Two Pairs

Poker’s two pair, dealt into digits.

Four or more digits, with exactly two digit values appearing twice each and the rest once — counted as a global multiset, adjacency not required: 1122, 1212 and 721174 all qualify; 112233 (three pairs) and 1112 (a triple) do not.

214,083
Exact matches
1 in 5
Odds
21.41%
Share
44 EP
Base EP

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There are 214,083 of them, 21.4% — one in five rolls, a commoner among structural features. But note its strictness: one pair too many (three pairs) or one digit too many (a triple) disqualifies it; exactly two pairs, everything else singleton.

The poker name and verdict make it the most approachable structural feature: read the number like a hand of cards. The interleaved form 1212 is also Periodic and Balanced — the family’s most beloved shape.

The global multiset rule is its soul: pairs need not touch. In 721174 the 7s and 1s each appear twice, answering each other across the whole number — not obvious at a glance, but the combinatorics says yes.

Smallest examples

Notable examples

1,212 The family star: interleaved pairs that also hit Periodic, Balanced, Two Symbols and Alternating Parity.
1,001 The smallest two-pair number — also a palindrome.

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