Ttyjukl

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}

usepackage{amsmath}       



title{Title of the article}

author{Author Name}

affiliation{Affiliation}



abstract{This is the abstract.}



begin{document}



    maketitle    

    section{This is the heading for the first section of the article.}

        Lorem ipsum.



        Results are presented in Table~ref{tab1}.



        begin{table}[!htb]

            caption{Sample table.}label{tab1}

            begin{tabular}{ccc}

                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

            end{tabular}

        end{table}



    section{This is the heading for the second section of the article.}

        Lorem ipsum.



end{document}

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}

usepackage{amsmath,booktabs,lipsum}  

letPrrelax % undefine "Pr"

DeclareMathOperator{Pr}{Pr}



usepackage{unicode-math} % choose suitable math and text fonts

setmainfont{Stix Two Text}[Ligatures={TeX,Common}]

setmathfont{Stix Two Math}



title{Title of the article}

shorttitle{Title}

author{Author Name}

affiliation{Affiliation}

abstract{This is the abstract.}



usepackage{luacode}

begin{luacode}

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

end{luacode}



begin{document}

maketitle    



section{In the beginning}

Lorem ipsum.



Results are presented in Table~ref{tab1}.



begin{table}[!htb]

caption{Fair coin tosses: Probabilities of runs of length $n$, in percent.}label{tab1}



$begin{array}{@{}lll@{}}

toprule

n & Pr(text{Run}) & 100-Pr(text{Run})\

midrule

%% Invoke the 'printrows' Lua function:

directlua{printrows(12)}

bottomrule

end{array}$

end{table}



lipsum[1-3]

end{document}