Quote:kubikulannThere we are...

You are not searching the truth collaboratively. You are in a contest of egos and you need to be the winner.

I am not searching for the truth. I already know it. I've known it since the beginning. The question was, does the true count tend towards (or away from) 0 as hands are dealt. The answer is no; the expectation of the true count after a hand is dealt is the true count before it was dealt. That's it; that is the truth. There is no more to it than that. The terms we are using are all well-defined; there is no wiggle room. That is the beauty of mathematics; there is no room for your opinion or my opinion. Statements are either true or they are false.

You have found out that you were wrong, so you are now changing the question to a different one and pretending that you were right all along. So, who is the one who is in a contest of egos and needs to be the winner? I have made false statements on this board before. When I realize that I'm wrong, I quickly admit to it, apologize, thank the person who pointed out my error, and move on. This happened recently in a blackjack discussion, in fact, which is an area in which I consider myself to have some level of expertise. No problem, everyone makes mistakes, and I'm no exception.

Quote:For the record, a person cannot be "wrong". It is a statement that is wrong. (Or I am missing some specificity of English?)

You are missing some specificity of English. This is how the term is commonly used. "False" is generally used as you are describing, but "wrong" is often used to refer to the person who makes the false statement. I'm not sure whether this is technically grammatically correct, but it is certainly common usage.

I'm afraid there is not one mention of "expectation" in my original post. Later on, we were driven towards that measure, and it is now a safe conjecture to say that in blackjack, the situation is similar to the simpler example I provided : the expected true count (ratio) is stable, while the ratio of expected contents is not.Quote:AxiomOfChoiceDo you understand what true count is? Or how it is defined? The original question was asking about the true count. Please don't go changing the question now. Obviously if you ask a different question, the answer is different. All I have been saying ALL ALONG is that the expected true count after a hand has been played is the true count before the hand is played.

I am neither right nor wrong, since I stressed the point that I did not know the answer. Now we have a double answer because I provided a valid proof of the second part (and also derived the other part, but waited for you to give a mathematical development). You just insisted "it's obvious", "you're an imbecile" (or equivalent, saying I'm advocating betting systems).

Please note that when I discussed the Element of Risk on the same basis, nobody was willing to sustain me. Probably because of Michael's aura, nobody dared to question the validity of his concept. My putting forward that E(x/y) is to be preferred to E(x)/E(y) was considered asinine.

Now you are stressing the same point, and again presenting me as asinine.

Where is the consistency? (Apart from the pleasure you seem to derive in proclaiming your superiority.)

Quote:kubikulannYou just insisted "it's obvious", "you're an imbecile" (or equivalent, saying I'm advocating betting systems).

I never said that you were advocating betting systems. I said that the result was obvious for exactly the same reason that it's obvious that betting systems don't work. If I give you some long complicated betting system to try to beat roulette, will you go through pages of calculations to derive my exact expectation to conclude that it is negative, or will you just say, you are making only negative expectation bets, therefore it is obvious that the total expectation is negative?

I was using the exact same argument. I am saying, I don't care what system you use to decide whether to draw another card. Drawing another card has an expected TC delta of 0, therefore, regardless of what method you use to decide to draw the cards, the expected TC when you finish is the TC when you started. As far as I'm concerned, that constitutes a rigorous mathematical proof (perhaps you could ask that I prove that drawing a card has an expected TC delta of 0, but you never seemed to dispute that so I assumed that you agreed).

Quote:Please note that when I discussed the Element of Risk on the same basis, nobody was willing to sustain me. Probably because of Michael's aura, nobody dared to question the validity of his concept. My putting forward that E(x/y) is to be preferred to E(x)/E(y) was considered asinine.

Now you are stressing the same point, and again presenting me as asinine.

Where is the consistency? (Apart from the pleasure you seem to derive in proclaiming your superiority.)

I'm perfectly willing to disagree with the Wizard (or anyone else) when I feel that he is wrong. I've done it before (rarely, but that's because I rarely feel that he is wrong)

I don't know exactly what thread you are referring to, but, for element of risk, I would agree that E(X)/E(Y) makes more sense than E(X/Y), because you care about totals (you are making use of the fact that expectation is an algebraic mean) It makes no sense in this case, because the whole point of calculating a true count is to estimate an edge. You are missing the point entirely if you calculate some other measure that does not estimate edge.