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.

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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.