>I was looking at the Exact True Count, and not an approximation.
>Consider this: Suppose you were looking at a random variable T.
>Suppose that there are two possibilities:
>T can down up 1 with a probability of 75%
>T can go down 3 with a probability of 25%.
>T is more likely to go down than up.
>The expected change in T is 0.
OK. I follow that easily enough...
>This is roughly what is happening with True Count, although obviously >that random variable is a lot more complicated.
What I didn't follow was your statement "The TC is more likely to increase".
Say we have exactly one deck left. And we have a RC of +4, which gives a TC of +4. This means that in 52 cards, ignoring the 7/8/9 since I'm a hi-lo'er, there must be 24 small cards and 28 big cards.
Now, on the next hand, and again I am assuming your statement above about exact true count is to be taken at face value, the curreent TC is clearly 4, with 24 small and 28 big cards left, and the TC is exactly 4.0...
To keep my head from exploding, I am going to play heads up. The dealer deals four cards, two to himself, one of which I can see, and two to me, both of which I see. It would seem to me that the probability of the first card dealt ... [interrupt...] wait a minute. I think I see your point.
In this case, your statement doesn't hold because there are no neutral cards in the deck. So lets change the above to 19 low cards, 23 high cards, and 10 neutral cards. Now I see where your statement is coming from. The TC will fall only if 10's are dealt. And that will happen with a probability of 23/52. But if a low card falls, the TC will increase, but also if a neutral card falls the same happens. So there is a 29/52 chance of a non-high card falling, and the TC will rise.
So OK. I see your point. Took a bit of thinking. And, in fact, I discovered this for myself in another discussion here a long while back. But apparently 57 years of age is enough to see some things go forgotten. I neglected the fact that when a neutral card falls, the denominator in the TC calculation gets smaller making the TC climb even though no low card fell.
Thanks for the hints... as counter-intuitive as it seems it makes perfect sense assuming I did not have a total mental failure above.