Frequent Doubles

[amlethus]

Has anyone else noticed that this game seems to roll an awful lot of doubles?  Something seemed off, so I decided to run some statistical analysis to see what's going on (because I'm a HUGE nerd).

In short, it is about 98% likely that the game rolls more doubles than should happen with random chance (assuming that Excel's random number generator is functioning correctly).

I'm unsure why it could be happening; it seems very unlikely that the code would be returning the value of a variable twice before generating a new random number, but that could be happening (and that would be a very interesting bug to track down).

I'm going to refrain initially from posting all of my methods and data, but if there are any other code and/or data nerds who want details, just let me know and I'll make it presentable and put it up.  Here's the short story:

I took about 250 different sets of rolls from game logs, scraped from multiple games, and separated the rolls out into rolls that I made, rolls an ally made, and rolls the computer made (stay tuned for next week's episode, "Does the computer actually get better rolls than me, or does it just seem like it?").

Next, I made an exact copy of the sets of rolls but replaced all numbers within each set with a number from 1 to 20 that Excel randomly generated.  For example, if the following are our original data set of rolls made in-game:
5, 20, 3
1, 13, 18
17, 14, 12, 16, 8

The new data might be:
19, 7, 17
3, 4, 19
13, 17, 16, 17, 1

I then performed a test of significance for two unknown means and unknown standard deviations (see: https://www.stat.yale.edu/Courses/1997-98/101/meancomp.htm ).  The t-score is 2.15, and my degrees of freedom (df) was 72.  This puts .02 > p meaning that the chance that the two sets of data are legitimately different is over 98%.

For those who are nerdier than myself, feel free to question my methods and help determine whether this is true or not.

[Ross Przybylski]

This tool was made especially for players like you: https://heromages.com/forums/index.php?topic=213.0

Enjoy!