When the Odds Are Ever Not in Your Favor, Wordscapes Edition

I was introduced to Wordscapes in late 2019, and still lightly compete for crowns on the weekends while getting steps.  During the week, there is a daily puzzle, but it otherwise feels like it's turned into a Tamagotchi game to give you rewards in the form of jeweled hearts (to get you more pets -- you can have one pet "active" at a time), cocoons (to hatch butterflies for a variety of settings), and binoculars (to find pieces of portraits that you can use).

For the month of October, there is a set of 12 portraits you can collect, and in order to get a portrait, you need to find 3 "pieces" of that portrait.  At this stage, where I'd collected 8 out of the 12 portraits, if the probability of finding each piece is roughly equal, I'd expect to get a new piece about 1/3 of the time.  Instead, I found 111 duplicate pieces before getting another pumpkin piece.  The probability of that happening is on the order of 10^-20, so that strongly suggests the probability of getting each piece is not equal.  Unfortunately, there's no indication of this in the interface.

This rabbit hole leads to Triple Town data analysis

Well, how did I get here?

1. Commenting on a previous post, a friend suggested a new game to try.  
2. The Wikipedia page for Gone Home notes it uses the Unity Engine.
3. The Unity Engine page lists Triple Town as a client app.
4. The Triple Town page notes some research done on the distribution of tiles
5. This Triple Town Tribune post by Andrew Brown mentions that the data was collected by David de Kloet.
6. The data was originally shared in the comments of this post, which I found by searching on "David de Kloet triple town" in G+. (NOTE: I also asked Andrew if he had a copy of the data, which he was kind enough to share)

Now, the distributions are a good start, but my first question is: does the probability of getting a particular tile on your next tile depend upon the tile you've just been given?  For example, if you've just been given a bear, are you more or less likely than the overall estimated probability of 0.15 to get another bear with your next tile?

A quick way to start examining this is to look at a crosstabulation of the tile you've just been given by the next tile.  In this table, the rows show the current tile, and the columns show the next tile.  Looking at the first row, what this means is that of the 1043 total times that a Bear appeared, it was followed by another Bear 157 times, by a Bush 157 times by Grass 637 times, and so on.  

The raw counts are useful, but it can be hard to compare rows to see if they're different.  So now let's look at the row proportions.  Again, the rows show the current tile, and the columns show the next tile.  Looking at the first row, what this means is that of all the times that a Bear appeared, it was followed by another Bear 15.1% of the time, by a Bush 15.1% of the time, by Grass 61.1% of the time, and so on.  Bears appear pretty consistently around the overall average of 15.1% of the time, though they seem to appear less often after a Hut (11.4%) and more often after a Tree (18.4%).  However, Huts and Trees don't appear very often, so these differences could be due to chance.
 

So let's look at the chi-square test.  SPSS Statistics produces both Pearson and Likelihood Ratio chis-square tests.  Since the significance values of the tests are each under 0.05, this suggests that there is, in fact, a relationship between what tile you have now and the next tile you'll get, but I'm a little worried about the large number of cells with low expected cell counts.  That can throw the results of the test off.

So another set of tests to look at are pairwise comparisons of the column proportions.  (NOTE: I really want to compare the row proportions, but that's not an option, so I've reorganized the table so that the current tile is in the columns and the next tile is in the rows)  At any rate, the tests suggests that when your current tile is a Tree, the distribution of your next tile is different from when you current tile is a Bear, Bush, or Grass.  

Looking back at the table of proportions, what's not clear from the test is whether the detected statistically significant differences come from the relatively higher rate of Bears and lower rate of Bushes when the current tile is a Tree, or whether it comes from the relatively higher rate of Huts and lower rates of Bots and Trees.  The latter sets of relative differences arises from very rare events, and I wouldn't trust results based on that.  We could re-run the test while ignoring those columns, but for now I'm pretty comfortable saying that there is no practically significant relationship between the current tile and the probability distribution of the next tile.

These tables were produced using this SPSS Statistics syntax on this text file.

Crackers, part II

I previously reported our children's attempts to crack our home computer password in order to play video games at 6am on weekdays.  Since then, on the weekends I've set the password to be the answer to a math problem in the hint text.  This doesn't really stop them from getting up at 5am to play, but while there are good controls on Vista and beyond, our desktop runs XP, where the parental controls are a little more crude.

But then I got tired of changing the password back and forth on the main account, and decided they didn't really need access to the account that has admin privileges (not that they know what to do with that, yet), so we finally created a second account on the box.  The problem: Steam won't run unless you have write privileges to the directory.  I read several unhelpful forum threads that indicated either no workaround or a complicated one, before stumbling across a link to Moving a Steam Installation and Games.  Perfect!  It can go somewhere under the "All users" directory or, better yet, to the external hard drive (which is 1TB, vs. 145GB on the main computer) -- and 30GB suddenly freed up.  w00t.  Now we'll just have to see if the gaming experience running across the USB connection is acceptable.

Fight, Fight, Fight, Parry, Parry, Parry

Because the kids are less than thrilled with the graphics in Proving Grounds of the Mad Overlord -- even I'm a little taken aback because the graphics are different from those on the Apple IIe -- they're not interested, and I'm free to do whatever I want with those characters, though I do plan on showing them the battle against Werdna. 

It's also even more brutal than I remember, possibly because we used the identify cheats back in the day.  The "evil" group died on the stairwell between the 4th and 5th levels, and then the "good" group, while getting strong enough to go after the evil group, died on the third level**, so a third group needed to level up to the point where they could recover the good group.  Finally, Gandalf (our original "good" mage) has learned Malor and we can start retrieving the evil group (because Gandalf will always try to save Saruman).

So let me back up a moment.  In some ways, Proving Grounds makes modern CRPGs look like they were designed for sissies, because nowadays you can always revert to a previous save.  OTOH, in modern CRPGs, you also only get one party/storyline, and if you make bad choices in character development early on, you can hose yourself down the road (Wizardry 8 and Dragon Age: Origins are especially guilty here), and starting over means a couple dozen hours of mind-numbing repetition of the quests you just completed with the first character.  By contrast, in Proving Grounds, you build up a stable of characters and can easily mix and match your party as you determine the "optimal" group, and leveling up a new batch of characters to where they're useful is only a few hours of mind-numbing dungeon crawling.

** the Samurai with 18 Luck keeps getting decapitated; after one battle in which he was beheaded, we ran for the stairs to the second level and were surprised by Rotting Corpses and Grave Mists.  Two characters paralyzed in round 1; the other three in round two; TPK.  Good times.

Accidentally waking a sleeping giant

Audiosurf is a great, cheap game that has maintained its interest for me for 2 years now.  The other day I was playing some R.E.M. songs and hit the top score on "The Wrong Child".  The problem is that artma3bk is a truly elite player who must have simply had a bad game. 

artma3bk quickly rectified the situation, and then went on to play some other R.E.M. songs that they hadn't played before...

Star Wars: Knights of the Old Republic (2003)

Woo, video games.  So, Steam was offering KotOR for $10, so now I've finally played some of it.  I didn't realize that it was based on d20, so that was an interesting surprise.  So far, the game holds up pretty well after 7 years, and loads pretty zippily on a 2006-era desktop.  It's neat to see where BioWare improved on the GUI for DA:Origins -- certain actions in KotOR (going into stealth mode, equipping your character, saving the game) require way too many clicks and are agonizing.  What's a little frustrating is that even DA's equipping GUI isn't as good as Wizardry 8's (a 2001 release).  Sigh.  How hard can it be to drag and drop from the inventory to the paper doll?

Dragon Age Heathers and free text dialogue

[Note: I originally wrote the draft of this on 1/12/10, but never posted it.  I'm posting the edited draft on 6/12/12, but backdating it to 1/12/10.]


So, I got Dragon Age: Origins for Christmas and have played through the game once.  I enjoyed it, but feel like I should have named my character Veronica, so I could have the following conversation:

"Morrigan, why can't you just be a friend? Why do you have to be such a megabitch?" 

"Because I can be."

Unfortunately, even if I did have the foresight to play Veronica, I still couldn't have that conversation because DA:O gives you a very limited set of choices for dialogue.  I cannot begin to count the number of instances in which my character's true response was not listed.  If only we had the technology to allow players to enter free text responses!  Oh, right.  Zork did that in 1980.  Well, if only a traditional RPG allowed you to talk to NPC's with free text!  Oh, right.  The Wizardry series did this in 1988 (though they have since regressed to dialogue trees).  Even though it was clear that Heart of the Maelstrom crudely mapped your responses to an underlying dialogue tree, it was far more satisfying to be able to say what you wanted, rather than be forced to choose a canned response.

Confessions:

• The only computer game I've played with any regularity since Elder Scrolls IV: Oblivion (in 2007) is Little Green Guys with Guns (which is tons of fun, but not an RPG). 
• The only other computer RPG game I played with any regularity in the 00's was Wizardry 8 (I'd played all previous installments in the series, and still have fond memories of Wiz 5).

So, any impressions I have of DA are coming through an Oblivion / Wizardry filter, with a little bit of memory of Wizard's Crown.  No KOTOR***.  No Fallout.  No MMORPGs.

*** This deficiency has since been corrected.  KOTOR is great, aside from the canned dialogue.