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A proof that HT is more likely to outnumber HH than vice versa in a sequence of n coin flips
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A proof that HT is more likely to outnumber HH than vice versa in a sequence of n coin flips
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Consider the following probability puzzle: A fair coin is flipped n times. For each HT in the resulting sequence, Bob gets a point, and for each HH Alice gets a point. Who is more likely to win? We provide a proof that Bob wins more often for every n>=3. As a byproduct, we derive the asymptotic form of the difference in win probabilities, and obtain an efficient algorithms for their calculation.
Forward citations
Cited by 2 Pith papers
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On Two Combinatorial Inequalities That Explain the Blimpy Shape of Heady-s and Taily-s Bit Strings
Generating-function proofs establish two binomial expectation inequalities that imply unimodality near zero and positive/negative asymmetry for heady-s bit-string score counts.
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Moments for generalizations of a coin flip game
Derives recursive and closed formulas for moments of waiting times for prescribed words in coin flips and die rolls using one-parameter Eulerian number extensions, Goulden-Jackson cluster method, and Faà di Bruno's formula.
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