Pith Number

pith:YTH6CP53

pith:2026:YTH6CP5343NZOXKXDOH7I455IX

not attested not anchored not stored refs pending

First server's effect on the expected number of games in tennis

Ali Mohammadi

Knowing who serves first changes the expected number of games in a tennis match by at most one.

arxiv:2605.04867 v2 · 2026-05-06 · math.PR

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\usepackage{pith}
\pithnumber{YTH6CP5343NZOXKXDOH7I455IX}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We show that information on the first server influences the expected total number of games and margin in a tennis match under the standard assumption that each player's serve point win probability remains constant, and identify the exact regions, in terms of these probabilities, in which this effect is non-negligible. We confirm numerically that this effect is bounded by at most one game at both the set and match level.

C2weakest assumption

each player's serve point win probability remains constant

C3one line summary

Knowing who serves first changes the expected number of games in a tennis match by at most one game when serve win probabilities are constant.

Receipt and verification

First computed	2026-06-03T02:05:48.183339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4cfe13fbbe6db975d571b8ff473bd45ef74e553f8055f28bb281899376a95d3

Aliases

arxiv: 2605.04867 · arxiv_version: 2605.04867v2 · doi: 10.48550/arxiv.2605.04867 · pith_short_12: YTH6CP5343NZ · pith_short_16: YTH6CP5343NZOXKX · pith_short_8: YTH6CP53

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YTH6CP5343NZOXKXDOH7I455IX \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c4cfe13fbbe6db975d571b8ff473bd45ef74e553f8055f28bb281899376a95d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4f1d43b313de6a1e57630d8f60fe2138786afe8071cd2bf1cab00c56d687f1f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-06T13:00:52Z",
    "title_canon_sha256": "8ae9df647f197c00433297db7c26081ae80fce7f661de99ba4bb98c323617823"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04867",
    "kind": "arxiv",
    "version": 2
  }
}