Upgrade your account to a Community Supporter account and remove most of the site ads.

Reply to thread

Message: <blockquote data-quote="Ovinomancer" data-source="post: 8123949" data-attributes="member: 16814">Sure, no problem.Nope, not a Monty Haul problem -- that one involves asking the same question but gaining information between asks.  This is about knowing which question you're asking.For instance, the odds of rolling a 1 on any given d20 roll is always 5%.  Never changes, no matter how many times we roll.  Similarly, the average number of 1's we roll over a sample of size n is also going to be 5%.  Average is doing a lot of work here, though.  In you earlier example, you were absolutely right that the expected average number of fumbles in 400 d20 rolls is 20.  Perfectly true, but, again, average is doing a lot of work there.  As I pointed out, 95% of the time the results of 400 die rolls will be between 13 and 27 fumbles, with approximately 9% of all 400 roll trials resulting in exactly 20 fumbles.  So, when you ask the question about what the average number of fumbles you'd get with 400 rolls, the answer to that is that the average number is 20.  Not, mind, the number you'll get, but the average if you did it an infinite number of times.When you switch to looking at a single round, or even sets of single rounds, you've changed the question.  Now we're looking at 4 rolls or sets of 4 rolls.  This is a different distribution of probabilities.  Even if you had 100 sets, equating to 400 rolls, the question is about the sets, not about the total population.  You'll have many sets with zero fumbles, some with 1, less with 2, very few with 3, and maybe 1 with all four (unlikely).  So, the average value of the sets having a fumble occur is different from asking what the total number of fumbles over 400 rolls is, and you get a different answer.  The trick with probability is being very specific with your questions and not confusing similar questions as being the same -- they're most likely not, even if apparently similar.Here's another example about how averages are not telling you what you think they might be -- if you ran a trial of 10,000 d20 rolls, the average expected value of fumbles is 500.  The odds of actually getting 500 fumbles in a single trial, though, is 1.8%.  The probability function is spread out over a wide area, but is a bell curve centered on 500, so it's average will be that.  But, you really shouldn't actually expect to get 500 fumbles.</blockquote>

Verification