&quot;1&#x2F;3 of the times I am awakened&quot; never happens though.  You&#x27;re either awakened once or twice, not 3 or 6 or infinite times.  I think the thirders get stuck on this &quot;if we do it infinite times&quot; or &quot;in the limit case&quot; thing, which is different from doing a single coin flip. <a href="http:&#x2F;&#x2F;stats.stackexchange.com&#x2F;a&#x2F;169582&#x2F;87304" rel="nofollow">http:&#x2F;&#x2F;stats.stackexchange.com&#x2F;a&#x2F;169582&#x2F;87304</a>