Etydhv

I have the following template for a journal article featuring a basic table:

The code looks something like this:

documentclass[jou,apacite]apa6
usepackage[utf8]inputenc
usepackageamsmath 

titleTitle of the article
authorAuthor Name
affiliationAffiliation

abstractThis is the abstract.

begindocument

 maketitle 
 sectionThis is the heading for the first section of the article.
 Lorem ipsum.

 Results are presented in Table~reftab1.

 begintable[!htb]
 captionSample table.labeltab1
 begintabularccc
 hline\[-1.5ex]
 AAA & BBB & CCC \[0.5ex]
 hline\[-1.5ex]
 1.0 & 2.0 & 3.0\[0.5ex]
 1.0 & 2.0 & 3.0\[0.5ex]
 hline
 endtabular
 endtable

 sectionThis is the heading for the second section of the article.
 Lorem ipsum.

enddocument

What I want to know is:
Rather than typing in every value of a table manually, and potentially mistyping a digit or a decimal point here or there; is LaTeX capable of evaluating the math for me?

Consider the odds or probability of a coin toss winning streak, for example:

Each flip has 50:50 (1:1) odds:
50% probability of winning
50% probability of losing

The odds of winning two consecutive flips are 75:25 (3:1):

25% probability of winning
75% probability of losing

The odds of
winning three consecutive flips are 87.5:12.5 (7:1):

12.5% probability of winning

87.5% probability of losing

The odds of winning four consecutive flips are 93.75/6.25 (15:1):

6.25% probability of winning

93.75% probability of losing

..and so on.

Probability of winning n consecutive flips is 2^(-n) * 100.

Probability of not winning n consecutive flips is 100 - (2^(-n))
* 100

Of course I could just calculate each value and type in every cell manually, but I might want to show ten or more flips. Anyway, is this something LaTeX can do?

Here's a LuaLaTeX-based solution to the problem of printing a table of run probabilities -- if the underlying experiment is tossing a "fair" coin.

% !TEX TS-program = lualatex
documentclass[jou,apacite]apa6
usepackageamsmath,booktabs,lipsum 
letPrrelax % undefine "Pr"
DeclareMathOperatorPrPr

usepackageunicode-math % choose suitable math and text fonts
setmainfontStix Two Text[Ligatures=TeX,Common]
setmathfontStix Two Math

titleTitle of the article
shorttitleTitle
authorAuthor Name
affiliationAffiliation
abstractThis is the abstract.

usepackageluacode
beginluacode

function run_prob ( j )
 return (0.5)^j
end
function printrows ( n )
 for i=1,n do
 runprob = 100*run_prob(i)
 runprobcomp = 100-runprob 
 tex.sprint ( i .. "&" .. runprob .. "&" .. runprobcomp .. "\\" )
 end
end

endluacode

begindocument
maketitle 

sectionIn the beginning
Lorem ipsum.

Results are presented in Table~reftab1.

begintable[!htb]
captionFair coin tosses: Probabilities of runs of length $n$, in percent.labeltab1

$beginarray@lll@
toprule
n & Pr(textRun) & 100-Pr(textRun)\
midrule
%% Invoke the 'printrows' Lua function:
directluaprintrows(12)
bottomrule
endarray$
endtable

lipsum[1-3]
enddocument