How to Answer Questions of the Type: If you toss a coin n times, how likely is HH to show up more than HT?

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Ekhad, Shalosh B., Zeilberger, Doron
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911884673810432
author Ekhad, Shalosh B.
Zeilberger, Doron
author_facet Ekhad, Shalosh B.
Zeilberger, Doron
contents On March 16, 2024, Daniel Litt, in an X-post, proposed the following brainteaser: "Flip a fair coin 100 times. It gives a sequence of heads (H) and tails (T). For each HH in the sequence of flips, Alice gets a point; for each HT, Bob does, so e.g. for the sequence THHHT Alice gets 2 points and Bob gets 1 point. Who is most likely to win?" We show the power of symbolic computation, in particular the (continuous) Almkvist-Zeilberger algorithm, to answer this, and far more general, questions of this kind.
format Preprint
id arxiv_https___arxiv_org_abs_2405_13561
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle How to Answer Questions of the Type: If you toss a coin n times, how likely is HH to show up more than HT?
Ekhad, Shalosh B.
Zeilberger, Doron
Combinatorics
Probability
On March 16, 2024, Daniel Litt, in an X-post, proposed the following brainteaser: "Flip a fair coin 100 times. It gives a sequence of heads (H) and tails (T). For each HH in the sequence of flips, Alice gets a point; for each HT, Bob does, so e.g. for the sequence THHHT Alice gets 2 points and Bob gets 1 point. Who is most likely to win?" We show the power of symbolic computation, in particular the (continuous) Almkvist-Zeilberger algorithm, to answer this, and far more general, questions of this kind.
title How to Answer Questions of the Type: If you toss a coin n times, how likely is HH to show up more than HT?
topic Combinatorics
Probability
url https://arxiv.org/abs/2405.13561