I had really hoped to avoid this. Heaven knows we don't need another treatise on a subject that's been beaten to death. Chapter 8 of BJA3 contains 39 pages on the topic, but, apparently, that's not enough for some people. So, with apologies for stating concepts that have been discussed, explained, and elucidated a hundred times, here's one more attempt to put the subject to bed -- one which, I know, will nonetheless be doomed to failure. And, of course, I apologize for the length.

There are any number of perfectly valid approaches to and definitions of ROR. Now, I know that comes as a great shock to Three, but I don't exist to make him happy.

One definition, which is extremely helpful for comparative purposes, which is always a valid goal -- and is what made SCORE so popular -- is to assume a starting bankroll and bet scheme, and then to further assume that one continues to play in that specified manner until one of three things happens: you win all the money in the world, you die trying, or you go broke before you die. And that (mathematical, if not entirely realistic) approach is both valid and popular, because it isn't nuanced; it's very absolute and unambiguous as to how you'll play. It is, of course, then infuriating when someone feels the necessity to point out 72 times that no one really plays this way, as if we are all too stupid to understand the obvious. But the metric is nonetheless extremely useful because we don't have to deal with 65 other ways that we might decide to play, each with its subsequent DIFFERENT risk of ruin. We then engender a ROR Tower of Babel that absolutely no one understands.

Of COURSE there are other definitions of ROR!! To imply that I have ever stated otherwise is sheer lunacy. Page 115 explains, in detail, one such concept: ROR if you decide ahead of time that, should you lose half your original stake, you will cut back to half stakes from that point on, but then not do it again. A valid approach? Sure. One of hundreds. Here's another: define ROR as the probability of losing your entire stake before, say, doubling it. Teams are fond of this expression of ROR, because, often, they set a goal of doubling a bank, before losing it, as a threshold for breaking that bank and distributing profits and/or starting a new venture.

Then there is trip ROR. Define the possibility of tapping out not if you play forever but only for a prescribed number of hands or hours. And then there are the double-barrier formulas: ROR given a certain amount of time to play OR goal to hit, or both, before stopping.

Then there's the ROR associated with playing less than full Kelly. Now, we have RORs for all different Kelly fractions! And, some will decide not to resize while playing this way, because they've already taken one precaution of avoiding full Kelly, which they deem too risky, so they feel they don't need to also stipulate that they'll resize along the way. Or not! And the beat goes on.

Want to express ROR as meaning ANY or all of the above? Be my guest! Knock yourself out. Who ever said otherwise? But when you're writing a book and creating hundreds upon hundreds of charts (think chapter 10, as just a start), you don't try to incorporate eight different definitions of ROR and apply them all simultaneously -- unless you're trying to create the maximum amount of confusion possible. So, we use a standard, SINGLE definition as a convention -- one that is simple to understand, simple to calculate, and doesn't lead to 100 different interpretations. (The same may be said for the edges we quote for BS. Technically, they're all "silly," because no one plays one hand off the top and then faces a fresh shuffle for each ensuing hand! But the edges we quote are USEFUL, because a) they're relatively easy to calculate, and b) they create a convention, such that, for the same game, we're not quoting 28 different BS edges!)

I know this post won't end the discussion, because, well, that's what people here are best at: dragging out the obvious ad infinitum and especially ad nauseam. Apologies to those who already have known all of the above for a long time. To the others, well, best I say no more.

Don