The TC Theorem is Still Denied by Some ...

apex said:
You are correct. A full deck will tend to average zero at all points. When you get to a point where a deck is say, +4, then if you take +4 as your starting points and run your sims, your average TC will be +4 at all remaining points.
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That is true, but then you have other times when TC is -4 and the shoe tends to end more often at TC -4. I guess my point is I do not see anything wrong with saying that overall the shoe ends with TC = 0 than any other TCs.
 
psyduck said:
That is true, but then you have other times when TC is -4 and the shoe tends to end more often at TC -4. I guess my point is I do not see anything wrong with saying that overall the shoe ends with TC = 0 than any other TCs.
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From the vantage point of the beginning of the shoe, then the average ending TC (the TC when there is one card left in the shoe) will be zero.

However, if when 4 decks remain, you have a TC of +12, this is new, more reliable information, and you now know that the average TC (i.e., if a sufficiently high number of trials were performed using a 4 deck slug with a TC of +12) when one card remains will be +12.

Spaw
 
Southpaw said:
What you are missing is that once the TC becomes large in magnitude you now have new information that is more reliable than what you knew at the beginning of the shoe. In fact, the shoe with a TC of +12 does not know that it has had more small cards taken out of it and that it needs to adjust itself to accord with what you knew at the beginning of the shoe (i.e., that the TC was 0); rather, on average, each round will decrease the RC by an amount that accords with the TC remaining constant, as your divisor becomes smaller.

Spaw
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I understand that, but then you will have times when TC = -12 to balance out your TC = +12 times. In the long run, the whole shoe tends to end more likely at TC = 0 than any other counts.
 
psyduck said:
I understand that, but then you will have times when TC = -12 to balance out your TC = +12 times. In the long run, the whole shoe tends to end more likely at TC = 0 than any other counts.
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Again, the TC theorem is valid under the constraint, that the TC has a given value at a given time. The theorem projects the TC into the future - given the chosen initial values.

If you are born in March, and the Birthday theorem states that your birthday is in the same month as the month you're born every following year - You cannot simply argue that on average you have your birthday on every month. (March will be in balance with June, July, ...)
Because the Birthday theorem is only valid under the constraint, that you have a given birth date.

There is no such thing as balancing out an initial +12 TC with an initial -12 TC, because you only average over those shoes where the initial TC is +12!

You should update your knowledge on conditional expectation values.
 
MangoJ said:
Again, the TC theorem is valid under the constraint, that the TC has a given value at a given time. The theorem projects the TC into the future - given the chosen initial values.

If you are born in March, and the Birthday theorem states that your birthday is in the same month as the month you're born every following year - You cannot simply argue that on average you have your birthday on every month. (March will be in balance with June, July, ...)
Because the Birthday theorem is only valid under the constraint, that you have a given birth date.

There is no such thing as balancing out an initial +12 TC with an initial -12 TC, because you only average over those shoes where the initial TC is +12!

You should update your knowledge on conditional expectation values.
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Was I wrong to say that in the long run the shoe ends at TC = 0 more than any other counts? If you believe it was wrong, then what TC do you think the shoe tends to end at?

BTW, your birthday theorem does not make any sense because I can only be born once.
 
psyduck said:
Was I wrong to say that in the long run the shoe ends at TC = 0 more than any other counts? If you believe it was wrong, then what TC do you think the shoe tends to end at?

BTW, your birthday theorem does not make any sense because I can only be born once.
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With "birthday" I meant the annual day you celebrate your birthday. Whatever that day is called in english ^^

If the TC is +12 at a given time (i.e. after 1 deck is dealt), at that time (i.e. without additional information about upcoming cards) the shoe is expected to end with +12 TC. That is the TC theorem. Note that the shoe is also expected to end with RC=0 - this is no contradiction!
 
Maybe I Can Help

:laugh:

Once you have a positive TC in a shoe
The TC on AVERAGE remains the same as the shoe is played
while the RC drops

The above has VARIANCE

How often have you played a shoe that remains the same TC for most of the shoe? The RC drops but as you calculate your TC, it's the same. This is the TC theorem in the real world.
 
I can't believe how patient you guys are being. Everytime I try to forgive this kind of ignorance I just find myself in another heated argument with them later trying to explain something else basic and obvious. If we were professional plumbers and somone was like

"wait, what? fluids be flowing through these pipes? Prove it!"

Would we react the same way? Its ok that they don't know but they should change their tone and go read a few books. Not just keep being stubborn until they start giving out cartesian defences. "Ok so 'fluids' maybe do flow through pipes, but does any of this exist? Maybe we're in the matrix right now! Think about it.....
 
And now psyduck is losing it. Psyduck, imagine a basket with 120 red apples, 120 green apples and 72 pears....

Was just gonna leave it at that but I wanna try 1 more time. At the beginning the first random fruit u grab and all future grabs CURRENTLY have a 120/312 120/312 and 72/312 chance of being a red green or pear respectively. When you pull a red one on first grab the next grabs and all future grabs chances change to 119/311 120/311 and 72/311 respectively. These numbers will chance again, but as of right now their expected probabilities are as stated.

(I can't believe I added to this abortion of thread. It seems so obv but its so hard to not try one more time to make it clear)
 
Yeah same here. I'm not going to get into the math because its already been well presented. I'll just say once more that this is the reason we can wong out of a deeply negative shoe and find a better shoe. There is no need to be concerned about the shoe coming back. On average it will end negative and we're just throwing money away if we stay. The guys that aren't getting this are only seeing the short term, not the long term picture here.
 
ohbehave said:
The guys that aren't getting this are only seeing the short term, not the long term picture here.
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And the funny part is: on average there is no difference between short term and long term :)

People always confuse expectation with long term or average over an infinite number of hands. Quite the opposite is true. Expectation is a property each and every hand has. The difference between short term and long term is purely variance, but the expectation of short term and long term are identical.
 
blackriver said:
And now psyduck is losing it. Psyduck, imagine a basket with 120 red apples, 120 green apples and 72 pears....
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Psyduck is losing what?

Trust me. There is really no need for you to use any analogy. You really don't think I can get it without? All I said was in the long run the whole shoe tends to end at TC 0 more than at any other TCs. Now tell me what is wrong with that statement.
 
Theories to Apples

I like the apple analogy:

Let's say you have a barrel
in the barrel are 100 apples
60 are yellow
40 are red

On average every time you pick out 10 apples what would you expect?
4 red and 6 yellow

If you do this 10 times what would the average be?
4 red and 6 yellow
If you refill the barrel and do it a billion times, what would you expect on AVERAGE
4 red and 6 yellow

This is what the TC theorem is, replace apples with hi and low cards. It is what you would expect on AVERAGE.

Now the above would have variance, sometimes you will get 4 red apples, sometimes more and sometimes less. The average will be 4.
 
psyduck said:
Psyduck is losing what?

Trust me. There is really no need for you to use any analogy. You really don't think I can get it without? All I said was in the long run the whole shoe tends to end at TC 0 more than at any other TCs. Now tell me what is wrong with that statement.
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That is true for TC=0. But when TC=ANYTHING ELSE then the shoe will on average end at TC=ANYTHING ELSE from that point forward in the shoe. If TC changes, then from that point forward, on average, the shoe will end at the new TC.

As has been stated TC tells you what is to come. RC tells you what has happened.
 
ohbehave said:
That is true for TC=0. But when TC=ANYTHING ELSE then the shoe will on average end at TC=ANYTHING ELSE from that point forward in the shoe. If TC changes, then from that point forward, on average, the shoe will end at the new TC.

As has been stated TC tells you what is to come. RC tells you what has happened.
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Which shoe starts with TC = anything else (not zero)?
 
Instead of being cynical about it, you could agree that once you have more information about cards being removed, you have better information about the average TC for the rest of the shoe.

Or you could chose to say "They will all end at zero!" If that is your choice you will only miss out on a few insights that are somewhat helpful.
 
Your arguing an irrelevant point. We all get what your saying. But if instead they used spanish decks and just burned cards face up until tc = 0 so that the deck is more similar to standard then would the expected tc for for all future points be 0 or would it still go back to +4 at some point just because that's what we started with? After each card comes out there is a more accurate description of thhe shoe than "a shoe that started out standard and had x cards removed" that's the entire point of counting!
 
psyduck said:
Which shoe starts with TC = anything else (not zero)?
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And how often does a shoe have the same TC throughout the shoe? For all practical purposes I've seen it happen where the RC never ventures more than a few points from zero yielding a more or less constant TC (of zero) throughout, but that indeed is rare. More likely is the case where the TC fluctuates throughout the shoe. Therefore, projecting the TC foward through a few decks of unseen cards is a bad idea IMHO.

Let's take the case of a team all playing at the same table with each of the team members leaving the table at different times during the shoe. After one deck has been played the TC=2 and player 1 leaves. After 2 decks have been played the TC=3 and player 2 leaves. After 2 and one half decks have been played the TC=4 and player 3 leaves. After 3 decks have been played the TC=5 and player 4 leaves. After 4 decks have been played the TC drops to -1 and all the players who left the table return. On the next hand everyone has different bets out based on what the respective TCs were when each left the table, but all are overbetting because they based their bets on the projected TC when they left the table. They should have looked at player 5 who never left the table and put a minimum bet out. ;)
 
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