Two agents play a game in which each agent needs to name a number between 0 and 9 and they win if their numbers add up to 13. The first player knows this, and he knows that the second player gets to see the number the first player chooses, but the second player mistakenly thinks that the two win if their numbers add up to any number greater than 8 (and the first player knows this as well). What number should the first player choose?
(define (sample)
(rejection-query
(define a (sample-integer 10))
(define b
(rejection-query
(define c (sample-integer 10))
c
(> (+ a c) 8)))
a
(= (+ a b) 13)))
(hist (repeat 1000 sample))
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