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Message: <blockquote data-quote="dok" data-source="post: 1018905" data-attributes="member: 12780">The illusions of probabilityI have some bad news for you, friend. Actually, bad news both ways...The first piece of bad news is that you can conduct statistical analysis on a sample of practically any size. In fact, once your sample size exceeds 30, it becomes pretty routine to anyone who knows the numbers.  By the way, you'll need more than just the mean, median & mode. If you really want someone to help you, you'll need to post not only those numbers, but also the total number of trials, and the standard deviation & variance of the set.  It'd also help to have the upper & lower quartiles. (I'll come back to this last line later)In terms of "controls", for this situation, I'd say simply record every d20 roll you make, regardless of the situaiton or which d20 you use. Since you're in a d20 system game, high is good & low is bad, so there's no fancy record keeping. Just have a notepad with 20 boxes, and put a hash in the appropriate box after each die roll. Here's where the second piece of bad news comes in: All the statistical analysis will tell you is whether or not the results you've experienced lie within the "probable" range of possible outcomes. And I'm fairly confident that it will.This is the biggest mis-conception people have about statistics. Statistics apply over huge sets. There's an old saw about a health worker coming into a resteraunt kitchen & telling them they can't serve a four-egg omlet because according to the USDA, one in four eggs contains salmonella bacteria.  You chuckle, but let me give you another example:The 'double-20-confirm-kill' rules variant says if you roll a '20', and roll a second '20' on your confirmation roll, and roll a confirmed hit on a  third roll, you kill your foe instantly. Most people, when considering this rule, think "The odds of even rolling for an instant kill is 1:400, so this seems like an OK rule." Here's where probability & statistics part ways. The odds of any single attack threatening an instant kill are 1:400. However, a random sample of 400 die rolls only has around a 50% chance of containing one or more instant kill threats. You're suffering from what statistics teachers like to call "Gambler's fallacy". It's the notion that any kind of short term results must mirror the population distribution. Normally, the example is "I've lost six hands in a row. I'm overdue to have a winning hand!" In this case, you've reversed the assumption: because your data set has a low mode (and an average median and we don't know the mean), that the "population" of your dice rolls overall must be similar. ("I'm unlucky")Remember how I mentioned the upper & lower quartiles being needed along with the median? That's to identify possible outliers, or unusual elements of the data set. Odds are, (forgive the phrase, please) that the range of 1.5 * (3rd quartile - 1st quartile) is larger than 1-20. Which means that every die roll is relevant; in other words, rolling higher than a '15' is not a fluke for you.Here's my prediction. Post the statistical data: Sample size, mean, variance, & standard deviation. Then either you or someone else figure out what the interval is for the population mean with a margin of error of +0.15%, (That's +/- 3 SD for any statistics buffs out there) and what the confidence level is. I'll bet money that the true population mean of 10.5 lies inside that range.</blockquote>

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