Jon Marino, a senior mathematics major, now counts among his honors the top student research prize from the spring meeting of the Maryland-DC-Virginia section of the Mathematical Association of America (MAA), held on April 26 at James Madison University. Marino earned first place in the student paper competition, which had a record number (23) of entries. His research with advisor Dave Taylor, titled Integer Compositions Applied to the Probability Analysis of Blackjack and the Infinite Deck Assumption, is on a counting problem associated with blackjack probabilities.
This is a different kind of card counting: for example, if the dealer has a 2 showing, in how many different ways can the dealer eventually end up at 17? With this and similar information, the probability of the dealer beating 16 can be computed. Jon’s involvement with the problem started when Taylor noticed an odd “coincidence” of binomial coefficients showing up in his blackjack probability calculations. Marino claimed the problem for his Honors in Mathematics project, and found several elegant formulas for the “compositions” involved. He proved the necessary lemmas (as Jon says, “when life gives you lemmas …”) and general theorems to compute related probabilities for any blackjack variant (e.g., playing with hexadecimal cards or forcing the dealer to hold at 15).
The blackjack connection gives Jon’s work a familiar and interesting context, but his enjoyment of the project was in the development of new mathematics. This is an exciting occurrence for any mathematician, and the quality of Jon’s work has now been recognized at the regional level. Jon will present this work at the national MathFest meeting in Portland, Oregon, in August. From there, it’s on to graduate school, although Jon is still fielding offers and has not yet chosen his destination. Wherever that is, we’re sure he will make graduate school count.