There is a certain group of people whom you can honestly take with the following suggestion "Go off and gather any set of numerical information about the World - populations of counties or countries; lengths of rivers; chemical molecular weights; street numbers of homes. You give me €1 for every such number that begins with a 1, 2 or 3; I'll give you €1 for every number that begins with 4,5,6,7,8 or 9". Don't do this with 5 year old children unless you also mug pensioners outside the post-office. Try maths students, who will have sufficiently well-polished crap-detectors to smell a rat, but nevertheless may be gullible enough and greedy enough to think you've lost your marbles. The uneven distribution of these first digits is known as Benford's Law of Anomalous Numbers because it caused a stir when Frank Benford published the idea in 1938. Simon Newcomb (Canadian-American astronomer, applied mathematician and autodidactic polymath!!) had pointed out one example of the Law in 1881 - as it applied to logarithms. He was induced to investigate the phenomenon because he'd noted that the earlier pages of his book of logarithm tables were more 'worn' than the later ones. Here 'worn' means grubby, dark and impregnated with sweat, sebum and a host of supported bacteria <eeeuw!>.
Benford built on Newcomb's finding and looked at a wide range of numerical data and found that many of them fit a distribution approximated by
P(D) = log (1 + 1/D)English words [the, of, and and are super common] and to letter frequencies: in English the commonest are etaoinshrdl[u|c] - jury is out on c and u.
Another distribution that follows a not Newcomb / Benford / Zipf distribution is birth-dates. They are uniformly distributed through the year and there is no evidence or suggestion that more people are born on the 1st of the month more than the 9th or the 31st. So it would require an exceptional dense and ill-informed person to take you up on your 1-3 vs 4-9 offer - that are no birth-dates that begin with 4-9! I used births - of "you and all your family and significant others" to have my Yr2 Quantitative Methods class to generate a 'flat' distribution that was clearly not Normal / Gaussian / Bell-shaped. There are some subtleties in the pattern of birthdays through the year which I've investigated before.
Funnily enough, although it is so widely distributed, for a long time there wasn't really a good explanation or proof of Benford's Law. 60 years after his 1938 paper, TP Hall published a neat explanation in American Scientist - which is behind a Sigma Xi paywall. Some of that is abstracted in a blog-post by Laura McLay and check out the comments of her post too, there's an interesting twist.