Wikipedia:Reference desk/Archives/Mathematics/2015 October 13

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October 13

Percent of a percent

Hi newbie here. I'm playing this RPG that offers many different shields, and I was wondering if one shield blocks an 15% of an attack 22% of the time, but the other blocks 22% of an attack 15% of the time, which one is better? Thanks --2connect4 (talk) 11:30, 13 October 2015 (UTC)

Both shields block the same amount of damage on average (3.3%), so to a first order approximation, they are equivalent.

To a second order approximation, you want to look at the variance. The first shield has a lower variance - standard deviation of 6.21%, whereas the 2nd shield is 7.85%. In general, this means that against stronger opponents, you want the 2nd shield - it will increase the chance of a lucky victory. But against weaker opponents, you prefer the 1st shield - it will decrease the chance of an accidental defeat.

There are other considerations, such as rounding issues caused by short, insufficiently random battles. Suppose you expect to face opponents that deal 100 damage per attack. If you have 335 HP - then with the first shield, even if it successfully blocks all attacks, you will still be defeated in 4 hits, just as if you had no shield at all (85*4 = 340). But with the 2nd shield, you have a chance (1.4%) to block some attacks and last 5 hits. If you had 356 HP, the 1st shield would have the advantage - with either shield, you need to block at least 3 attacks to last 5 hits, and the 1st shield has a better chance for that (4.5% vs. 1.4%). Either shield can be better depending on your HP.

It's impossible to tell whether any of these considerations are important enough to bother with, without knowing more about the game. But my guess is that not - you're best off simply comparing average damage reduction, calculated by multiplying the two figures. -- Meni Rosenfeld (talk) 12:04, 13 October 2015 (UTC)

Yeah, that's what happens in a game with a lot of customization. Thank you so very much for all your help, you opened my eyes to so much lol. I'm not really sure what you mean by approximation, is this the right wikipedia article to read about? Orders of approximation --2connect4 (talk) 01:29, 14 October 2015 (UTC)

This article is relevant, yes. The basic idea is that the shields are very similar, but there are some subtle differences you can notice with a more careful analysis. -- Meni Rosenfeld (talk) 09:50, 14 October 2015 (UTC)

My belated thank you very much, sir. 2connect4 (talk) 17:02, 16 October 2015 (UTC)

Anyone old enough to answer this?

I am trying to remember the name of those wonderful swirly patterns the edges of which are recursive repeats of themselves as you zoom in on them. I used to have some fascinating programs on old 3.5" disks that drew them for you but I had to scrap them when PCs had evolved so far that they wouldn't run them any more.

Can anyone remember what the patterns were called? The name is (annoyingly) on the tip of my tongue.

Thank you Gurumaister (talk) 13:11, 13 October 2015 (UTC)

Mandelbrot set is probably what you're looking for. I'm not that old! :-) --LarryMac | Talk 13:18, 13 October 2015 (UTC)

You are absolutely right!! And if you aren't that old then you are probably more maths aware than I am. Thank you!! Gurumaister (talk) 13:25, 13 October 2015 (UTC)

Mandelbrot set and many, many other fractals. --CiaPan (talk) 14:45, 13 October 2015 (UTC)

I am that old, and the program I was running off 3.5" disks back in the day was Fractint. Their project page is at http://www.fractint.org/ and under http://www.fractint.org/ftp/current/ you will find directories with the latest versions of the program to run under DOS, Windows, and Linux. I don't believe that Fractint has an Android app. I run the free and open source app Fractoid on my phone and tablet, but there are a lot of options out there and I've not done much comparison. As CiaPan alludes, you would be better served by searching on "fractal" instead of "Mandelbrot set", as most fractal generators can display many types of fractals, though the Mandelbrot set is the best known. -- ToE 01:11, 14 October 2015 (UTC)

IMHO, Fractint is still king. It builds without a lot of dependencies, the source code is easily hackable. Sławomir
Biały 01:36, 14 October 2015 (UTC)