After having read the paper it becomes evident that both authors have a liking for analyzing the problem in a discrete light. My degree is in mathematics, number theory so I am slightly biased myself. For that matter, I got intrigued by the fact that when dealing with the continuous version of gambling one does deal with unrealistic assumptions. One of which is ... money is indefinitely divisible which of course this is a bonkers assumption. Now assuming money has finite integral values, the analysis becomes much more difficult, particularly in the light of edge effects. So, that is why the authors seem to resort to heavy computer simulation.