 If B = W then those players wearing black hats see B−1 black hats and B white hats, so wait B−1 seconds then correctly guess that they are wearing a black hat.
<meaning-changed>  If B = W then those players wearing black hats see B−1 black hats and B white hats, so wait B−1 seconds then correctly guess that they are wearing a black hat.
 If B = W then those players wearing blue hats see B−1 black hats and B white hats, so wait B−1 seconds then correctly guess that they are wearing a black hat.