Paths of Attack - an intro to Outwitters math

[vivafringe]

“90% of games go like this: I turtle, opponent attacks me, he dies because he doesn't understand Outwitters math” - garcia1000

Garcia1000 is a great guy who also happens to be pretty good at turn-based strategy games. This post is an attempt to be the guide garcia would have made. It is aimed at people in clever, gifted and master leagues.

Before I give you a formal definition of Outwitters math, let me start with an example question:

Which is the best attack path? Green, red, or blue?



If you have advanced past Clever, you should hopefully have realized that red is a terrible attack path. Whenever I see a player doing this, I imagine a cantankerous old man, waving his cane and yelling, “where are you going?!? His base is THAT WAY!” The red path is the shortest path if your goal is to kill their units. But that has never been the actual goal of Outwitters. The reason the red path is so tempting is that often there is a juicy unit that you can kill. So you kill it! Your opponent reacts by sending more units from his spawn at your force. You kill those too! Like a trail of breadcrumbs, you are eventually led to his spawn (images of Napoleon overextending into Russian winterland come to mind). Suddenly, a sniper appears from his spawn to wreck the remnants of your once mighty force!

If you find yourself being lured toward his spawn point, STOP. You will find yourself making worse and worse trades, until you make a trade so bad that your opponent has suddenly taken a huge lead. Instead, divert them around the spawn point and towards their base or wit point.

Okay, so Red is not the answer (Red is never the answer). But the choice between Green and Blue is not immediately obvious to an intermediate player. If you aren’t sure which path is best, go here and open up a bunch of super titan replays on Sharkfood Island. If you’re not on an iOS device, copy and paste the replay link here. Go on! I can wait. I’m not even here! These are just words.

.
.
.

If you did what I asked, you’ve found that every single Super Titan replay chooses the green path. If the result isn’t surprising, it’s because you’ve played so many games that this weird, backwards looking path now looks normal to you. But really, this is goofy! Why are all of these players doing this? They are being guided, whether consciously or unconsciously, by the invisible hand of Outwitters math. It’s almost like magic.

Your long-term goal is to kill their base. To accomplish this, nearly every game is governed by your short-term goal, which is to gain a wit advantage. Doing this involves 2 subgoals, which I will call the goals of Outwitters math:

1) Minimize the amount of wits needed to move units from your spawn to their base.
2) Maximize the amount of wits needed for your opponent to kill those units.

Look at the above diagram, and imagine a soldier moving from arrow to arrow. Notice that the amount of wits needed to move a soldier all the way to attack their base is the same! (3) Even though the blue path is shorter, there is no “2 and 2/3” in Outwitters.

Now, unless you have an unusually altruistic opponent, she probably isn’t too keen on you moving soldiers towards her base. In the diagram below, how many wits would it take to kill a 3 hp soldier at point 1 (green path) and point 2 (blue path), using units from her spawn point?



To kill a soldier at 2, your opponent only needs 5 wits. All she needs to do is spawn a sniper, move it, and then zap the poor guy into oblivion. Ouch! To kill a soldier at 1, the answer is less clear. The best to me seems to be to spawn a soldier, move. Then, on the next turn, move and attack with a soldier, then spawn, move and attack with a scout. All together, this sums to 8 wits. So at no cost to you (remember, the number of moves is the same), you are making it considerably more expensive for your opponent to kill your attacking units under the green path.

All of this has been leading to a great general principle of Outwitters. I’m tempted to follow the math theme and call it a “theorem,” but since I haven’t actually proven anything let’s just call it a golden rule:

The Golden Rule of Outwitters Math:

Follow paths to their base and to wit points that minimize distance from your spawn and maximize distance from your opponent’s.

Here are some diagrams for the 5 remaining maps. Vivafringe APPROVED paths of attack are marked green, intuitive but suboptimal paths are marked blue, and bad newbie traps are marked red. Not every map has a blue or red path.











These diagrams come with some caveats.

- Note that the arrows are exactly 3 spaces long, so they mark the number of turns a soldier needs to get there. Soldiers will almost always comprise the majority of your force, since they have the most efficient HP to wits ratio. That said, it would be misleading to say you should only send 1 soldier along this path! In actuality, this is the path the main body of your force should take (since you have multiple units that can't occupy the same space, you won't be able to follow the path exactly).
- Scouts have considerably more freedom. Most of the time they can reach anywhere with just 2 movements. As a result, the only real restriction on them is that you need to be getting value for whatever they trade with. Moving a scout twice to trade with a scout that moved once is a no-no. But using it to snipe an unboosted sniper is almost always a great deal. On Long Nine, Scouts often attack along the red line as minor harassment. Check out awpertunity's post below for a great explanation.
- If you have a giant lead, often it’s better to crash through the blue route. The blue route is often quicker, and taking the slower green route will allow your opponent more time to recover from his deficit and get defenses ready. Furthermore, if you have already moved into an area and are simply sending reinforcements, use the blue path.
- You will notice that some of the green paths stop at wit points. This is not an accident! Unless you have a massive wit lead, you will need to secure them before you can kill their base.
- In the case of Sharkfood Island, the best path to attack and the best path to defend against that attack happen to be the same. This is not true on maps like Peekaboo. Unfortunately, properly balancing attacking and defending is beyond the scope of this article (and, arguably, of yours truly).

To conclude, here are some alternate ways of looking at the same concepts. Hopefully by this point, they will make sense and not require much explanation. Full credit goes to Garcia for the general concepts.



An important part to remember is that a unit isn't just worth what it cost to make it, but also how many wits you used to move it. For that reason, snipers get pricy fast, and tend to be better defenders than attackers! When you attack, you need to be careful to not trade too many 5-wit soldiers for 4-wit soldiers - a dangerously easy thing to do when you are fighting on your opponent's home turf. Ways to combat this are to take wit points, kill your opponent's base before he can start a war of attrition, or attack in a single devastating turn, robbing him of any ability to counterattack.



Hopefully by now, you have come to realize that the yellow zone (everything within 3 spaces of their spawn) is a ZONE OF DEATH. In that area, your opponent can spawn a sniper and immediately zap a unit... without even moving it (well, almost, there are 2 spots on the above map that are blocked by terrain)! What is less obvious, however, is that the orange zone is nearly as precarious. A soldier can spawn, then move and attack you. A sniper can too! If your strategy involves journeying into the orange DANGER ZONE, you might want to rethink what you are doing! Notice that the blue path travels straight through DANGER ZONE. The red arrow marches boldly into the ZONE OF DEATH.

A note: witpoints are usually an exception to the DANGER ZONE rule of 4 spaces from spawn. Even though your opponent can efficiently kill whatever lands there, simply landing there in the first place will deny him at least 1 wit. Furthermore, he will feel compelled to waste a wit moving a unit there, which can help restrict his counterattack options.

[Szei]

Nice article. I'm sure it will be helpful for new players. One thing though, in your final diagram you neglect the fact that snipers are blocked by terrain so the yellow zone isn't actually accurate there.

[TheQwertiest]

(09-29-2012 02:41 PM)vivafringe Wrote:  If you did what I asked, you’ve found that every single Super Titan replay chooses the green path. If the result isn’t surprising, it’s because you’ve played so many games that this weird, backwards looking path now looks normal to you. But really, this is goofy! Why are all of these players doing this?

replay
i did what you asked and this ST chose the red path and won. xD

[garcia1000]

Spawn point takeover is an advanced tactic and the force required is way way more than what you'd estimate. Clever/Gifted/Master players will just endure misery if they try it. I think general rules are more helpful than highlighting exceptions.

[TheQwertiest]

(09-29-2012 05:26 PM)garcia1000 Wrote:  Spawn point takeover is an advanced tactic and the force required is way way more than what you'd estimate. Clever/Gifted/Master players will just endure misery if they try it. I think general rules are more helpful than highlighting exceptions.

i actually win a lot of my games this way. (pathetic clever leaguer)
but i know what you mean and my post was only meant as a joke cause vivafringe said "every single Super Titan replay chooses the green path"

[Harti]

I don't want to sound like a douchebag but is there a TL;DR version of this? Like with the most important reasonings emphasized?

[Kamikaze28]

(09-29-2012 07:26 PM)Harti Wrote:  I don't want to sound like a douchebag but is there a TL;DR version of this? Like with the most important reasonings emphasized?

Enemy Spawn Space -> bad, you no go there. Instead you go to enemy base while avoiding enemy Spawn Space and towards enemy Wit Space!

(unless of course you know what you're doing and you are confident in your ability to 'take' the enemy Spawn Space and hold it)

[awpertunity]

This is definitely a great general rule, but as already noted, there are plenty of uncovered exceptions, which may only be obvious in high level play. Perhaps a better way to think of it is this the path (green path) that the body of your entire army should be taking as a hole, so it's a little unclear when marking it as the path of a single soldier.

As viva mentions briefly about Long Nine in that runners harassing the red path is a viable tactic, it's not so obvious why using his 'golden rule.' Since it's not a "proven" theorem it should be called a conjecture rather than a rule too .

Anyway, the reason the runners harassing the red path have three advantages (especially on Long Nine as noted).

The first is that by doing this, you are forcing your opponent to also take the red path themselves, which is wit-wasteful as noted. If possible (your runner is close enough) they can deal with your runner with a soldier, but this still costs them at least an extra wit to move it on a suboptimal path to deal with your pesky runner.

The second and third are kind of tied together. Often times you be untempted to land on an opponent's wit space because you see that they can and will clearly retake the witspace in the very next turn, but this is still a huge advantage in many cases. In the general case, it will cost you 3 wits (to spawn a runner and move it twice to their wit space) to briefly take it, and this is if your runner does not even kill or attack anything on the way! Even in this case, in general, this costs your opponent FOUR+ wits to deal with. Two to kill your runner, one to retake the space, and one for the one wit they lose with your runner being there for one turn. The reason I have the "+" there is that not only has it cost him an extra wit already just to deal with your 3 wit runner, but the two units he required to deal with this are now out of position (i.e., closest to the red path!). This is perhaps most dramatic on the red path shown on Long Nine, so arguably that is an extra two wits it costs your opponent to reposition his units that are now way out of place in the corner of his side of the map. Other cases can only make this better, such as killing an opposing runner on your way to his wit space. Not only that, but this forces your opponent to make VERY predictable moves. There is often only one way (if any) to deal with your runner landing on his wit space, and often times it is a runner of his own to either kill your runner or reclaim his wit space. This is a fantastic distraction for you to continue an attack along the green line in the same turn! In the one turn you use to take his wit space with a runner, it only costs you one wit! You can spend the rest advancing an army along the green line and likely taking a unit or two along the way. This forces your opponent to make a decision as to whether spawn a soldier or sniper to deal with your main advancing army, or waste all the aforementioned wits dealing with your pesky runner. Regardless, you come out on top!

If your opponent decides to reclaim his wit space, he has at least two units out of position (and the inability to spawn another defending unit) that will make your attack along the green line much smoother. If on the other hand your opponent ignores the stolen wit space for now, you can turtle your main army as they stand and reinforce them, and gain a +2 wit advantage per turn that they continue to ignore the wit space.

TL;DR: Basically, if you can make moves that FORCE your opponent into making some obviously optimal choices, you can plan a lot more of your future turns, while your opponent is simply making rebuttal moves. If instead your opponent decides to make suboptimal moves, that's a small victory in itself!

[vivafringe]

Thanks for the feedback, everyone! I will make some edits when I get back from vacation.

[vivafringe]

Okay, minor edits done to clarify that it's your *main force* that moves along the arrow, not just one intrepid soldier. Also referenced awpertunity's great post on why you harass the top on Long Nine.

(09-29-2012 07:26 PM)Harti Wrote:  I don't want to sound like a douchebag but is there a TL;DR version of this? Like with the most important reasonings emphasized?

This made me