#| 

  Always take the middle taxi in Racket/Gamble 

  From 
  https://www.janestreet.com/static/pdfs/real-numbers/RN_PDF_02.pdf
  """
  In the busy city center of Metropolis, exactly half of the cars are yellow taxis. You are
  trying to catch a taxi with your friend, who is superstitious and will only ride in a taxi that
  is both directly behind another taxi and directly in front of another taxi. If a stoplight in
  Metropolis has six cars stopped at it, and each car is a taxi independently with probability
  1/2, what is the probability that there are three yellow taxis in a row at the traffic light?
  """

  Via Pascal Bercker: "Jane Street — Problem Of The Week #2 — Take the Taxi in the Middle"
  https://medium.com/@pbercker/jane-street-problem-of-the-week-2-take-the-taxi-in-the-middle-fb5cf988cb84


variable : cars
(0 0 0 0 1 1): 1/64 (0.015625)
(1 1 1 1 0 1): 1/64 (0.015625)
(1 0 1 1 0 1): 1/64 (0.015625)
(1 1 0 1 1 0): 1/64 (0.015625)
(1 0 1 1 1 1): 1/64 (0.015625)
...
(0 0 1 0 0 1): 1/64 (0.015625)
(0 0 0 1 1 1): 1/64 (0.015625)
(0 1 1 1 0 1): 1/64 (0.015625)
(1 0 0 0 0 0): 1/64 (0.015625)
(0 1 1 1 0 0): 1/64 (0.015625)

variable : s
0: 11/16 (0.6875)
1: 3/16 (0.1875)
2: 5/64 (0.078125)
3: 1/32 (0.03125)
4: 1/64 (0.015625)
mean: 1/2 (0.5)

variable : p
#f: 11/16 (0.6875)
#t: 5/16 (0.3125)
mean: 5/16 (0.3125)

variable : p2
#f: 13/16 (0.8125)
#t: 3/16 (0.1875)
mean: 3/16 (0.1875)



  Cf my Picat PPL model ppl_always_take_the_middle_taxi.pi

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Racket page: http://www.hakank.org/racket/

|#

#lang gamble

; (require gamble/viz)
(require racket)
(require "gamble_utils.rkt")
; (require "gamble_distributions.rkt")


(define (model)
  (enumerate
   ; rejection-sampler
   ; importance-sampler
   ; mh-sampler

   (define n 6)
   (define taxip 1/2)

   (define cars (for/list ([i n]) (bernoulli taxip)))

   (define s (count-occurrences-sublist '(1 1 1) cars))
   (define p (> s 0))  ; at least 1 occurrence of three taxis in a row
   (define p2 (= s 1)) ; exactly 1 occurrence of three taxis in a row
   (list cars
         s
         p
         p2)

   )
)

(show-marginals (model)
                (list  "cars"
                       "s"
                       "p"
                       "p2"
                     )
                    #:num-samples 1000
                    #:truncate-output 5
                    ; #:skip-marginals? #t
                    ; #:show-stats? #t
                    ; #:credible-interval 0.84
                    ; #:hpd-interval (list 0.84)
                    ; #:show-histogram? #t
                    ; #:show-percentiles? #t
                    ; #:burn 0
                    ; #:thin 0
                    )