💾 Archived View for thrig.me › blog › 2024 › 05 › 08 › old-math.gmi captured on 2024-05-10 at 10:49:14. Gemini links have been rewritten to link to archived content
-=-=-=-=-=-=-
Or, unpacking some BASIC from some version of Oregon Trail (1971). For some 1971 will be extremely recent, but the context is computer games which have not got much history, yet.
RND(0)*10>((M/100-4)^2+72)/((M/100-4)^2+12)-1
AppleSoft RND returns "the same number" for RND(0) which here would likely not make sense, so we will assume that RND(0) returns something in the 0..1 range, times 10. A math type might look at the rest of the equation and could tell you things about it; for us neck-bearded unix admins another method is to plug numbers into it.
But first we need to have code that works, and hopefully not introduce errors during that process. This is where worked examples are beneficial, as someone then will have data points on what you thought the code should do. Luckily there is some context here that M is for miles and that the Oregon Trail is less than 3,000 miles in length.
$ perl -E '$M=100;say( (($M/100-4)**2+72)/(($M/100-4)**2+12)-1 )'
2.85714285714286
$ perl -E '$M=1000;say( (($M/100-4)**2+72)/(($M/100-4)**2+12)-1 )'
1.25
$ perl -E '$M=3000;say( (($M/100-4)**2+72)/(($M/100-4)**2+12)-1 )'
0.0872093023255813
This is an easy conversion; prefix "M" with a "$" and change any "^" to "**", try some numbers. Converting it to Common LISP is a bit more work, though may better show the structure of the equation, and gives us a second opinion that our numbers are at least wrong in the exact same way (or, possibly, are right).
(defun calc (miles)
(1- (/ (+ (expt (- (/ miles 100) 4) 2) 72)
(+ (expt (- (/ miles 100) 4) 2) 12))))
(dolist (m '(100 1000 3000))
(format t "~&~f~&" (calc m)))
The results are the same as the Perl, so if we made an error we made the same error using two very different syntax (but using the same brain that may be prone to the same problem, which is where opinions from other people can help).
$ sbcl --script oregon-trail-danger.lisp
2.857143
1.25
0.0872093
And now with a loop we can table the equation. I'm using a custom program to feed LISP from vi(1) to SBCL, hence the up-casing of the code.
SBCL> (LOOP FOR M FROM 0 TO 3000 BY 100
DO (FORMAT T "~&~d ~f~&" M (CALC M)))
0 2.142857
100 2.857143
200 3.75
300 4.6153846
400 5.0
500 4.6153846
600 3.75
700 2.857143
800 2.142857
900 1.6216216
1000 1.25
1100 0.9836066
1200 0.7894737
1300 0.6451613
1400 0.53571427
1500 0.45112783
1600 0.3846154
1700 0.3314917
1800 0.28846154
1900 0.25316456
2000 0.2238806
2100 0.19933555
2200 0.17857143
2300 0.16085792
2400 0.14563107
...
SBCL> (LOOP FOR M FROM 0 TO 1000 BY 50
DO (FORMAT T "~&~d ~f~&" M (CALC M)))
0 2.142857
50 2.4742267
100 2.857143
150 3.2876713
200 3.75
250 4.2105265
300 4.6153846
350 4.897959
400 5.0
450 4.897959
500 4.6153846
550 4.2105265
600 3.75
650 3.2876713
700 2.857143
750 2.4742267
800 2.142857
850 1.8604652
900 1.6216216
950 1.4201183
1000 1.25
NIL
This is a probability distribution curve; other instances of such code would be rnz from NetHack.
https://nethackwiki.com/wiki/Rnz
Enjoy!
Such equations can be built up and fiddled around with until they give roughly the the desired results. Generating an equation on the fly (for example if the distances or danger levels vary depending on the location or other details) would be a bit more work, but not impossible. Players of Oregon Trail may learn of the equation (or intuit it) and might try to move quicker around the 400 mile mark? (The code involves how likely an attack is on any given turn.)