Abstract / résumé
Name / nom: Eric Hart
School / école: Queen's University at Kingston
Length / durée: 25 min
Title / titre: An Unanswered Coin-toss Problem and Solutions Using the Catalan Numbers
Abstract / résumé:
An interesting problem that has been asked with yet no definitive answer
takes the form of a game: the player of the game is allowed to flip a coin
as many times as he/she wants. After stopping, the player will be paid in
dollars, the total number of heads divided by the total number of flips of
the coin. The question posed is "What is the best strategy for the player
to use in order to maximize his/her expected payout?" The question also
comes with a possible answer attached to it. The strategy suggested is to
play until one more head has been tossed than tails, and then to stop. In
other words, the player should wait until the amount of money being won is
greater then 50 cents, then take what he/she has.
In order to determine the actual expected payout of this strategy, a
sequence of numbers known as the Catalan numbers must be defined. These
numbers show up repeatedly in probability type questions, and some
applications will be discussed in this presentation. Furthermore, we will explore how these numbers allow for the expected
value of the given
solution to be obtained, and also discuss their shortcomings in solving for expected
values in other solutions. Finally some other solutions to the original
problem will be discussed which need to be solved numerically, but can
have larger expected payouts.
Prerequisites / choses nécessaires: None listed.
PDF format / format PDF: hart.pdf