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4 claims

The constant c(n) attached to the coin-flipping game (its exact values, e.g. c(k^2) = 1/k, and its asymptotic behavior, e.g. sqrt(n)·c(n) -> 1 as n -> infinity). Claims defining, computing, or bounding this constant belong here; claims about unrelated games' constants or general probability theory do not.

For all n, the coin-game constant satisfies c(n) ≥ 1/f(n), where f is the square-packing constant.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · verifiableA factual claim that could be checked directly against observation or primary records.constitution →Square packing constant Discrete geometryimportance · minorImportance 0.25, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

The coin-game constant satisfies c(k^2) = 1/k, and √n·c(n) → 1 as n → ∞.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · verifiableA factual claim that could be checked directly against observation or primary records.constitution →Mathematicsimportance · minorImportance 0.35, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

The constant c satisfies c(n) ≥ (1/√2 − o(1))/√n.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · verifiableA factual claim that could be checked directly against observation or primary records.constitution →Combinatoricsimportance · minorImportance 0.25, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

The constant c satisfies the upper bound c(k^2) ≤ 1/k.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · verifiableA factual claim that could be checked directly against observation or primary records.constitution →Mathematicsimportance · minorImportance 0.25, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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