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

Only in combination with 0% luck (if you only ever use low numbers of armies a few percent of luck would also work). Even with deterministic rounding, at some point you'll need to have a "cut-off" between rounding up or rounding down. You can put it anywhere you want, but unless you use 0% luck, the attack might still end up killing either just below or just above that cut-off point.

Do keep in mind that if you do this, it might be possible (I don't have a proof or example, just a gut instinct and not nearly enough motivation to look for an example :p ) that you could "trick" the average offence kill ratio to be higher than the average defence kill ratio. (This is most likely to be possible when you mainly perform attacks with very low numbers of armies.) This also seems undesirable.

Maybe you don't yet understand the significance of having your spares well placed.

I was trying to explain it wasn't talking about any other considerations, only about the chance of a successful attack. And in that case, the difference between 3vs2 and 4vs2 is the same as between 3vs2 and 3000vs2: none at all.

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.

The Wiki is not proposing Monkey's solution, Monkey is! I agree with the Wiki that straight rounding has downsides. I also think Monkey's alternative has those same downsides (albeit less severe, since in a very real way it's a compromise between the current system and straight-rounding).

Okay, so if we take the parameter of Monkey's approach and set it to 1, we have the current situation. If we set it very high it becomes very close to straight rounding (in fact, if we'd set it at positive infinity, it actually is straight rounding). But since it kind of make a whole lot of sense that properties change when a parameter changes, I fail to see how this would imply a "mutual exclusivity in their implementation" (to be fair though, I'm not entirely sure what that even is...).

And maybe the most important point:

Even though I don't like Monkey's solution, disagree the situation he wants to solve is a problem in the first place and am unlikely to use this even if it were implemented,
I do think his mathematics checks out, it would solve the "problem" (if you think there is one) and it is probably feasible to implement.

I may not like Monkey's idea, but I do not think it's a bad idea (which is an entirely different and near-unrelated matter).

If you go back, you will notice that once I correctly understood what Monkey is proposing (this post), I stopped objecting to it, even pointing out that the option to use a parameter to keep the current situation is a good thing. (Just about everything I posted in this thread after that is to explain the Wiki is not "blatantly wrong".)

@Kingu, regarding partially relearning the game:
You do have a point. However, unless there's a very good reason (and we seem to disagree whether this is) I think it would be better if there were as few of those "subtle changes with considerable impact" as possible.

Another thing we seem to disagree about is the need to eliminate every last bit of luck from the game. Sure, there are games which get very, very close to removing luck from the game (chess and go come to mind, where only "who plays the first move" remains), but many other games and sports don't even attempt to "outlaw" the luck factor. Any game involving dice (like, to take a not-so-random example, Risk) by definition relies at least in part on luck. Any realtime computer game (both shoot-em-ups and RTS) cannot possibly remove chance from the game (even if it was just because of variations in packet delay on the network, or the chance of a disconnect occurring in a situation where some people think one of the players had practically lost, while other people think he still had a realistic chance).

Do keep in mind that if you do this, it might be possible (I don't have a proof or example, just a gut instinct and not nearly enough motivation to look for an example :p ) that you could "trick" the average offence kill ratio to be higher than the average defence kill ratio. (This is most likely to be possible when you mainly perform attacks with very low numbers of armies.) This also seems undesirable.

I don't think so. The best case scenario is pretty much a 1v2 attack, which would then guarantee 1 kill on either side. The 0.6 ratio of the attack rounds up while the 1.4 kills of the defence rounds down. That's the biggest abuseable I see here: keep throwing armies of 1 at a defending stack to whittle it down. Effectively, you'd "trick" the offensive ratio to be 1. Of course 1v1 becomes an impossibility, so in the end you'd still have to attack 2v1 in order to take a territory, but it would be an efficient way of weakening a defensive stack before throwing your main stack at it. You would need fewer armies to take a territory that way.

Example: A territory with a defensive stack of 11 would need at least a stack of 18 attackers to fall (10.8 kills). However, if you would attack with 1 beforehand from an adjacent territory, you would guarantee 1 enemy kill, turning it into a stack of 10. But this stack only needs 16 attackers to fall (9.6 kills). So effectively it takes one less army to take that territory than you'd expect. The losses are in both cases 7.7 armies (8 after rounding), so there is no downside for the attacker. Perhaps this is the exploit your gut instinct warns you about :P

And @RvW, regarding your latest post: I do not feel that there is a need to eliminate luck from the game completely. I fully acknowledge that it is just not possible, and that at the start you'd need to make two coinflips anyway (one for determining pick order, a second for starting the cycle round). Moreover, even then there is luck involved that isn't part of the game engine: luck in correctly predicting the enemies' movements and correctly countering them. You can 'read' your opponents to some degree (even moreso if you have played against them previously, or by looking at previous games they've played in a tournament), but you can never be certain he's going to do what you have prepared for. Whether you classify this as 'luck' or not is a rather murky philosophical point I'd rather not discuss, but even I will from time to time flip a coin when I have to choose between two options. For instance, when I can break an enemy bonus by attacking one of two territories in that bonus I can reach. Both are equally valid but my opponent can only defend one of two successfully. In such a case I will often just flip a coin. The random decision has the added benefit of making myself unable to be completely 'read' by the enemy.

But I digress. My point is: I am not arguing for completely removing luck. If that's the idea you got from my posts, my bad. The only problem I have with it right now is just the fact that the random rounding has a pretty big impact on early-game expansion speed, and can be potentially decide competitive games on luck alone. And that is something it may never do. Game results may be impacted by luck, but not be dominated by it. It's very frustrating to lose a pefectly symmetrical game by turn 3 just because you have a string of max losses while your opponent has minimal deaths. Such results are undesirable if you want to have an interesting competitive scene for your game, since the outcome of that game was completely beyond the player's control. And I do feel that Monkey's suggestion is on the right track of lessening the chances of this occuring immensely, which is why I am arguing in favour of it.