Why would you count in 3 year slots? You're saying that it could happen on 1950, but not 1951, and not 1952, but again on 1953?
What if there was La Niña on 1952, 1953 and 1954? Your method does not account for that. Natural events and climate do not adhere to someone's made up "mod 3" date statistics.
Let’s try going from contrary. You said 2 in 72. Imagine a situation when it’s 72 in 72, which means, 72 years straight, each year had a three-year streak. This doesn’t make any sense. Surely the maximum amount of three-year groups in 72 years is far fewer than 72.