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==A coin puzzle==
[http://wordplay.blogs.nytimes.com/2014/03/17/coin/?module=BlogPost-Title&version=Blog%20Main&contentCollection=Numberplay&action=Click&pgtype=Blogs&region=Body A coin problem]<br>
by Gary Antonik, Numberplay blog, ''New York Times'', 17 March 2014


The post begins with this simple problem, posed by Daniel Finkel:
==Big data surprises==
<blockquote>
[http://online.wsj.com/news/articles/SB10001424052702303369904579423132072969654 Big data uncovers some weird correlations]<br>
Consider this simple game: flip a fair coin twice. You win if you get two heads, and lose otherwise. It’s not hard to calculate that the chances of winning are 1/4… . Your challenge is to design a game, using only a fair coin, that you have a 1/3 chance of winning.
by By Deborah Gage , ''Wall Street Journal'', 23 March 2014
</blockquote>
 
Continues "And here is my recipe for getting the most out of this problem: if you can solve it, do not stop with one answer. Rather, see how many answers you can come up with. I’ve posed this problem to many people, and I continue to hear novel solutions."
The article is subtitled "There's a Link Between Sales and Phases of the Moon, Among Other Things."  It includes the following graphic, which could qualify as a Forsooth!


Here are three ways that suggested themselves (I notice they also had soon showed up in readers' comments to the ''NYT''!):
<center>[[File:MoonMetrics.jpg | 400px]]</center>
*  Toss the coin until the first head appears.  You win if this takes an even number of tosses
*  Toss the coin twice.  You win on HH and lose on HT or TH.  If TT appears, ignore the result and make another two tosses.
*  Toss the coin until the first appearance of HTT or HHT on consecutive tosses.  You win HTT.


The third is an instance of the game [http://en.wikipedia.org/wiki/Penney's_game Penney-Ante], invented by William Penney.  It is a famous example of a non-transitive game:  whatever triple the first player chooses, I can choose one that has a better than even chance of coming up first.  So if the first player chooses HTT, the second will choose HHT.  But I did not know, until searching for an online description of Penney-Ante, is that there is a variation with cards, called the Humble-Nishiyama Randomness Game.  As described  [http://en.wikipedia.org/wiki/Penney's_game#Variation_with_playing_cards here]
Here is another example:
<blockquote>
<blockquote>
At the start of a game each player decides on their three colour sequence for the whole game. The cards are then turned over one at a time and placed in a line, until one of the chosen triples appears. The winning player takes the upturned cards, having won that "trick". The game continues with the rest of the unused cards, with players collecting tricks as their triples come up, until all the cards in the pack have been used. The winner of the game is the player that has won the most tricks.
The online lender ZestFinance Inc. found that people who fill out their loan applications using all capital letters default more often than people who use all lowercase letters, and more often still than people who use uppercase and lowercase letters correctly.
<br><br>
ZestFinance Chief Executive Douglas Merrill says the company looks at tens of thousands of signals when making a loan, and it doesn't consider the capital-letter factor as significant as some other factors—such as income when linked with expenses and the local cost of living.
<br><br>
So while it may take capital letters into consideration when evaluating an application, it hasn't held a loan up because of it.
</blockquote>
</blockquote>
In this scenario, the advantage of going second is even greater. 


Submitted by Bill Peterson
Submitted by Paul Alper

Revision as of 00:03, 21 April 2014

Big data surprises

Big data uncovers some weird correlations
by By Deborah Gage , Wall Street Journal, 23 March 2014

The article is subtitled "There's a Link Between Sales and Phases of the Moon, Among Other Things." It includes the following graphic, which could qualify as a Forsooth!

MoonMetrics.jpg

Here is another example:

The online lender ZestFinance Inc. found that people who fill out their loan applications using all capital letters default more often than people who use all lowercase letters, and more often still than people who use uppercase and lowercase letters correctly.

ZestFinance Chief Executive Douglas Merrill says the company looks at tens of thousands of signals when making a loan, and it doesn't consider the capital-letter factor as significant as some other factors—such as income when linked with expenses and the local cost of living.

So while it may take capital letters into consideration when evaluating an application, it hasn't held a loan up because of it.

Submitted by Paul Alper