I sent a PM about this, but I am aware that the composition of the 2 decks is different and that after the first card is revealed and more information is available, if additional cards are to be drawn, the probability of such additional cards being a particular value will be different in the two different decks.

.

ppp123,
ppp231,
ppp231,
ppp213


123,
231,
231,
213
ppp
ppp
ppp
ppp



spot the difference competition.

You were too careless here, but I missed it. Here you say that even though every card that was selected and put into the new deck is unknown, they each have a 1/52 chance to be any particular card.

Then you change your mind for no reason and decide that you have no idea what the chances each card in the new deck has of being a particular value:

Like you do not know the values of bus 101. The odds of 1/52 are dependent to the deck X, new deck Y is independent of deck X and has differential odds.
and does not have a constant golden ratio,

φ{X}=1:52

φ{Y}=0_52:52

On a graph it is a 45 degrees angled line variance difference.

How can the new deck be independent when it is made up of cards from the other decks?

Where you write in one of the above quotes that the standard on the new deck is ?/52, I would think that your question mark shouldn't be a question mark. Each card in your new deck has a 1/52 chance of being each particular card in a standard playing card deck, as you seem to have stated in one of the above quotes, so shouldn't the numerator be the sum of fifty-two fractions with a numerator of 1 and a denominator of 52?

In a standard playing card deck 1 card has a 1/1 chance of being the Ac and 51 cards have a 0 chance of being the Ac. So we add 1 and fifty-one 0's together and get 1 for the numerator. There are 52 cards to draw from so that is the denominator. So 1/52.

In the new deck each card has a 1/52 chance of being the Ac. So we add fifty-two fractions with a numerator of 1 and a denominator of 52 together and get 52/52 for the numerator (52/52 simplifies to 1). There are still 52 cards to draw from so that is the denominator. So 1/52.





Let's please try to go through an example in a few steps through few posts starting with Step One below so that I can try to learn where I'm doing something wrong (it would be nice to see you answer the questions in post #72 to try to help me figure this out also):


STEP ONE:

We have 52 standard playing card decks.

- We randomly draw one card from deck 1 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 2 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 3 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 4 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 5 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 6 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 7 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 8 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 9 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 10 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 11 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 12 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 13 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 14 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 15 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 16 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 17 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 18 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 19 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 20 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 21 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 22 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 23 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 24 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 25 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 26 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 27 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 28 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 29 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 30 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 31 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 32 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 33 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 34 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 35 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 36 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 37 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 38 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 39 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 40 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 41 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 41 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 42 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 43 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 44 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 45 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 46 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 47 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 48 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 49 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 51 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

- We randomly draw one card from deck 52 and put such card on the kitchen table. What are the chances that this card is each particular card in a standard playing card deck?

In reply to your scenario,


draw any card from any of the 52 sets/decks of cards, place it on your kitchen counter. the cards by the golden ratio has a 1:52 chance to be any card,

repeat this for another 51 times, each time you draw , each card has the same chance to be any card, the golden constant of 1:52


Event (A) picking each card from 52 independent decks, all with a golden constant ratio of 1:52


Event {B} pick a card from the unknown new formed independent deck on the kitchen counter, we know the chance of golden ratio 1:52 is almost impossible.
A third party looks at these cards and tells us there is 5 aces

what is the independent ratio of aces in the new deck ?

So you're adding new information? Of course that changes things.

One example at a time and one step in such example at a time please or else I am liable to get confused.

So are you saying that the answer to all of my questions in the above quote is "1/52"?

I've lost track of who is leveling who here. I'm pretty sure both sides know it's bull**** and both know the other knows it.

I am not levelling anyone, I am deadly serious, the maths does not lie.


''One example at a time and one step in such example at a time please or else I am liable to get confused.

So are you saying that the answer to all of my questions in the above quote is "1/52"?''


Yes and the golden ratio constant φ{X}=1:52

Each draw is independent, 1/52 being dependent to the individual deck you have drawn from.


I.e you drew a second card from the same deck, 1/51

I have it simplified for you all.

draw card 1 from deck 1, a 1/52 to be any value

draw card 1 from deck 2, a 1/52 to be any value



1/52=1/52


Both cards have equal chance to being the same value.

pkdk, this changes everything. If someone's going to tip you off to the composition of the new deck, then of course that information is relevant.

However WITHOUT that information we can say that there is;
x0% chance that there is 0 aces and 0/52 chance that you will draw an ace
x1% chance that there is 1 ace and 1/52 chance that you will draw an ace
x2% chance that there is 2 aces and 2/52 chance that you will draw an ace
x3% chance that there is 3 aces and 3/52 chance that you will draw an ace
x4% chance that there is 4 aces and 4/52 chance that you will draw an ace
x5% chance that there is 5 aces and 5/52 chance that you will draw an ace
x6% chance that there is 6 aces and 6/52 chance that you will draw an ace
x7% chance that there is 7 aces and 7/52 chance that you will draw an ace
x8% chance that there is 8 aces and 8/52 chance that you will draw an ace
x9% chance that there is 9 aces and 9/52 chance that you will draw an ace
x10% chance that there is 10 aces and 10/52 chance that you will draw an ace
x11% chance that there is 11 aces and 11/52 chance that you will draw an ace
x12% chance that there is 12 aces and 12/52 chance that you will draw an ace
x13% chance that there is 13 aces and 13/52 chance that you will draw an ace
x14% chance that there is 14 aces and 14/52 chance that you will draw an ace
x15% chance that there is 15 aces and 15/52 chance that you will draw an ace
x16% chance that there is 16 aces and 16/52 chance that you will draw an ace
x17% chance that there is 17 aces and 17/52 chance that you will draw an ace
x18% chance that there is 18 aces and 18/52 chance that you will draw an ace
x19% chance that there is 19 aces and 19/52 chance that you will draw an ace
x20% chance that there is 20 aces and 20/52 chance that you will draw an ace
x21% chance that there is 21 aces and 21/52 chance that you will draw an ace
x22% chance that there is 22 aces and 22/52 chance that you will draw an ace
x23% chance that there is 23 aces and 23/52 chance that you will draw an ace
x24% chance that there is 24 aces and 24/52 chance that you will draw an ace
x25% chance that there is 25 aces and 25/52 chance that you will draw an ace
x26% chance that there is 26 aces and 26/52 chance that you will draw an ace
x27% chance that there is 27 aces and 27/52 chance that you will draw an ace
x28% chance that there is 28 aces and 28/52 chance that you will draw an ace
x29% chance that there is 29 aces and 29/52 chance that you will draw an ace
x30% chance that there is 30 aces and 30/52 chance that you will draw an ace
x31% chance that there is 31 aces and 31/52 chance that you will draw an ace
x32% chance that there is 32 aces and 32/52 chance that you will draw an ace
x33% chance that there is 33 aces and 33/52 chance that you will draw an ace
x34% chance that there is 34 aces and 34/52 chance that you will draw an ace
x35% chance that there is 35 aces and 35/52 chance that you will draw an ace
x36% chance that there is 36 aces and 36/52 chance that you will draw an ace
x37% chance that there is 37 aces and 37/52 chance that you will draw an ace
x38% chance that there is 38 aces and 38/52 chance that you will draw an ace
x39% chance that there is 39 aces and 39/52 chance that you will draw an ace
x40% chance that there is 40 aces and 40/52 chance that you will draw an ace
x41% chance that there is 41 aces and 41/52 chance that you will draw an ace
x42% chance that there is 42 aces and 42/52 chance that you will draw an ace
x43% chance that there is 43 aces and 43/52 chance that you will draw an ace
x44% chance that there is 44 aces and 44/52 chance that you will draw an ace
x45% chance that there is 45 aces and 45/52 chance that you will draw an ace
x46% chance that there is 46 aces and 46/52 chance that you will draw an ace
x47% chance that there is 47 aces and 47/52 chance that you will draw an ace
x48% chance that there is 48 aces and 48/52 chance that you will draw an ace
x49% chance that there is 49 aces and 49/52 chance that you will draw an ace
x50% chance that there is 50 aces and 50/52 chance that you will draw an ace
x51% chance that there is 51 aces and 51/52 chance that you will draw an ace
x52% chance that there is 52 aces and 52/52 chance that you will draw an ace

If you calculate all the probabilities x0% all the way to x52% (and you can) and multiply with the probability of drawing the aces as above, then add them all up to get the total probability of drawing an ace, then the answer is;
(a) 1/13
(b) 4/52
(c) 208/2704
(d) all of the above

Now if some third party intervenes before you draw the ace and tells you which of the cases above applies - e.g. "there are 5 aces" - then you know your probability is exactly 5/52.

But without that information we use the information we have - i.e. that each card was drawn from a separate fair deck - and calculate it exactly as above.

I will paypal you $10 if you work out the probabilities above correctly.

I do not want your money David thanks.

Have you ever heard of the word Paradox?


''a seemingly absurd or contradictory statement or proposition which when investigated may prove to be well founded or true.''

I have just explained this elsewhere and the reasons why a Paradox exists.

Your odds are totally correct, I can not argue your assumptions. However!

If we have 52 deck of cards, and all the decks are shuffled, we then take the top card from each deck and keep these values hidden. We place this new deck into a lottery type draw machine keeping the values hidden.


We will call the machine , machine Y.

You will agree that every top card off each of the 52 decks has a 1/52 chance to be any specific value.

We place these cards in the machine, we know that each card of the 52 cards in the machine has a 1/52 chance of being any specific value,

but also the paradox is we also know that each card in the machine has a 1/52 chance of being the same value.



Deck 1, card one, a 1/52 chance to be any specific value


Deck 2, card one a 1/52 chance to be any specific value


Card one a 1/52 chance of being the same value as card 2 a 1/52 chance


So put 52 random picked cards from 52 packs of cards in to an independent deck, the odds are 1/52 and ''1/52'' at the same time.

This is gibberish.

It is not has you put it gibberish

1/52=1/52=1/52=1/52=1/52=1/52 etc etc 52 times, each card has an equal chance to be the same value card.

I accept that to some people this would seem counter-intuitive. It is not so to me, or most posters in this thread.

Here's a paradox for you; consider the game where I flip a coin a number of times until it comes up heads. If it comes up heads the first time, I pay you a dollar. Every time I flip tails, the prize doubles, and keeps doubling with every tails flip until I hit heads and pay you.

How much would you play to play such a game?

Ok.

So, to clarify: We now have 52 cards on the kitchen table and each of such 52 cards has a 1/52 chance of being any card that would be found in a standard playing card deck. Am I correct?

yes and each card also has 1/52 chance of being an identical card to any of those on the kitchen counter.

You draw a second card , it has a 1/52 chance of being the same value card as you first drew from the kitchen counter even though there is only 51 left.

I have no idea what you mean by the bold bit?

Cool ... I am following so far.


I put my hand on one of the cards on the kitchen table. What are the chances such card is the Ac?

1/52

Hmmm ... ok.

What are the chances such card is the Ad?

1/52