Answer
You draw to 21 about 5.5% of the time (including doubles). You get a natural 21 4.75% of the time. Together, you get a 21 just over 10% of the time (10.25%). (See BJA3, p. 50.)
To get four 21s in a row, for any designated four consecutive hands, is, therefore, .1025^4 = one chance in 9,066.
As with all such calculations, the event becomes much less rare when you play thousands upon thousands of hands, including thousands of such four-hand streaks. Sooner or later, you see just about everything.
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