probability - Monty Hall Program Simulation (C#) -
i trying simulate monty hall problem (because read book think statistics guy in particular convinced after seeing computer simulation) in c#, programming language familiar me. scenario such position of prize random (in each run), choice random, , game host's choice of opening door random (it can't random if picked non-prize).
surprisingly though, program achieves result of 50:50 chance of winning no matter whether switch or not. here's code (pardon me lengthiness):
class program { static void main(string[] args) { random rand = new random(); int noswitchwins = rungames(rand, false, 10000); int switchwins = rungames(rand, true, 10000); console.writeline(string.format("if don't switch, win {0} out of 1000 games.", noswitchwins)); console.writeline(string.format("if switch, win {0} out of 1000 games.", switchwins)); console.readline(); } static int rungames(random rand, bool doswitch, int numberofruns) { int counter = 0; (int = 0; < numberofruns; i++) { bool iswin = rungame(rand, doswitch); if (iswin) counter++; } return counter; } static bool rungame(random rand, bool doswitch) { int prize = rand.next(0, 2); int selection = rand.next(0, 2); // available choices list<choice> choices = new list<choice> { new choice(), new choice(), new choice() }; choices[prize].isprize = true; choices[selection].isselected = true; choice selectedchoice = choices[selection]; int randomlydisplayeddoor = rand.next(0, 1); // 1 of choices displayed var choicestodisplay = choices.where(x => !x.isselected && !x.isprize); var displayedchoice = choicestodisplay.elementat(choicestodisplay.count() == 1 ? 0 : randomlydisplayeddoor); choices.remove(displayedchoice); // switch? if (doswitch) { choice initialchoice = choices.where(x => x.isselected).firstordefault(); selectedchoice = choices.where(x => !x.isselected).firstordefault(); selectedchoice.isselected = true; } return selectedchoice.isprize; } } class choice { public bool isprize = false; public bool isselected = false; } this entirely own interest's sake, , wrote in way familiar , comfortable me. feel free offer own opinion , critique, thank much!
rand.next(0,2) only returns 0 or 1; upper bound exclusive. never picking third door (unless switch), , third door never has prize. modelling wrong problem.
try instead:
rand.next(0,3) likewise:
int randomlydisplayeddoor = rand.next(0, 1); only ever selects first of candidate doors; should be:
int randomlydisplayeddoor = rand.next(0, 2); now get:
if don't switch, win 3320 out of 1000 games. if switch, win 6639 out of 1000 games. note - upper bound inclusive when equals - i.e. rand.next(1,1) returns 1.
