Mailbag

    Every now and then I receive questions from readers about the mathematics of gambling or just a question about some specific aspect of a gambling game.  This month I want to devote my column to answering questions from two of my readers: Maxine Nelson from Tampa, Florida and Carl Huzzen from Annandale, Virginia.  Nice to hear from you both.

    To begin with, Maxine had two questions.  The first was in reference to the Florida Lottery's list of ball sets in use on specific lotto drawing dates.  This list is published on their web site, specifically the link flalottery.com/MachinesAndBallSets.do.  Occasionally the words "Travel Set" and "End Travel Set" appear on the list and Maxine wanted to know what this meant.  I thought I knew the answer, but just to make sure I wrote to the Florida Lottery and asked them.  They graciously replied and confirmed that occasionally they take the lotto drawing "on the road" for promotional purposes and that they have a special set of balls and equipment for this purpose.  Easy enough.  Maxine's second question was harder.  I'll use her own words (slightly edited):

If and when I do have a winning lottery ticket, I read that I should not sign it and instead take the ticket to an attorney ASAP.  Once you sign your own name on the winning ticket you are at the mercy of the state's Lottery rules.  Your name will be made public and you'll have to go through their little publicity show -- getting your picture taken holding a goofy oversized check with the winnings on it.  Once your name is made public you are going to be hounded night and day by all kinds of scam artists (that would be a nightmare).  If you have the law firm handle your winnings, you are listed as a trust and can remain anonymous.  Is that true, Don?

Good question, Maxine. I was aware of team players forming trusts or corporations for tax purposes.  I discuss this in my book The Lottery Book, The Truth Behind the Numbers soon to be published by Bonus Books of Chicago.  But anonymity?  I simply didn't know.

    Checking various lotteries around the country I observed that every time there was a prize paid to a trust or corporation, it was also true that the members of the trust or corporation were listed by name elsewhere on the web site.  It did not appear to me that one could remain anonymous by forming a trust.  Nevertheless, I am not a lawyer; maybe it is possible and simply nobody has tried it.  So I wrote to I. Nelson Rose, Professor of Law at Whittier Law School in Costa Mesa, California with the question.  Professor Rose is a noted authority on the relationship of gambling issues to the law and is a frequent contributor to this web site.

    Professor Rose was kind enough to send me a reply.  Essentially he said that lotteries and the IRS want to know the names of winners.  In rare circumstances the lottery might be persuaded to keep a person's name secret; usually not.  They will, however, help to make sure that nobody knows how to find the winner if the winner does not want to be found.  I replied to this and asked Professor Rose if his answer meant that there is no need to hire a lawyer and form a trust.  He told me that I was correct but pointed out that this was not a legal opinion and that he could not guarantee that things work this way in every state and province.  Professor Rose gave me permission to quote him in my book and his exact reply will appear there.

    So, Maxine, I don't think you'll be able to remain anonymous.  That said, I hope that you get to have your picture taken holding one of those "goofy" big checks!  Thanks for the interesting question.

    Carl from Virginia had three items.  First he caught an error in my article Taking Advantage of an Advantage, Kelly Betting.  The right-hand side of equation 2A in my appendix contained a plus sign between the two terms and it should have been a minus.  Thanks for the correction, Carl.  Second, regarding the same article, Carl wanted to know how I came up with the figure $10.95 as the expected profit when the player bets it all every time.  The answer is that equation (11) with f = 1 produces an expected stake of $60.95.  Since the player stared with $50.00, $10.95 of this is profit.  Carl's third question was an especially interesting one..  Here it is in his own words:

I do have one terminology question.  In some of my probability textbooks they make a distinction between a probability "density" and a probability "mass", one being continuous and the other discrete.  You chose to use the term probability density when discussing Cardano, etc.  Was this an arbitrary choice on your part?

The answer is that probabilists use the term "density" to describe a probability function whose argument is a point, that is, a single outcome.  They use the term "mass" or, more commonly, "measure" when discussing a probability function whose argument is a set of points, that is, a set of outcomes.  A set of outcomes is generally referred to as an "event."  These terms apply in both the continuous and discrete cases.  If one works with both kinds of probability spaces, then one uses the adjectives "continuous" or "discrete" to clarify things.  The relation between densities and measures is as follows:  If P( E) is the probability of event E in a discrete space, then P( E) would be the (usually finite) sum of all of the terms p(x ) for each outcome x in E, p being a discrete probability density function.  If the situation was continuous, then P (E) would be the integral of the continuous probability density p over the set E.

    Thanks to both Maxine and Carl for taking the time to write.  If any of the rest of you out there have questions, mathematical or otherwise, please write.  You can get a link to my email by simply clicking on the word Technigame that appears in the "About the Author" box at the end of this or any of my other articles.  See you next month.