"Risk of Ruin is a well defined term in statistics. It's the probability
of losing an entire given starting bankroll with indefinite play on a
certain game, with nothing going into or out of that bankroll other than
the game's wins and losses..."
Dan, that is not the only way Risk of Ruin is used in statistics or in gambling. ROR is not limited to an assumption of "indefinite play", nor does it preclude the possibility of incorporating pre-determined interim additions and subtractions to bankroll. There's nothing very complicated about the term Risk of Ruin. It's the probability of not being able to continue betting because you don't have enough money to make the next bet.
As far as additions and subtractions to bankroll, we all routinely include the effect of cashback on long-term ("indefinite play") Risk of Ruin. Collecting cashback at the end of the day is not fundamentally different than, say, paying myself a "salary", based on how much VP I play.
Short-term ROR is an extremely important and useful number. If you go to a casino for a weekend with $5,000 and plan to play 12 hours of $5 10/6 DDB, you most certainly have a Risk of Ruin. And that ROR is about 70%. (assuming 600 hands/hr.) In fact, 34% of the time you won't even last 3 hours. Being able to come up with a ROR figure like that would probably convince you to either bring more money, or play a lower denomination, or play a less volatile game, or plan to play fewer hours. But first you need to be able to calculate that short-term Risk of Ruin.
There was a positive EV $10 Pick'em game at Mohegan Sun over a decade ago that I wanted to play. From the jazbo-Sorokin equation*, I knew how much it would cost to play that game indefinitely. I forget the EV, but the long-term bankroll requirement for a 1% ROR was something pretty large, like $300K. I didn't want to bring $300K to Mohegan Sun, but I didn't know how much I'd need for 3 days of play. I wrote a program to give me that answer, and that program eventually morphed into Dunbar's Risk Analyzer for Video Poker.
--Dunbar
*Dan, you referred to the long-term ROR formula as "the Sorokin formula", but a better/fairer name is the jazbo-Sorokin formula (or equation). I'll accept part of the blame for the misnomer, though, since I'm partially responsible for it initially being called the Sorokin formula. In Fall 1999, I co-authored (along with MathBoy) the first article on the use of that formula to solve long-term ROR problems in Video Poker. (see http://www.blackjackforumonline.com/content/VPRoR.htm )
Some background info: In early 1999, Evgeny Sorokin had posted an interesting ROR problem on the old BJMath website. His post did not explicitly mention video poker, but MathBoy and I realized that his observations could indeed be used to solve the long-term ROR problems of video poker. In our article, MathBoy and I credited Sorokin with leading us to the video poker solution. However, it ultimately became clear that jazbo had come up with the same formula a few months before Sorokin's post. (jazbo had shared his formula only with members of his listserv group.) I thereafter have always referred to the formula as the "jasbo-Sorokin equation".
