{"id":382,"date":"2008-06-18T21:01:57","date_gmt":"2008-06-19T02:01:57","guid":{"rendered":"http:\/\/www.wurb.com\/stack\/archives\/382"},"modified":"2017-05-20T20:18:55","modified_gmt":"2017-05-21T03:18:55","slug":"etherlords-big-o","status":"publish","type":"post","link":"https:\/\/www.wurb.com\/stack\/archives\/382","title":{"rendered":"Etherlords: Big O"},"content":{"rendered":"

In my last post, I described a very effective combo using Kobold Elders and Kobold Shamans. By the end of map 4, I had two high-level heroes, one of whom was using this combo. The other, which had progressed around the map by a different route and had encountered different spells, was using a different technique, one that’s more elementary (so much so that I hesitate to call it a combo) but also quite effective: a deck made mostly out of rats and anger.<\/p>\n

The common stink rat is the beginner’s monster for team red: it’s 1\/1 and costs 1 mana to cast. Anger is an enchantment that gives all your creatures +1 to their attack power. This bonus stacks, so your damage potential increases with both the number of rats and the number of Angers. Of course, the same bonus applies to non-rats, and that’s important sometimes — I put a couple of bats into this deck as well, because a couple of the enemies had a spell called Flood that disables anything that can’t fly — but the rats were cheap and disposable, and the strategem works better with lots of creatures than with a few powerful ones.<\/p>\n

Both of these decks have the advantage that they start damaging the opponent immediately: kobold shamans and stink rats both cost 1 mana, so you can summon them on your very first turn. But more importantly, they’re both O(n2<\/sup>)<\/a>. That is, your potential to do damage on a turn, barring interference, is roughly proportional to the square of the number of turns that have passed. Even though the amount of mana available to you increases with every turn, you still only get to draw cards at a constant rate per turn. So in the long run, the number of instances of a spell active at any moment is going to be linear on the more limiting factor, time. But the damage potential of these strategems is determined by the product of the number of instances of two different spells.<\/p>\n

There are other combos with this property; it may in fact be a feature of every deck that wins at high levels. In fact, there’s one instance I’ve observed of a spell that’s O(n2<\/sup>) without a combo: Grass Snakes. Every time a grass snake hits the opponent hero for damage, its attack power (and health, but that’s not what I’m considering here) increases by 1. I suppose this means that a snakes-and-anger deck would be O(n3<\/sup>).<\/strike> [Edit: Not really, see comments.]<\/strong> (Actually, that combo is impossible: Anger is red, and snakes are green, and never the twain shall meet. But apparently there are a few rare green spells that have a similar buff-all-friendlies effect.)<\/p>\n

But I doubt that such a deck would actually function as O(n3<\/sup>) in practice, because the bonus on the snakes is per-snake, which makes it vulnerable. Every time a snake dies, any bonus it built up dies with it. The other decks I described are more robust: if you kill my rat, the next rat I summon will be just as angry. Catching up to where you were is linear (that is, O(n)) on the number of rats killed. For snakes, in the worst case it’s linear on the number of turns the oldest snake was alive… which, now that I think about it, makes it also linear on the number of snakes killed, because both the maximum age and the number of snakes are linear on the number of turns played so far. I guess big-O notation doesn’t tell us everything.<\/p>\n

Here’s a better analysis: If you can kill my (oldest) snakes at the same rate as I can summon replacements, my damage potential from snakes will never increase. Whereas in the rat\/anger deck, a rat equilibrium will just slow me down from O(n2<\/sup>) to O(n), because I’ll still be casting Anger at a constant rate. Unless you have spells that remove enchantments and we have equilibrium there too. I suppose what I mean by “robust” is that disrupting it completely requires more things.<\/p>\n","protected":false},"excerpt":{"rendered":"

In my last post, I described a very effective combo using Kobold Elders and Kobold Shamans. By the end of map 4, I had two high-level heroes, one of whom was using this combo. The other, which had progressed around the map by a different route and had encountered different spells, was using a different […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[32,19],"tags":[214,557],"class_list":["post-382","post","type-post","status-publish","format-standard","hentry","category-ccg","category-strategy","tag-etherlords","tag-math"],"_links":{"self":[{"href":"https:\/\/www.wurb.com\/stack\/wp-json\/wp\/v2\/posts\/382","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wurb.com\/stack\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wurb.com\/stack\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wurb.com\/stack\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wurb.com\/stack\/wp-json\/wp\/v2\/comments?post=382"}],"version-history":[{"count":1,"href":"https:\/\/www.wurb.com\/stack\/wp-json\/wp\/v2\/posts\/382\/revisions"}],"predecessor-version":[{"id":1324,"href":"https:\/\/www.wurb.com\/stack\/wp-json\/wp\/v2\/posts\/382\/revisions\/1324"}],"wp:attachment":[{"href":"https:\/\/www.wurb.com\/stack\/wp-json\/wp\/v2\/media?parent=382"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wurb.com\/stack\/wp-json\/wp\/v2\/categories?post=382"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wurb.com\/stack\/wp-json\/wp\/v2\/tags?post=382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}