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A simulated game of chess is programmed between two computers. The game is supposed to be biased in favor of player B winning 4 out of 5 times. Which is the most suspicious set of outcomes of 30 games played between the two computers?

A.

AABABBBABBBBBBBBABBBABBBBBBBBA

B.

ABBABBAABBBBBABBBBBBBBBBBBBABB

C.

ABBABABABABBABABABABABABABABAA

D.

 ABBABBBABBBBBBBBABBBABBBBBBBBB

 Nov 9, 2018
 #1
avatar+601 
-1

Let's see all of them.

 

It seems like for all of them B overpowers, except for C.

A, B, D have mostly B's but C has a general mix, therefore, the answer is C.

 

You are very welcome!

:P

 Nov 9, 2018
 #2
avatar+4471 
+2

CoolStuffYT is correct but here's a more rigorous analysis

 

 Nov 9, 2018
 #3
avatar+27566 
+2

A slightly simpler way of looking at this is to note that the expected number of games won by B is (4/5)*30 = 24.

 

Number of games apparently won by B: 

A:   23

B:   24

C:  15

D:  25

 

Clearly C is suspicious!

 Nov 9, 2018

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