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A sure day for a double whammy?
Bad news squared?
Here, we throw light on two interesting facts.
Worried about planning something on an 'unlucky' Friday the 13th that also happens to be Butsumetsu? Don't worry; it only happens on the rare occasions when the cosmos feels mischievous, as you can see in the Butsumetsu days on Friday the 13th table below.
Intuitively, since there are six Rokuyō days, you might think there's a 1 in 6 chance that a Friday the 13th will be Butsumetsu. But in fact, the chances are much lower than that.
Why is the probability of the two unfavourable days colliding so low? And exactly how low?
Determining the exact mathematical probability of a specific Gregorian calendar date (like a Friday the 13th) also falling on a specific day of the Rokuyō calendar (like Butsumetsu) is difficult. It's not a simple calculation, since the two calendar systems are not synchronized.
Because the patterns of the two calendars don't align in a simple, repeating manner, a precise mathematical probability would require a complex analysis over a very long period, such as the full 400-year Gregorian cycle.
But since our Rokuyō database knows the weekday and date of every Rokuyō day, we've run a search and found that over those 200 years there are only 58 times where Butsumetsu falls on a Friday the 13th.
Knowing that the value 58 represents the frequency of this event, and knowing the number of days in those 200 years, we can easily calculate the probability as follows.
Given that (1) a normal (non-leap) year has 365 days, (2) a leap year has 366 days, and (3) a leap year is a year divisible by 4, except years divisible by 100 unless divisible by 400, the number of non-leap and leap years from 1900 to 2099 is:
Number of days from 1900 to 2099
Number of Friday 13th Butsumetsu days = 58
Probability 𝑃(Friday 13th Butsumetsu) =
| number of such days | 58 | ||
| = | ≈ 0.000794 | ||
| total days | 73,050 |
So the probability of any day in 1900–2099 being a Friday 13th Butsumetsu day is less than 0.08%, i.e., roughly once every three and a half years.
As the list below shows, Friday the 13th occurs on Butsumetsu multiple times in some years and doesn't occur at all in other years - sometimes for more than a decade.
Fact #1 = the double-trouble day is not a 1 in 6 chance, it's a 1 in 1,259 chance!
History confirms; there's been no apocalyptical calamity on any past Friday the 13th Butsumetsu.
The cyclical nature refers to the fact that the pattern of days, dates and leap years repeats every 400 years in the Gregorian calendar.
That's because:
This leap year rule creates a 400-year cycle.
After 400 years, the dates of the week, months and leap years line up exactly the same as they did at the start of the cycle.
That means Friday the 13ths repeat in exactly the same sequence every 400 years.
See Rokuyō explained