Bad beat with 5 AK & 7 AA in 12 hours (offline)

Offline session. Over 12 hours of play (Texas Hold'em) - approximately 300 hands - I received the pair KK 5 times and the pair AA 7 times.
I lost 4 times with KK to random hands, and once I won, going all-in against AA but hitting a set.
Out of 7 AA, I lost 6 times to random hands, and once l ended in a tie, facing another AA.

Al's opinion - verbatim quote:

"Let's calculate the probability of your specific series of events over 300 hands and estimate how many such sessions you'd need to play to encounter something like this at least once. This will be an interesting mathematical challenge, as we have 12 specific outcomes with KK and AA within 300 hands. Since the exact hands of your opponents and the boards are unknown, we'll use reasonable approximations...
1. The probability is approximately 3.68 * 10^-16
(extremely small).

2. Sessions - 2.72 * 10^15 sessions of 300 hands, or roughly 3.73 * 10^12 years of continuous play (3.7 trillion years).

This is such a rare combination of events that the age of the universe (13.8 billion years) is just a speck compared to it.

You 'got lucky' stumbling into a unique anomaly."

What was that?