Reply to thread

Message: <blockquote data-quote="Esker" data-source="post: 7890263" data-attributes="member: 6966824">I would have thought mathturbation was doing a bunch of math which is ultimately inconsequential in practice because the process is enjoyable... But that's neither here nor there.It's not a coincidence, and the numbers weren't picked arbitrarily. The scaling was by the standard deviation, in order to match the first two moments of the distributions. Except that really it should have been 2*3d6-10.5, not 11, but [USER=72555]@NotAYakk[/USER] acknowledged that that was done because AnyDice doesn't like non-integers. I guess we should do 4*3d6-21 vs 2*1d20 and just halve the numbers on the axis. But it won't look hugely different.Rescaling doesn't make the two distributions identical, but it does self-evidently make them more similar than before the scaling. Probabilists and statisticians of a more theoretical bent do this sort of thing all the time: approximate one distribution with another by matching lower order moments and then show that the error (measured by cumulative probabilities) is bounded by a function of the higher order moments.I'm not sure why the comparison to the non-standard-deviation-matched version of the distribution is relevant to the argument. (I assume also that you mean CDFs rather than PDFs? Not trying to be pedantic, just make sure I'm following you)Here I have to confess that I don't follow what you are trying to say. What same point? You need 13 on 3d6 to have 2*3d6-11 equal 15, so that's presumably not where the 12 is coming from. Maybe you mean that 12 or higher on 3d6 is where you have about the same likelihood as 15 or higher on 1d20, and 15 or higher on 3d6 is less likely than 20 on d20. Ok, but what does that imply about the argument? Just that even after matching standard deviations, you still have a lower chance of getting a 20 with 3d6-11 than you do with 1d20? Everyone agrees on that point.But nobody is arguing that the curve is actually a line... they're similar to the extent that the probabilities are similar. Now if you wanted to make an argument that linear comparison of probabilities isn't necessarily the right metric, you might have a point (I have at times argued that "rolls per success" is a more useful metric in some contexts than "successes per roll", for example), but that doesn't seem to be what you're doing.</blockquote>

Verification