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We conjecture that the probability of ties goes to 0 as $n$ grows. We conjecture and provide some supporting evidence that---contrary to intuition---each of the $2^{k \\choose 2}$ assignments of $\\succ$ or $\\prec$ to each pair is equally likely asymptotically. For a specific example, suppose we randomly select $k$ dice $A_1,\\dot"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1311.6511","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-25T23:05:45Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"ff1cb69100355820852139a02e3385c6ce71b306d32da62fd25cd50c1466500a","abstract_canon_sha256":"736a06766971061d0ef66e052347c0419766ba494742e61350393c2c9bdc6071"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:21.965853Z","signature_b64":"nLfp9Mo9TwC2zPgo7h0ScbfJFgftbckdea9e8ISEbgK5tpx/MoxKNUZONQDhC0WN5Ga5SmgmTr+xwfJO03twAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa82648b892622913c289d50a02191c1a1a01636298ca5c4cc31ac5be71b5285","last_reissued_at":"2026-05-18T01:11:21.965337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:21.965337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intransitive Dice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Andrew Liu, Brian Conrey, James Gabbard, Katie Grant, Kent Morrison","submitted_at":"2013-11-25T23:05:45Z","abstract_excerpt":"We consider $n$-sided dice whose face values lie between $1$ and $n$ and whose faces sum to $n(n+1)/2$. 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