## Friday, September 28, 2012

### very big numbers

So a while back I wrote some regarding complexity in the game we're making, Scrolls. Tweeted links to it asking for some reality checks. ( http://twitter.com/carnalizer/status/248884698804281344 )

In the article I stated that in a card game like Scrolls, one of the factors of it's complexity is the huge number of combinations you can theoretically get when building a deck. I made a very safe assumption that "the number of theoretically possible decks are above 100 000." Boy, was that a cautious number.

A few days later I get an email from a nice guy named Drew. I'm quoting:

"Hi!

I saw your post/tweet concerning the number of possible decks in a game of Scrolls. I am a junior rocket surgeon, so I did the math:

Although I don't have an alpha code *nudge* *nudge* I did come across a forum post claiming that decks consist of 40 cards with no more than 3 of any particular card. Using this information and the assumption that there are 120 unique cards in the game, the answer comes out to 40995107806965869988005360387065928751 (or approximately 40 undecillion) possible decks. So even if only .00000000000000000000001% of all decks are strong enough to used by a reasonable player, there are still over 4 trillion usable decks. [...]"

Attached was the java code he'd written to figure this out. I showed this to Måns and Aron at work. They had a look and said it looked legit.

That is way way way more "theoretically possible combinations" than 100 000! I'm blown away. Not at the numbers per se, but rather by what it implies about the human mind. A fact of the matter is that out of the testers we've invited so far, all of them has decided that there is no point in logging in to play Scrolls at the moment. There are a few simple and known reasons to this, so don't read anything into that statement.

When you start to slice that number down by how many combinations that are useless according to experience, estimation and by the fact that a few cards are powerful enough to be "must-haves", the number get well below 4 trillion. When you sort the decks by pattern, i.e. the number of reasonably viable/recognizable strategies in your deck building, the number drops below a hundred by a fair bit. There are plenty games with less than hundred game pieces that have game play depth and interest proven to be higher than that of Scrolls.

I am currently shaking my head repeatedly, periodically seeing if this new information falls down in a way that can inform me about how to proceed. I'll report progress if that happens.