I plotted the function, think this will clear up a lot. Remember this is the exact same as what I mentioned. It is indeed a quadratic function. Left half is this and the right half is this. You can calculate it yourself if you'd like, with the information I gave you.

Btw, this is the S-curve you wanted. If you add more random numbers, you can make it more extreme.

I'd personally like to see a system in which taking territories and the associates losses were entirely deterministic. It would also have a very simply solution: just round to the nearest integer.

Maybe there could be a setting for this so you could chose the linear, parabolic or deterministic function?

Yeah, that is what I mean by this. You can chose how many random numbers you wanna use. Every increase, would mean it would be more extreme. If you would do a limit over these numbers, that would get you when it is 1/2 the chance is 50/50 and the rest is rounding up when above and down when below 1/2. Chosing that 1/2 would be rounding up, is of course an option.

For convenience, here it is in one plot. Now I also understand how you can get away with a quadratic (which' second derivative is never zero, necessary for the inflection point (is that the English word??) at ( 0.5; 0.5 ) ), you simply use two of them.

@apex:
There's a very good reason why it's not a simple round. See this wiki page for the full explanation.

@Monkey:
Do I understand correctly that using "1 random number" would simplify to the case we currently have? That would enormously increase the chances of this ever being implemented, since it would be easy to "turn off" for people who don't like it.

That is correct. That is just the chance that a random number is lower or equal than the original. Btw, I think you should pick a number excluding 0, cause otherwise the chance would be higher.

You really need to exclude 0 from the random numbers, otherwise you have a chance to round down, when chance is 0 xD. It is more for explaining and programming reason, that I chose to use random numbers like that. I studied uniform numbers between 0 and 1, which are below the current. In that case the chance is the same.

What the Wiki states is blatantly wrong. One army IS very significant in a lot of cases, especially with low luck settings. Even stronger: at 16% luck the random rounding is the dominant factor with small army attacks, not the luck factor itself!

Plus, I don't see how this would become an exploitable. In competitive matches every army matters, and bad luck you can have with 4v2 attacks (guaranteed victories) having a 40% chance to incur 2 losses instead of 1, a string of bad luck here early on can be game deciding. Now THAT is what takes the fun out of the game, NOT the extra micromanagement, since careful micromanagement is what you really need anyway in these low-luck competitive games. Sure, without random rounding, 3v2 becomes the standard. But is that so wrong? If anything, it makes games faster and more dynamic.

Perhaps we are making this more complex than it needs to be. My only problem with the current settings is that there is no way to adjust them. So, that 2 army spread (one for attacker, one for defender) always exists in a place where we can't do anything about it. What if, instead of changing the formula for how those odds are calculated, we add the ability to change the luck factor of the rounding instead?

With 0% luck on the rounding factor and 0% luck as normal, 3v2 would always work. Alternately, with a 50% luck on rounding, 3v2 could still fail (albeit less often), but something like 5v3 could not, even on 16% luck in the conventional sense. Luck calculations already exist in Warlight, so I would think that porting the code over to a new area shouldn't be too hard, compared to re-writing the code for rounding. This would also allow for the single player boards to remain unchanged.

@RvW:
First off, my (user)name is Huruey, not apex. Apex is the name of my team/clan/group.

Regarding the reasons the wiki gives for not having a deterministic setting, I am in agreement with Kingu. I think the wiki is mistaken in multiple ways.

First off, the 1 army from the luck is very significant. This 1 army can reduce the fun of the game. Furthermore, it is mistaken in saying that an attack of 4 would never be useful. Firstly, it would be useful in order to have your troops finish in positions which will be useful on the next turn. Furthermore, by deploying 4, you have a chance of doing greater damage and surviving to make a small in small defensive situations in which microattacks may be important. However, I am also in agreement with Kingu on his point that there is nothing wrong with 3v2s becoming a standard. Adding an extra deterministic micromanagement factor to the game would often be preferable to luck.

I think a key issue with the current solution as described in the wiki is that it seems to assume that only a single global rounding function must be used exclusively. I would absolutely agree that the deterministic setting would not work were it the sole rounding function used throughout the game. The luck setting has its place, for sure. However, is see no reason why players shouldn't be allowed to have the option to create a game with a deterministic rounding function.

@The Duke of Ben
The luck system and the round up system are 2 totally different things. Luck is just how much the deviation can be. That is done with a random number. Round up is just the chance of rounding up, again here is used a random number. Kinda same thing, but totally different objective. We don't really make it complex, cause only thing we do is add more random numbers and take the average of those numbers. There isn't much going on, but calculating it out requires a bit of probability study. Also, my suggestion works. Isn't that the main thing. Easy to program, handy to adjust and works good in gameplay.

Currently, the rounding system acts as if there is 100% luck present for any calculation that involves rounding numbers. All I am suggesting is to be able to change the luck for that rounded figure. I realize that they are not the same function.

How would you go about adjusting it? I'm not the best at math, but from what I can see, you are talking about changing how the background calculations work in a permanent fashion, not on a game to game fashion. If you are talking about making it available for game creators to adjust, then you just lost 90% of the players, because they have no idea what variables to put where in any of the calculations presented so far.

While there is nothing mutually exclusive about my idea and yours, Fizzer has mentioned before that he doesn't want to change any of the factors present in the single player games, which means no coding changes to how losses are calculated. That's the main reason that I offered an alternative to your system. The math can work the same as it does now, but with an added feature of being able to affect the rounded numbers in Member created games.

Monkey wrote:

You really need to exclude 0 from the random numbers

Isn't that a rather technical issue? Last I checked, the uniform distribution on the interval [0..1] has a zero chance of returning zero anyway. :p

Kingu wrote:

What the Wiki states is blatantly wrong. One army IS very significant in a lot of cases, especially with low luck settings. Even stronger: at 16% luck the random rounding is the dominant factor with small army attacks, not the luck factor itself!

What the Wiki states is that the "weighted rounding" exists to make sure every army matters, how is that at odds with "one army IS very significant"...!? If you were to switch to "normal rounding", then you get situations where extra armies don't matter. And, as far as I care, there's a pretty big difference between micromanaging "where to use my armies (because I never have quite enough of them)" and "which exact number of attackers should I use (to exploit the rounding mechanism)".

(@Duke of Ben: See Monkey's post directly above mine. Apart from me still wondering whether I like this suggestion, I completely agree with him.)

Hureuy wrote:

First off, my (user)name is Huruey, not apex. Apex is the name of my team/clan/group.

Then put it on square brackets already. ;)

First off, the 1 army from the luck is very significant. This 1 army can reduce the fun of the game.

There's nothing you can do about this (apart from playing with 0% luck and implementing Monkey's suggestion (and turning the slider to "infinitely many random numbers"). In every other case, you will always have one army which could go either way.

Firstly, it would be useful in order to have your troops finish in positions which will be useful on the next turn.

Oh come one, it obviously means it doesn't give you an attack advance (so you might as well deploy that reinforcement somewhere else). Sure, if there's already enough attackers (or you have absolutely no other place to deploy them to) then you might as well use all of them in the attack. But that's the same as saying a 101-vs-1 attack gives you an advantage over a 100-vs-1 attack; sure, it's an advantage if you consider the entire state of the game, but it's not an advantage in the attack itself.

I think a key issue with the current solution as described in the wiki is that it seems to assume that only a single global rounding function must be used exclusively. (..) However, is see no reason why players shouldn't be allowed to have the option to create a game with a deterministic rounding function.

The way I read the Wiki it only explains how the system works and why it works. I don't see any claim it's the only possible system which could work... Also, Monkey is proposing a tunable system, which can go all the way from the current situation to the (in my opinion broken) situation of "normal rounding".

The Duke of Ben wrote:

Currently, the rounding system acts as if there is 100% luck present for any calculation that involves rounding numbers. All I am suggesting is to be able to change the luck for that rounded figure. I realize that they are not the same function.

That's also what Monkey is proposing... (Well, technically Monkey's solution (for a finite number of random variables) is still 100% random, in the sense that the "decision" is entirely based on randomisation. However, it does address your issues with the current system.)

How would you go about adjusting it? I'm not the best at math, but from what I can see, you are talking about changing how the background calculations work in a permanent fashion, not on a game to game fashion. If you are talking about making it available for game creators to adjust, then you just lost 90% of the players, because they have no idea what variables to put where in any of the calculations presented so far.

The mathematical solution proposed by Monkey could be used either to change the settings for each game (Fizzer chosen a variable and uses that for all games) or to allow players to choose it themselves. What gets implemented depends on what people vote on UserVoice and what Fizzer thinks himself of course.

While there is nothing mutually exclusive about my idea and yours, Fizzer has mentioned before that he doesn't want to change any of the factors present in the single player games, which means no coding changes to how losses are calculated. That's the main reason that I offered an alternative to your system. The math can work the same as it does now, but with an added feature of being able to affect the rounded numbers in Member created games.

Huh?? At least Monkey's approach lets people change it gradually (like luck factor, and offence/defence kill rates), you propose two entirely different systems people have to choose from (like whether or not multi-attack is on). However, both proposals allow people (or, single-player templates) to choose the current setting, so on that count, it doesn't matter at all. Also, I see no particular reason why this should become a members-only feature...?

but since it's only one army it's not too significant

This is the part of the Wiki's explanation I'm referring to, not what you mention.

I understand the argument against using deterministic rounding. In most cases, you'd just want to use the minimum amount of armies needed to guarantee a takeover, so you'd try to calculate it in such a way that you just make it round up. But this argument kind of falls apart when you consider that at 'normal', or 75% luck, the luck factor dominates so much that you cannot play on just making the rounding or not. For casual play, the rounding is just swamped by it, so players will hardly notice it.

The place where the rounding is dominant, however, is in competitive low-luck play. Here, games are ideally won through superior skill instead of randomness. You need this if you ever want a truly competitive metagame. Here you can assume that both players are highly competent and have their micromanagement skills 'down to a t'. And a possible exploit here isn't an exploit anymore if both players are completely aware of it and use it. It just becomes integrated in the metagame and players handle accordingly. Moreover, in cases of doubt, one can just check with the analyzer tool, which eliminates the need of a calculator as losses can be entirely determined from the graph.

So yeah, in short the luck factor does a pretty brilliant job of separating casual and competitive play, and it counters the 'deterministic rounding exploit' quite perfectly. Your exploit just becomes one of the 'rules of the metagame' someone would need to understand to become a top player. There is nothing wrong with that.

And, to add on your latest post, the reason I would personally propose it to be a member-only feature is precisely because it's closely tied with the luck factor. A rounding slider wouldn't have very much of an effect if the luck modifier isn't changed accordingly. To avoid confusion and needlessly complicate the interface, I'd lock it for non-members.

but since it's only one army it's not too significant

I thought you meant a one army difference in the number of attackers.

this argument kind of falls apart when you consider that at 'normal', or 75% luck, the luck factor dominates so much that you cannot play on just making the rounding or not

But you can still calculate how many armies you need when the 75% luck part of the equation "is against you".

a possible exploit here isn't an exploit anymore if both players are completely aware of it and use it.

But then people have to (partially) relearn the game once they switch from casual play to highly competitive play...

in cases of doubt, one can just check with the analyzer tool, which eliminates the need of a calculator as losses can be entirely determined from the graph.

Except that the analyser is not perfect either...

the reason I would personally propose it to be a member-only feature

Ah okay, that makes a lot of sense, good point.

. >There's nothing you can do about this (apart from playing with 0% luck and implementing Monkey's suggestion (and turning the slider to "infinitely many random numbers"). In every other case, you will always have one army which could go either way.

The whole point I, and others, are making with the deterministic solution is that you CAN do something about it, i.e. allow for the use of a deterministic rounding function. :P

. >Oh come one, it obviously means it doesn't give you an attack advance (so you might as well deploy that reinforcement somewhere else). Sure, if there's already enough attackers (or you have absolutely no other place to deploy them to) then you might as well use all of them in the attack. But that's the same as saying a 101-vs-1 attack gives you an advantage over a 100-vs-1 attack; sure, it's an advantage if you consider the entire state of the game, but it's not an advantage in the attack itself.

Maybe you don't yet understand the significance of having your spares well placed. The wiki suggested that an attack of 4 would NEVER be required. I offered a situation in which it could in fact be very useful. It doesn't matter if its an "advantage on the attack itself", its a situation in which making an attack of 4 is better than making an attack of 3, and that is all that matters.

. >The way I read the Wiki it only explains how the system works and why it works. I don't see any claim it's the only possible system which could work... Also, Monkey is proposing a tunable system, which can go all the way from the current situation to the (in my opinion broken) situation of "normal rounding".

The wiki presents the two functions the (random rounding and straight rounding) as alternatives. In the same paragraph it suggests that the random function is important because the deterministic function has problems. To make such a case assumes that there must be mutual exclusivity in their implementation, because if they could coexist, then you cannot use a disadvantage of one to justy the use of another.

Maybe you don't yet understand the significance of having your spares well placed. The wiki suggested that an attack of 4 would NEVER be required.

the point is that the advantage of having a 4v2 over a 3v2 is the same relative advantage as having an 8v2.. you are only placing the extra armies in anticipation of future attacks, or in anticipation of an enemy attack.. for pure expansion, examples being with no fog/light fog, or good use of intel cards, you would use almost entirely 3v2, because using 3 4v2's would mean that you are not expanding in one direction that you could be despite having a 100% chance of success since 3v2 with 16% luck deal a minimum of 1.512.. and the fact of expanding slower is the exact reason people use 3v2's now despite the chance of failure, to out-grow their opponents..

RvW wrote:

But then people have to (partially) relearn the game once they switch from casual play to highly competitive play...

But that's already what you have to do. 16% luck, the standard for competitive play, completely changes the battlefield already. There are different 'rules' about expanding, attacking and defending. You need to understand the subtleties of cycle order (if used), the pick order algorithm, etcetera. A lot of things that are not much of an issue in casual games matter a great deal competitively. But that's the case for every game.

You can play through every single Pokémon game without ever learning about EVs, IVs, natures and whatnot, but if you want to play it competitively PvP those are among the first things you need to know. Familiarity with the mechanics is a requirement for becoming a competitive player, simple as that.