Originally Posted by
tableplay
The expectation is constant and exerts itself after M grows sufficiently large. That is, when M is sufficiently large the actual results will converge to expectation. If the expectation is positive then profit will occur if M is big. M for the casino is extremely large and that is why a profit occurs for the casino. It is up to the player to bet sufficiently small and to play at a positive expectation in order to get in enough plays to make M sufficiently large to converge to positive expectation (i.e. to act as a mini-casino). A single loss is not viewed as successful or not successful (in reply to your 2nd question) - success (or failure) is an adjective that is attached to a series of plays in aggregate where the series is very, very large and the expectation is positive for the player. The answer to your first question is Yes - but M must be very large. How large is a function of the variance of the game and the magnitude of the positive expectation.
With regard to question #3, success is applied to the sum of all plays of a positive expectation game, not to an arbitrary dividing line of the first X plays and the ensuing X+1 plays up to when the player plays his or her last hand. The game must converge to its expectation for a large M. So play games with a positive expectation and play sufficiently small to make M large and profit (success) will be achieved. This is what KewlJ meant - if you and/or others wish to focus on the semantics of Kewlj's delivery of this important message, then you will miss this important point. My goal here was to say what I said in red and bold above, so I will not comment further on this topic - that is, I am satisfied with what I have stated there whether others here are or aren't and so will not comment further on it.
Wow. Tableplay, you are making me look smarter than I am.
I am just a simple guy, playing a simple game, using simple techniques (perhaps the simplest by AP standards) to play at an advantage. Nothing new about what I do, although I have put some of my own 'twists' on some things. I am not a "math guy". The formulas and such (like you are laying out) are often far over my head. But that is the beauty of card counting. I don't have to be Einstein. I can rely on 'math guys' like yourself and others that have done the math before me.
My whole approach is about simplicity. People that know me from other forums know I often argue for simplicity. I think many players get into trouble trying to overthink the game, go in a direction of complex counts and approaches thinking that adds strength. For most it does just the opposite. As a matter of fact, when I was working on my book 2 years ago, before I put the project on hold and returned the money I was paid, I referred to my style of play as
"Blackjack Fusion", a fusion of simple techniques and approaches resulting in a sum greater than it's parts. (yeah somebody will probably steal that before I get back around to working on that project, if I ever do
)
And you are quite right, my 'delivery' of things is often what gets me into trouble. I am not a great communicator, orally or written. I frequently have trouble getting across what I am trying to convey and/or say/write. And often do so in such a manor as to turn people off. I will continue to try to improve in that area.
The thing is that my simple delivery of things is usually enough to have people/players understand the basis of what I am talking about and while I can't lay out formulas and such like you do, they are able to understand that there is solid math behind what I say and do. Problem with this site is there are deniers of that math. Deniers of all thing reality, actually. Guys that live in an alternative universe that believe total nonsense, like that they can will a million dollars profit from long-term negative EV play.
Neither you, nor I are going to get these folks believing anything but their own alternative reality.