Peters_Coin-Toss_Time Average+Ensemble Average_Ergodicity-Break.nb

simulateCasinoGame[g_, t_] := 
 Module[{money, coinToss, plotData, timeAverage, ensembleAverage, 
   gamblerPlot, averagePlot},(*Initial money for each g*)
  money = Table[100, {g}];
  (*canino game*)
  plotData = 
   Table[(*gia kathe gambler*)
    coinToss = RandomChoice[{0.5, 0.5} -> {1.5, 0.6}, g];
    money = money*coinToss;
    money, {t}];
  (*plot gia kathe gambler's money me basi to time*)
  gamblerPlot = 
   ListLinePlot[Transpose[plotData], 
    AxesLabel -> {"Number of Tosses", "Money"}, PlotRange -> All, 
    Frame -> True];
  timeAverage = Mean /@ plotData;(*mesos oros gia kathe periodo*)
  ensembleAverage = 0.5*1.5 + 0.5*0.6;(*Plot time-avg kai ensemble-
  avg*)averagePlot = 
   ListLinePlot[{timeAverage, 
     ConstantArray[ensembleAverage*100, Length[plotData]]}, 
    Frame -> True, 
    AxesLabel -> {"Number of Tosses", "Average Return (%)"}, 
    PlotLegends -> {"Time Average", "Ensemble Average"}];
  (*ta results*){gamblerPlot, averagePlot, timeAverage, 
   ensembleAverage}]


simulateCasinoGame[100, 1000]