PREDICTING THE NUMBER OF PARTICIPANTS

It is said that the most recent common ancestor of every European today lived around 1400. In other words, every European has a great, great, ... grandparent in common, and that man or woman was alive in the year 1400. To phrase it differently again, I am a direct descendant of Charlemagne, of William the Conqueror, of Constantine and Caesar (and so are you). The mind boggles, but let's focus here on what really matters: what impact will this have on the Bunny Cup? Let me paint a picture:

To start, we'll say every Bunny Cup participant from the ages of 6 to 80 (sorry Grandad). Then that everyone has a child at 30, and a 60% chance of another at 32. This simple model let's us see how the Cup will grow.

YEAR	PARTICIPANTS
2022	10
2023	10
2024	9
2025	9
2030	9
2040	14
2050	15
2075	30
2150	86
2200	215
2250	341
2300	1010
2400	4059
2500	14783

Yet such a method is slow and laborious. A family grows like a virus spreads: exponentially (i.e., growing by mulitiplying by X, rather than adding X). Accordingly, our model above can be exponentially modelled itself: number of participants = 0.0000000000011286*2.7183^(0.0149*year). The number of participants will double every 50 years, quadrupling every century, and getting about a million times larger every millenium.

The Dodgy Bit

Here's the thing: if Charlemagne – who lived 1200 years (or 40 generations) ago – had two children, who each had two children, ..., he should have 1,099,511,627,776 living descendants. He does not ^{[citation needed]}. There is no elegant way to explain why: people had children with their (hopefully distant) cousins, something our model doesn't factor in. When that assumption becomes untenable, the model falls apart and hence – sadly? – there won't be 86,399,240,400,000 participants by the year 4000 (and I might actually be able to win one).

To conclude: let's hope this model is right.