB is better for triple borders or to count triple borders as two double borders.



Currently I think your formula essentially treats them as a one 'double border' since in the Liguria example I'm using, you arrived at 4 for DBOs and DBWs. Each one affects the bonus value by 0.2 just like the other double bonuses. The above however could take into account the strength/weakness of triple border positions.

Correct, right now my formula doesn`t take 3+ borders into account. It is something I need to work on. They are obviously special and very strong positions, so they do need to be in the formula.


Alternatively, you could introduce a new constant for triple borders that has a weaker effect than the above calculations give. For example, 0.4*TB would skew bonus values by 0.4 as opposed to 0.2 or 0.6. Lowering the constants would be probably be better than taking the double bonus combinations value; it would not have as heavy handed an effect as the above calculations which look at every double border combination.

I like the 0.4*TB idea! Good solution accually. The 0.3 I was thinking about was a bit weak I thought, but at the same time the 0.6 sounded too strong. 0.4 would indeed be a good idea.
Someone Make a Bonus Algorithm Plox: 2/8/2016 15:04:08

wct
Level 56
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@wct so where do you want me to start?

Collect data from just any map that I find balanced so that way we can try and find the hidden mechanics in them?

Precisely.
Someone Make a Bonus Algorithm Plox: 2/9/2016 07:13:43


chuck norris
Level 58
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im using one which seems to work: (x+(y/2))/2
x is amount of territories in a bonus, y is amount of territories inside the bonus which border territories outside the bonus

Edited 2/9/2016 10:07:30
Someone Make a Bonus Algorithm Plox: 2/19/2016 22:35:43


҈ TeeMee123 ҈
Level 45
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Me and zxctycxz use no. territories / 2, round up.

I personally don't see how you will be able to measure how balanced a map is. you cant use rating as that depends on other stuff.

Edited 2/19/2016 22:38:06
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