21gunsalute
Well-Known Member
That's exactly my point. The TCT tells you nothing of any value or usefullness. All it gives you is an expected value which is not likely to reflect any actual cirmustances.
Ploppy would do whatever I want him to do
- Thread starter BJgenius007
- Start date
That's exactly my point. The TCT tells you nothing of any value or usefullness. All it gives you is an expected value which is not likely to reflect any actual cirmustances.
21gunsalute
Well-Known Member
You can beat a dead horse and you can lead it to water but you can't make it drink when the fat lady sings. :laugh:
This discussion was about the player before you taking one card. The people who said that it was a high count so he is going to take my ten are wrong. The point is every card has the same likelihood to a high card or low card. It is not until the card is seen that you know the cards effect on the TC. If it is a high card your chances the next card is a ten go down a hair but if it is a low card your chances of drawing a ten go up more than they go down in the other case. These 2 events balance each other perfectly in frequency times effect showing the true count theorem applies in this situation. The other player doubling has no effect on your play. If you were playing in a store where the double card is dealt face down the situation would be the same. I doubt people would be arguing he is going to take their ten. They would look even more foolish than they already do.
Whether or not TCT is useful on any given situation, it is never a bad idea to know as much as possible about the game you're playing. I see it as a long-term investment, since you never know what kind of other game will come across in the future, where TCT (or other theorems) will come handy.
aslan
Well-Known Member
I have been translating "expected" to mean "probable". If that is true, why wouldn't it "likely" reflect actual circumstances? Or am I still missing the point?
"Expected" doesnt have much to do with "probable" or even "most probable".
Example:
On a fair coin flip game of a billion rounds paying even money, the most probable outcomes are well ahead or well behind. However, being behind and being ahead has same probability (since the game is symmetric to your opponent's side). That means the expected win of that game is zero. Of course only in rare cases you come out at exactly zero after a billion rounds.
21gunsalute
Well-Known Member
Do an experiment and True Count several shoes, recording or remembering the TC at various intervals such as a deck or 2 decks. According the the TCT, the expected TC will be the same at each interval. In actual practice though the TC rarely remains constant. You could probably even use the strategy trainer here for such an experiment.
aslan
Well-Known Member
So expected is more like the middle ground or average, but you can expect the actual case to usually fall somewhere on one side or the other. Then, the only probably is that you are probably not "far" off, lol, but that does not give a whole lot of comfort-- still, it's better than nothing. Anyway, am I getting warm?
Yes, expected value is commonly referred to as "average". They are not the same in statistical terms (the expected value of the average is the expected value, but the average is not the expected value). But to keep it simple - yes if you average over a "large enough" set, the average will be the expected value.
Your next question "what is large enough" is valid, it depends on the variance of the quantity you are studying. For high quantities, you need a larger set to get the average reasonable close to the expected value.
aslan
Well-Known Member
So when you say "expected" it ironically is not that you expect this to be the actual value, or even very close to it, but that it is the best you can do considering the wide range of possibilities. You can probably surmise that the actual value will likely be closer to the expected value than to either extreme. Can you say any more than that? So when we pick the strategy with the highest EV, we are actually picking our best educated guess as to what the actual result will be.
You are not trying to predict or guess any specific result. That is what gamblers do. "You missed your winning result ? Oh no problem, let's try again, eventually we must hit the win - right ?"
What APs do is something different, which is enjoying the "central limit theorem" (call it long run): If you average a random quantity over a large set, your result will be reasonable close to the expectation value of that quantity. You can even compute how likely you are how close. Nothing more, nothing less. If you play a positive expectation strategy long enough, you are expected to be close to that value.
Statistics is never about the single value of an individual observation. It is about this beautiful property - which, although all individual observations are intrinsically random, - guarantees you the expectation value "almost surely".
I don't find it ironical, maybe you don't agree on the wording "expectation" with literature. You have all right to disagree with the wording. You can claim you don't live for the central limit and this is perfectly right. But that doesn't alter statistical laws within that limit.
aslan
Well-Known Member
Expected value over the long run I can live with, and I see now that that's how it is meant, but expected value in the short run, well, that is what seems (or seemed) to me a bit ironical. OF course now I see the context in which it is used, so it is not ironical at all. If that makes any sense
:laugh: