This isn't a web app, but if you know your way around programming, I have a Racket script that does this. It looks like this when you use it (from the command line):

~ λ demon
Out of the blasted gates of hell spawns a demon -- the demon of epistemology. It thunders, I HAVE BEEN SUMMONED. WHAT PROPOSITION DO YOU PONDER? REMEMBER, I KNOW THE TRUTH OR FALSITY OF ALL THINGS.
> the european union will exist in year 2100

CHOOSE ONE --
[1] IF THE EUROPEAN UNION WILL EXIST IN YEAR 2100, I BESTOW ON YOU A BEAUTIFUL PALACE OF UNIMAGINABLE RICHES. IF NOT, YOU GET NOTHING.
[2] IF MY 1d10 DIE ROLLS A 5 OR LOWER [=====-----], I BESTOW ON YOU A BEAUTIFUL PALACE OF UNIMAGINABLE RICHES. IF IT ROLLS HIGHER, YOU GET NOTHING.
[3] YOU ARE UNSURE.
> 1

CHOOSE ONE --
[1] IF THE EUROPEAN UNION WILL EXIST IN YEAR 2100, I BESTOW ON YOU A BEAUTIFUL PALACE OF UNIMAGINABLE RICHES. IF NOT, YOU GET NOTHING.
[2] IF MY 1d10 DIE ROLLS A 7 OR LOWER [=======---], I BESTOW ON YOU A BEAUTIFUL PALACE OF UNIMAGINABLE RICHES. IF IT ROLLS HIGHER, YOU GET NOTHING.
[3] YOU ARE UNSURE.
> 1

CHOOSE ONE --
[1] IF THE EUROPEAN UNION WILL EXIST IN YEAR 2100, I BESTOW ON YOU A BEAUTIFUL PALACE OF UNIMAGINABLE RICHES. IF NOT, YOU GET NOTHING.
[2] IF MY 1d10 DIE ROLLS A 8 OR LOWER [========--], I BESTOW ON YOU A BEAUTIFUL PALACE OF UNIMAGINABLE RICHES. IF IT ROLLS HIGHER, YOU GET NOTHING.
[3] YOU ARE UNSURE.
> 2
VERY WELL, the demon sighs. YOUR CREDENCE THAT THE EUROPEAN UNION WILL EXIST IN YEAR 2100 IS 75%.

Source code:

#! /usr/local/bin/racket
#lang cli

(require racket/list)
(require racket/string)

(help (usage "Figure out how certain you are that something is true using the equivalent bet test."))

(program (demon)
         (displayln (string-append "Out of the blasted gates of hell spawns a demon -- the demon of epistemology. It "
                                   "thunders, I HAVE BEEN SUMMONED. WHAT PROPOSITION DO YOU PONDER? REMEMBER, I KNOW "
                                   "THE TRUTH OR FALSITY OF ALL THINGS."))
         (display "> ")
         (letrec ((lower-bound 0)
                  (upper-bound 10)
                  (prop (read-line))
                  ;; TODO: use regexes here to match i at beginning. also fix me, we, us
                  (prop-upper (string-replace (string-upcase prop) " I " " YOU "))
                  (consequent "I BESTOW ON YOU A BEAUTIFUL PALACE OF UNIMAGINABLE RICHES")
                  (visualize-prob (lambda (n)
                                    (string-append "["
                                                   (string-join (make-list n "=") "")
                                                   (string-join (make-list (- 10 n) "-") "")
                                                   "]")))
                  (run (lambda (min max)
                         (if (<= (- max min) 1)
                           (/ (+ max min) 2)
                           (let ((n (case '(min max)
                                        ['(lower-bound upper-bound) 5]
                                        ['(lower-bound 5) 1]
                                        ['(5 upper-bound) 9]
                                        [else (quotient (+ min max) 2)])))
                             (begin
                               (displayln
                                (string-append
                                 "\nCHOOSE ONE --\n"
                                 "[1] IF " prop-upper ", " consequent ". IF NOT, YOU GET NOTHING.\n"
                                 "[2] IF MY 1d10 DIE ROLLS A " (number->string n) " OR LOWER " (visualize-prob n) ", "
                                 consequent ". IF IT ROLLS HIGHER, YOU GET NOTHING.\n"
                                 "[3] YOU ARE UNSURE."))
                               (display "> ")
                               (case (read-line)
                                 [("1") (run n max)]
                                 [("2") (run min n)]
                                 [("3") n]
                                 [else (run min max)])))))))
           (let ((percentage (* (/ 100 upper-bound) (run lower-bound upper-bound))))
             (displayln
              (string-append "VERY WELL, the demon sighs. "
                             "YOUR CREDENCE THAT " prop-upper " IS " (number->string percentage) "%.")))))

(run demon)