Because of Nethack I've found myself often wondering "how many times do I have to do this before there's a good chance of it working?" Then when I've bothered to sit down and work it out properly I've found that there's a kind of a pattern. Namely that if you have a chance of 1 in some large number, you expect to have to make about two thirds of that large number of attempts.
Earlier today I got annoyed enough to try to prove it. Suppose you have some event that has a probability of p. Now the event happening at least once after n attempts is equivalent to it not being the case that the event failed to happen n times in a row. Now the probability the event failed to happen n times in a row is (1-p)^n. Thus the probability that this is not the case is 1-(1-p)^n.
You would expect the event to have happened once this probability exceeds 50%. So we have 1-(1-p)^n > 0.5, that is (1-p)^n < 0.5, but for simplicity let's forget the inequality.
Take logs so that you have n.ln(1-p)=ln(0.5). Rearranging that we have the exact answer, which is that you need to make ln(0.5)/ln(1-p) attempts to expect the event to happen. This is obviously too awkward to do in your head.
However you can approximate it if p is small; you can just look up the Taylor series expansion for ln(1+x), the first term of which is simply x. Therefore we have that for small p, ln(1-p) ~= -p.
So we have -ln(0.5)/p as an approximation. As ln(0.5) = -ln(2) it can be written ln(2)/p.
And that's it! ln(2) is very roughly two thirds (more like 0.7 but okay) So if we write p=1/L for some large L, we have the expected number of attempts being very approximately two thirds L.
Back to Basics A vanilla-compatible replacement Ep.2. Very good. Great use of interconnection and height and all that stuff. I remember the first map when it first came out. Recommended.
Lethe Single, large map requiring the Plutonia IWAD. Decent, playable, highly detailed ("modern"). There's nothing wrong with it but there's loads of maps as good as this. I guess what I'm saying is, I would enjoy this a lot if I weren't so jaded.
NORDHELL A Doom2 version of a GZDoom map, apparently. It works fine, don't worry about any -isms. Tons of new graphics. Idea is a snowed-in mansion. Slightly confusing route.
WolfenDoomed 11 remakes of Doom IWAD maps in Wolfenstein in Doom. To clarify, remake a Doom map, still in the Doom engine, but the Wolfenstein style - textures, no height changes, 128 grid etc. The question was asked, why not make this wad for Wolfenstein itself - to which the author replied that he doesn't own Wolfenstein and has no interest in mapping for it. I blame id for this, they put Wolfenstein in Doom2 in the first place, but I digress. The wad itself is well-made and succeeds in what it's trying to do, but is not interesting, unless you either really like Wolfenstein-styled Doom maps, or enjoy trying to guess which map the author has recreated. (I admit the latter)
Ultimate DOOM 2 A megawad spanning a 13-year editing career. Warning: author's first maps within. Some maps have Zdoomisms. A lot of maps have long switch quests where you press a button and don't know what it does. (Contrast this with Back to Basics where nearly every switch is places so you can see what it did.) There is also far too much waiting around for lifts. A few of the maps are all right but it's probably not worth doing the whole wad.
