> other=: 2 1 2 0 1 0 _1 {~ (_2]\0 1 0 2 1 0 1 2 2 0 2 1) i. ,.
One of the requirements for simulation is that
it is clear and convincing.
The choice of the lookup for other is not clear.
Because of that, it is not clear if it does
not contain a reduction either (a codified sample space).
--- Roger Hui <[EMAIL PROTECTED]> wrote:
> The object of the game is to win a car.
>
> Two goats and a car are hidden behind 3 doors, one
> item per door. You choose a door. The gamemaster
> (Monty Hall), who knows what's behind the doors,
> opens one of the other doors, revealing a goat, and
> offers you the opportunity to change your choice of
> doors. Your chosen door is then opened and you get
> what is behind.
>
> Should you stick or switch?
>
> Many people get this wrong, including people with
> Ph.D. degrees in mathematics and statistics, and
> including Paul Erdos as recounded in chapter 6 of
> Paul Hoffman's "The Man Who Loved Only Numbers".
>
> The present task is to write two simulation
> programs, one for the strategy of sticking with
> the original choice and another for the strategy
> of switching. The argument is the number of
> simulations of the game; the result is the number
> of cars won.
>
> Spoiler alert: Solution below.
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> stick=: 3 : 0
> c=. y [EMAIL PROTECTED] 3 NB. where the car is hidden
> i=. y [EMAIL PROTECTED] 3 NB. your choice of door
> c +/@:= i NB. number of cars that you win
> )
>
> switch=: 3 : 0
> c =. y [EMAIL PROTECTED] 3 NB. where the car is hidden
> i =. y [EMAIL PROTECTED] 3 NB. your choice of door
> h0=. ((_2]\0 1 0 2 1 0 1 2 2 0 2 1) i. c,.i){2 1 2 0 1 0 _1
> h1=. (y [EMAIL PROTECTED] 2){"_1 i{_2]\1 2 0 2 0 1
> h =. (c=i)}h0,:h1 NB. Monty Hall opens this door
> j =. ((_2]\0 1 0 2 1 0 1 2 2 0 2 1) i. h,.i){2 1 2 0 1 0 _1 NB. your
> switched choice
> c +/@:= j NB. number of cars that you win
> )
>
> NB. h0: Monty Hall's choice if a goat is behind your door
> NB. h1: Monty Hall's choice if a car is behind your door
>
> stick 1e6
> 333143
> stick 1e6
> 332564
>
> switch 1e6
> 666771
> switch 1e6
> 665859
>
>
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
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