A whole draw, folded onto one line.

A one-to-one coordinate

For sorted one-based values $a_1,\ldots,a_k$, the colex rank is

$R=\sum_{i=1}^{k}\binom{a_i-1}{i},$

from $0$ to $\binom{N}{k}-1$. Plotting $(R+1/2)/\binom{N}{k}$ gives one open-unit-interval coordinate per draw. Permutation entropy reads ordinal patterns of three consecutive ranks.

A map, not a lucky ordering

No rank is luckier than another, and another valid ordering would redraw the river. Its use is compression with a proof of one-to-one correspondence, exposing serial structure in complete draws without choosing “interesting” features first.