This may be true in theory, but in practice most miners are part of a mining
pool. Therefore they participate in the block reward every time that someone
from their pool "gets lucky" and manages to claim the block reward.

In the long-run this smoothes out the mining income and enables mining
on a more industrial scale. Of course there is still the possibility of mining
less than your expected share for a long time, but still taking part in a mining
pool reduces the variance inherent to a system that was designed as a
winner takes all system.

I wonder how Bitcoin would have turned out if we had never seen the emergence
of mining pools. The hashrate would probably be lower, because higher variance
would have made long-term planning and therefore industrial mining much more
difficult.