The original monument to the Battle of Grunwald was erected in Kraków for the battle's 500th anniversary. It was destroyed during WWII by the Germans and rebuilt in 1976.
Broadly speaking, the Teutonic Player must absolutely protect the camp hexes in his rear at all costs. The Allied Player can win the game immediately if he takes possession of those hexes. The Allied Player's two Polish Wings have the best chance of grabbing it, mostly because they're the ones that are going to stay on the map during the entire game. Naturally, if the Teutonic Player is able to box in the Polish Wings and contain them, it's going to go a long way toward protecting his rear. His better Heavy Horse Units, which make up the White Wing, are probably his best tool to do this. They're also more likely to cause the kind of damage and score the kind of VP that will allow him to win the game. There's a sort of a time pressure element involved, however; the longer the game lasts, the more it favors the Allied Player, especially once the Lithuanian Wing reappears. And it's possible at that moment that in boxing the Polish Wings in, the Teutonic Player leaves a hole in his line that will either allow the Allied Player to sandwich the Teutonic Units between the Poles and Lithuanians, or will give the Lithuanians easy access to the Teutonic rear.
The net result of this, in my experience, has been a number of very tense contests in which every time you strengthen your position in one part of the battlefield, it necessitates weakening your position in another. Every time you exploit a hole in your opponent's line, you leave one in your own for him to exploit. Whether he's able and ready to exploit it depends an awful lot on tempo. If one player is always reacting to what the other one is doing, then the latter is dictating the terms of the game. Conversely of course there is a danger in not reacting, and good play turns around knowing when to react, and when to give your opponent something to react to. This general pattern is dominated by the retreat and return of the Lithuanians, which can alter the tempo drastically-- or disastrously. There's definitely a right time and wrong time to both withdraw and return, but that timing is going to be highly contextual, and usually only visible in hindsight.
These are factors that both players should keep in mind when playing the game, and that definitely includes the question of the game's first few turns. That's what I'm going to talk about today. But before we get to that, we should say a few words about Set-Up.
I always try to give gamers a bit more latitude when setting up their forces. None of this "this guy in hex 2312, but that guy in hex 2413" stuff. This holds true with The Grunwald Swords, where the set-up basically amounts to, "Allied Player, see this line? Set up anywhere on the other side of it. Teutonic Player, see that hill? Your guys go on that hill." And that's pretty much it. Players generally tend to clump the members of each Wing together-- I've seen some players intersperse them, like a checkerboard, but since those Units cannot Activate together and cannot Support each other's Attacks, that doesn't really make a lick of sense.
If players want their set-up to be more strictly historical, the rules do advise that, on the other side of that line, the Lithuanians should be on the right, the Poles on the left, and their foot soldiers in the middle; on that hill, the White Wing, comprising heavy cavalry, opposes the Lithuanians, while the Gray Wing opposes the Poles, with some foot soldiers in the rear to protect the camp.
Usually when testing the game, we used some version of this deployment, because we're generally historical gamers. But you don't have to. In fact, non-historical deployments within the parameters of "this side of the line for you, on the hill for you" could be very interesting and worthwhile. If the Teutonic Player sets his White Wing (Heavy Horse) in opposition to the Poles instead of the Lithuanians, for example, he can try attacking the Poles directly, right from the get-go, while using his Gray Wing's mixture of Light and Heavy Horse to harass the Lithuanians until they disperse. Or maybe he stretches his White Wing to cover his entire front, deploying his Gray Wing a few hexes behind it to protect the camp hexes in depth. The Poles actually have two Wings, and instead of a front and a rear, they could become a new left and right, screening the Lithuanians. That last one's a little "gamey" for me-- what, the Lithuanians are protected by the Poles, but they retreat anyway?-- but it's potentially viable and changes the dynamic. The foot soldiers on both sides seldom see any action in practice-- it is primarily a cavalry battle, after all-- but that doesn't stop the Allied Player from deploying his Yellow Wing on a flank instead of the center, and on using them to advance aggressively against the Teutonic-held High Ground.
Differing deployments will have an effect on how the game plays out, especially the early game. For the purposes of this article, however, I'm going to assume a "strictly" historical set-up: Polish left, infantry middle, and Lithuanian right opposed by a Heavy left and a Light right on the Teutonic side. Each side sets up more-or-less at the "edge" of their designated set-up zone, so the Poles and Lithuanians are right on the line, while the Teutons are occupying the crest of the hill.
OPENING # 1: LITHUANIAN ADVANCE
The Battle of Grunwald began with the Lithuanian right engaging their opponents on the Teutonic left. A "strictly historical" opening move would involve activating the Lithuanian Wing on the right and advancing them toward the High Ground.
There is an average distance of about eight hexes from the edge of the set-up line to the edge of the High Ground. The Allied Player could use either "Bonus + Move" or "Horse + Move" commands to move his Units a maximum of six hexes. This of course would allow the Teutonic Player to respond with a "Move + Combat" for his White Wing, immediately attacking on his first turn. This is perfectly acceptable; while the Lithuanians might take some losses, his Light Horse can likely convert at least some if not most of these to a retreat.
When I play the Allies and open with the Lithuanians, I tend to be more cautious, advancing only three or four hexes. This way, if the Teutonic Player decides to move his White Wing out in response, he can't move and attack on the same turn. If he moves out, then on my next turn I can move my slippery Light Horse in to take some potshots and hope for the odd DL result (taking EX results as ARs). The Light Horse Units aren't exactly something for the Heavy Horse to be scared of, but if they can reduce a few of them, the Polish Heavy Horse can probably seal the deal later (at the very least, the Teutonic Heavy Horse Units are less formidable on the attack when they're one bad roll away from Elimination).
Because of all this, does it make sense for the Teutonic Player to spend his turn moving forward, allowing the Allied Player to use his second turn to close the final gap and make a few attacks? On the one hand, as the Teutonic Player I'd much rather not let the Allied Player begin grinding me down in a battle of attrition, especially because (1) he has more Units and (2) his attacking Light Horse can effectively call a mulligan every time he gets an EX.
But on the other hand, most of his attacks aren't going to amount to anything more than a disregarded EX or a DR, and then on my second turn, I can try a "Bonus + Combat" for two rounds of Attacks on my turn, or a single round at +1 CC. I'd go with the former because I already have a lot of high-quality "A" Units (sure, attacking at "AA" is nice, but the difference isn't as telling as say that between C" and "B" or "B" and "A"),and the built-in time pressure of "the longer the game runs, the more it turns in the Allied favor". The more Lithuanian Units I can Eliminate before their Retreat off the battlefield, the less are going to be coming back to bug me when they Reform. And, the more Eliminations and Step Losses I inflict on the Lithuanians, the more likely they are to Retreat faster, which diminishes the VP gain when they Reform.
So, I think there's a compelling reason to take the bait, so to speak, but implicit in that is the fact that I'm spending my first two turns doing what the Allied Player wants me to do. That's not a pattern I want to get locked into. So, it might be better to react by ignoring the Lithuanian invitation to the dance, instead putting pressure on the Polish left, starting to bottle them up before they get too mobile. Then it's up to the Allied Player to decide whether he wants to use the Poles to react to that, or whether he wants to nudge the Lithuanians a little further forward. (In which case, I might be able to use my second Turn to close the gap and to Attack without first having to weather his attacks.)
There's a danger, however, in leaving the Lithuanians unmolested for too long. Which brings me to the next option.
OPENING # 2: HURRY UP AND WAIT
This "opening" for the Allied Player is to essentially "pass" by issuing Commands and then not doing anything with them, or shuffling guys around in the line. Basically, this is letting the Teutonic Player have the first "real" move.
Reasons not to do this: it gives the Teutonic Player a head-start on bottling up your forces, limiting your mobility. Now you might have a situation where you need to use your next move to react to whatever the Teutonic Player has done; now, maybe you're spending your turns doing what he wants you to do.
Reason to do this: to keep your Lithuanians as fresh as you can for as long as you can. The more turns that elapse before you're forced to pull them off the field, the longer you can wait to bring them back, and the bigger your VP gains when they come back. A good Teutonic Player isn't going to let you get away with this, and is going to try to put maximum pressure on your Lithuanians to minimize the impact if and when they Reform. But then, in a way, you're dictating what the Teutonic Player is going to be doing in the early game. And if you're able to incentivize them into focusing on the Lithuanians, while simultaneously driving your Poles as hard as you can, you might just give him more problems than he can solve.
OPENING # 3: THE POLISH CAVALRY
The final "standard" opening that I see with an historical set-up is to activate one of the Polish Wings (usually the Red Wing is in the front), usually with a "Bonus + Move" or "Horse + Move" to move forward. Unlike the Lithuanian advance above, where you could move each Unit six hexes but probably shouldn't, I tend to go for broke here, covering as many hexes as I can. Two reasons for this.
First, because they're not going to run away at some point in the next eight turns, and because they're generally higher-quality Units, my Poles are much more formidable than the Lithuanians. When the Lithuanians move six hexes, it's to invite the Teutons to get in some licks. When the Poles do it, it's because they're sharpening their swords. It's a legitimate threat, especially when they're opposed by the Teutonic Player's Light Horse and foot Units. (When the Teutonic Player doesn't use a historical set-up, and the White Wing's Heavy Horse is squaring off against the Poles, I'm more likely to be cautious in my advance.)
Second, it might be that I'm not making a beeline for the Light Horse/foot at all, but rather I'm trying to move around the flank so I can push my way up the side of the hill and into the camp hexes so I can win the game early on. It would only take two turns of "Bonus + Move" to get from the edge of the set-up zone to the opposite edge of the map, and then just a couple more turns to get to the camp hexes.
That of course assumes that the Teutonic Player is just twiddling his thumbs which, if he's at all competent, is not going to happen. Instead, he's going to spend his first turn bringing out some guys to slow down my Poles. It's really very seldom that the Allied Player will win by taking the camp, because the Teutonic Player can and should be super-paranoid about protecting his rear. So instead of making a mad dash for the victory hexes, what I'm really doing as the Allied Player is forcing the Teutonic Player to react to the action on his right flank. This isn't really a case where he can afford to ignore it, either. Every turn he's doing that is a turn that he isn't attacking my poor Lithuanians. In a way, this opening has the same effect as number two-- as far as the Lithuanian side of the equation is concerned, I'm stalling for time.
The risk with this opening, compared to number two, is that I can over-extend myself. My Poles are going to see combat early and often, without the Lithuanians serving as an early, diversionary punching bag to absorb the wrath of the Teutonic Heavy Horse. The Teutonic Player might be able to quickly rack up some nice VP, perhaps enough to win the game before my Lithuanians are able to Reform, or at least enough where the Lithuanian Reform VP isn't enough to make a difference.
I wouldn't say that any of these openings or their various counters are the "right" one; each has their pluses and minuses, are dependent on player strategies and tactics, and have broader implications for the flow of the game as a whole. I hope you have as much fun exploring these possibilities as I did during testing.