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The 11th International Conference on Gambling and Risk Taking was held this past June at the MGM Hotel in Las Vegas. This is an event that is held every three years and is organized and run by Bill Eadington and Judy Cornelius, the Director and Codirector of the Institute for the Study of Gambling and Commercial Gaming at the University of Nevada, Reno (UNR). Peter Griffin, a Professor of Mathematics and Statistics at California State University, Sacramento (CSU) and author of the definitive book Theory of Blackjack (Huntington Press), was always an enthusiastic attendee at these conferences. Sadly, Peter was not at this last conference; he had died on October 18, 1998. One of the conference's sessions, however, was entitled "Theoretical Contributions to the Theory of Blackjack: The Legacy of Peter Griffin." This was a session moderated by John Gwynn, a long-time friend and collaborator of Peter's, and included talks by some of Peter's close friends and colleagues: Dennis Conrad, Stuart Ethier, Olaf Vancura, Arnold Snyder, Hal Marcus, R. Michael Canjar, and Stanford Wong. It was a very moving session.
I did not speak at the session, and appropriately so since I was not a close friend of Peter's. Nevertheless, we were friends even though I had only met Peter on one occasion. It was a memorable occasion for me and I think it well serves Peter's legacy to relate it to you as I remember it.
I had been collaborating with Lenny Frome at the time; we were doing analyses of new casino games for gaming developers. One of the games we worked on was based on the proposition bets in Craps and contained a bet that was really a long shot. I calculated the probability for the bet and Lenny suggested that I present my solution at the next gaming conference; that conference was the 10th International Conference on Gambling and Risk Taking which was held in Montreal in June of 1997. I did submit my solution as a paper. I don't wish to get into details about the bet nor its solution, since that is not what this article is about. If you are interested in the details they can be found in the new book, Finding the Edge, which is published by Eadington's institute at UNR. The name of the article is "A Really Hard Hardway Bet."
Peter Griffin attended this conference and that is where I first met him. As it turned out, I was asked to moderate the session that included one of Peter's papers, as well as a paper by Olaf Vancura, who I also met for the first time there. I was very fortunate as both Peter's and Olaf's papers were first rate. Anyway, it is customary for the moderator to write to the presenters and obtain biographical and professional information for the purpose of preparing a suitable introduction of the presenter for the session. I did this.
When I wrote to Peter, I mentioned that I was familiar with his groundbreaking book Theory of Blackjack and in particular I was delighted with the last three paragraphs in his section "Use of Computers" on pages 4 and 5. Let me quote those for you since I believe they are a significant part of this story. The emphases are Peter's.
I went on to tell Peter that these paragraphs leaped out at me when I first read his book, especially the very first paragraph. Moreover, as I told him, my own school is guilty of the mind-numbing use of calculators in calculus and I wish that someone here would wake up to the validity of his observations. Peter was delighted. He wrote back and told me that he considered those paragraphs to be "... the most important passages in my book." And that is a direct quote; he meant exactly that. What is more, when I finally met Peter in Montreal and we shook hands, we spoke for close to an hour, not about Blackjack, not about gambling, and not about probability theory; we spoke about teaching mathematics to young people. It was a very pleasant and stimulating discussion. There's more.
When I got around to giving my talk, there in the front row was Peter along with his close friend Anthony Curtis, the publisher of Huntington Press. The talk seemed to go well and I left feeling happy. The next day I bumped into Anthony and he was chuckling as he told me that Peter had been up half the night working on the problem I had presented and that he was still working on it, scratching on the backs of envelopes and so on. I was rather surprised at this so I went looking for Peter. When I found him he asked if we could sit down somewhere and discuss my problem. I agreed and we spent about 45 minutes talking. It turned out that Peter had not really understood my solution and was honestly concerned that it might be incorrect. Understand, Peter was not "sharpshooting;" his concern was genuine and it was for me. I explained what I had done and in the course of hashing things out Peter observed that I was constructing something called Catalan numbers (I was unaware of them) and we laughed at the resemblance to my last name. Well, the empty cocktail lounge in which we were sitting opened up and were were faced with the dilemma of whether to start drinking at 3 PM or to leave. We left and Peter agreed to keep in touch with me about my problem.
The next afternoon I was sitting in one of the talks when I felt a tap on my shoulder and someone handed me a scrap of paper. When I turned I saw Peter sitting in the back of the room indicating that the paper had come from him. Peter had produced some approximate solutions that were listed and wrote the following:
Nothing further was said at the conference as Peter had a couple of his own talks to give and had to concentrate on those.
When I was back at the University I received a Fax from Peter on June 13th saying "This is not an exact calculation but more like a truncation of an infinite series. But the programming is simple and it runs quickly." Attached was a program along with a printout that confirmed my answer. Four days later on June 17th I received another fax from Peter containing a somewhat longer program. In part the message said: "This is my 'finite' program to solve your problem exactly by going through 10395 sequences (rather than your 'Catalan' number of 132). I had quite a bit of trouble determining d1 and e1, not quite getting 10395 cases for a while. It was harder than I thought. As Paul Newman said when eating 50 eggs in Cool Hand Luke, 'Just something to do.' Best, Peter" My answer was confirmed by him at the bottom of the page.
The point of the above story is that Peter was first and foremost an educator. That was clear in our first meeting. He took teaching very seriously. He was, however, a first rate mathematician with a healthy curiosity. There was really no need for him to attack my problem with such fervor. He simply thought it to be an interesting challenge and he was (initially) concerned that I might have made a mistake. (I've certainly made my share.) In brief, he was an enthusiastic educator and an enthusiastic mathematician; he was good at both tasks.
It is ironic that the same passages of his book that brought Peter and me together as friends were involved in our parting. On October 20, 1998 I sent the following fax to Peter.
The same day I received a return fax from Kay McMillan, an Administrative Secretary in Peter's department at CSU. It said:
I miss him too. See you next month.
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