Friday, 3 January 2014

Less Reading, More Clicking

At some point, answering a logicat question becomes something you can do whenever you like.  There is only so fast you can move the mouse to click those buttons, especially given that the buttons aren't alway totally responsive, so when your caged logicat gets 18 extra questions every 8 mNP you can't actually run them out.  When you are at that point, you have to seriously reconsider the worth of getting the answers right.

Answering a question wrong costs you.  At a base getting a question right earns you 0.2 levels and getting one wrong costs you 0.1 levels.  As you scale up your getting-it-right value, your getting-it-wrong value scales up by the exact same amount.  A right-wrong pair is always worth 0.1 levels, regardless of how much a right question gets you.  I currently get 1.9 levels per correct answer.  So if I get a question right I get 1.9 levels and if I get one wrong I lose 1.8 levels.

Suppose instead of reading the question I just click the first answer and then the second if the first was wrong.  If I have two chances at a 50-50 guess then I have a 75% chance of getting the right answer.  But I don't have two chances at even odds.  Actually the numbers are more favourable.

First of all, there is no replacement.  If there are four responses, two of which are true and two of which are false, I have a 50% chance of getting it right immediately and if that fails I have a two in three chance of getting it right since I presumably will not choose the same incorrect answer.  That gives me a five in six chance of getting it overall.  If there are eight statements then my chance of getting it right is 50% followed by four out of seven, which is nearly 79%.

But it gets better than that too.  The game does something to gaurantee that you aren't given an impossible puzzle.  Given that you can have a 100% chance to get it right but you can't have a 0% chance, we might immediately suspect that as guess is better than 50%.  The mechanism for ensuring this determines how much more.

Rather than simply choosing whether you need to pick a true or a false response, it chooses a random response and assigns the truth values you need to pick to the truth value of that response.  So if there are two true and two false statements then there is an even chance of being asked to find a true statement versus a false one, and out first guess is a 50-50.  But if there are three true statements with only one false, then there is a 75% chance we are asked to find a true statement and a 25% chance being asked to find the false one.  What's more, if we are asked to find the true one we will always get the right answer because we have two guesses, only one of which can be wasted on the false statement.

In the end, the odds of guessing the right answer for a four question puzzle is actually 87.5%.  An eight question puzzle is worse, but still 81.25%..  Overall, guessing gives us very close to an 84% chance of a right answer.  The average value for a guess for me, then, is 1.3 levels.

Now I haven't actually timed myself answering questions but the idea that reading enough of a question to get it right is worth those extra 0.6 levels seems pretty far fetched.  I think I got pretty quick at answering questions but blind clicking has to be more than twice as fast.  Correct answers are more favourable at higher logicat levels, but the ratio between guessing and getting it right approaches an asymptote above two-thirds, so there is just no way that reading questions will ever be right when unlimited questions are available to be answered.

As an update, I plan to have infinite glass by the end of the weekend and I've already unlocked two things to spend it one, one of which appears to seriously invalidate the other.  Then again, I don't yet know the mechanism for generating another resource I will need, so the one might be useful in the short term.

5 comments:

  1. i'm sorry; what game is this?

    sometimes i can follow and sometimes i can't. sometimes when i'm reading along and it doesn;t sound like a game i would like, i skim so i maybe miss a detail that would tell me if you;re still talking about the same game in a later post.

    please assist the memory-challenged.

    it think: hm. that sounds interesting enough to look at.

    and then i can;t figure which game you're talking about.

    i miss the old days.

    ReplyDelete
    Replies
    1. Sandcastle Builder at visit http://castle.chirpingmustard.com (and my pick for second best game of the year).

      Of course I can't disagree with your guess that you wouldn't like it. I'm sure that most people, even most people who play a lot of games, wouldn't like it.

      Delete
  2. How do you use a caged logicat thing? I clicked rather randomly on the option to buy it from Rosetta three times a while ago but could never find a place where it did anything.

    ReplyDelete
    Replies
    1. Once you buy it from Rosetta the cages cat is a boost that you can spend blocks on to get a puzzle right away. It comes with 10 puzzles per ONG but as suggested by the post, that eventually goes through the roof.

      Delete
    2. Weird. I tried buying it again and it gave me the boost. I wonder why it ate 3000 of my blocks a couple weeks ago.

      Delete