Four 4D myths, tested properly.

Every 4-digit number has the same 1-in-10,000 chance, so a family of numbers should take exactly the share of draws its size entitles it to. This counts every prize slot ever published by every operator — 715,271 of them — and checks each family against that share.

Quads, triples, two-pairs, one-pairs and all-different are mutually exclusive and add to exactly 10,000, which is why they can be tested together in one goodness-of-fit. ABBA, AABB and ABAB all sit inside the two-pair shape (90 × 3 = 270) and are listed separately only because players name them separately. Each family gets a two-sided binomial test with a continuity correction.

The classic operators draw on Sunday, Wednesday and Saturday, plus the extra special draws the Ministry of Finance approves — historically almost always a Tuesday. Each group's numbers are compared with the others', digit by digit and by digit shape.

1,411 special-draw dates were identified in the archive by weekday. The curated 2026 special-draw list covers 6 of them, because that list only carries the current year — deriving the group from the weekday rather than from the list is what lets this test reach back to 1985.

Grand Dragon, 9 Lotto and Lucky Hari Hari draw seven nights a week and are excluded entirely; pooling them would compare draw schedules instead of numbers. One honest wrinkle: the special-draw group also contains Magnum's and Sports Toto's pre-1995 Monday and Thursday schedule, so it mixes eras as well as days.

Every slot on a board comes out of the same machine on the same night, so a 1st prize's ending digit and digit shape should be indistinguishable from a consolation number's. Both are compared across all five tiers.

The tiers have very different sample sizes — three slots a night against twenty — which chi-square handles, but it does mean the two big tiers dominate the total. Numbers within one board are also drawn without replacement, a dependency of roughly 23 in 10,000 that is far too small to matter here and errs on the conservative side.

Each operator's top-three numbers are broken into digits and the operators are set against each other. The test runs twice: once across every operator with enough history, and once across Magnum, Sports Toto and Da Ma Cai alone — the longest and most heavily regulated archives, and the three the myth actually names.

This is the test most exposed to sample size. Magnum's archive starts in 1985 and Grand Dragon's in 2020, and chi-square grows with the number of observations, so a longer history produces a smaller p for exactly the same sized difference. That is why every row also carries the largest gap between an operator's digit share and a flat 10% — a plain-percentage-point measure that does not move when you add more years.