MA215 Shuffles

A card deck is shuffled if the cards are not in a pre-determined order.
A shuffled deck is a deck where the ordering of the cards is based upon a random element and the order is not known. This is achieved by throwing the cards on the ground and picking them up on by one.
My definition of a shuffled deck is a deck whose order of cards is different than the starting order of the cards. The knowledge of the order does not determine if it is shuffled. A good shuffle would rearrange the cards into a new order where no cards are in the same order as the starting order.
Assuming the shuffling process involves an element of randomization, shuffling a deck will randomly and indiscriminately place cards in new positions. A shuffled deck is where each card has equal probability of being in a given position in the deck.
A deck in which all cards are randomly arranged, and the position of each card is unknown and completely independent of all cards preceeding or following.
A shuffled deck is one that has been mixed together so as to make a random order of arrangement. You know that the deck has been "shuffled" when the probability of the next card in the deck is equal for all cards.
A shuffled deck is a deck in which each card has been moved to a different location in the deck. A person walking into the room would have no idea that the deck had been shuffled, until he or she would witness a shuffling. I don't think that each card has to be in a different location, but a majority of the cards should have changed locations.
A shuffled deck exits when the order that the cards had before being shuffled is changed to a new order where the principle being used to order the cards is different than the first. For a deck to be shuffled you can't know the layout of the cards.
I would consider a deck of cards to be shuffled if there was no repeating pattern that could be determined based on the order the cards were in.
A deck is shuffled if and only if all those using the deck have an equal probability in guessing the same card.
Factoring a fallible person a deck of cards is completely shuffled for a specific person when said person's ratio to predict the next card is 1 to the number of cards remaining within the deck. If this specific person's ratio is better than 1 to the number of cards remaining in the deck, then the deck is not completely shuffled, but instead a particular degree shuffled dependent upon the predictability.
In order for a deck of cards to be "shuffled" they must be in a random order. A Totally random shuffle can not be achieved.
A shuffled deck is one in which any card has the same probability of appearing at any point in the deck as any other card. The cards are in a random order, with no predictable pattern in their order.
A deck is shuffled when it has been mixed together enough in reference to the person shuffling. What is shuffled to one person may not be to a person who just walked in a room. It could be considered shuffled when a majority of the cards have been moved from their initial position and placed in a new disjoint cycle. Repeat until the number of disjoint cycles reaches the highest number of disjoint cycles.
I believe that there is no such thing as a shuffled deck. The first reason being that everyone's opinion of a shuffled deck is a little different and even in some cases people themselves have multiple definitions of shuffled. Secondly, there is no way with any number of cards that a definable pattern won't be produced as was demonstrated in class with the three ways the so called random cards were picked. Finally, if a deck ever was found to have seemingly no defined pattern, it would not stop a person from memorizing that "shuffled" deck.
A shuffled deck is a deck that has been rearranged. Therefore any deck of n cards can be shuffled.
Cards are shuffled as long as you don't look at the cards and you do not know the order of the cards.
A shuffled deck is when you mix the cards up in such a way you have no idea what the order of the cards will be.
A deck may be considered shuffled once the cards have been rearranged in a non-precalculated way so that the new order of the cards is unknown to call concerned parties.
A shuffled deck can be any arrangement of cars but an obviously predictable pattern may cause me to suspect the shuffler is trying to cheat me.
A shuffled deck is one in which the order of the cards are changed in a non-predetermined fashion.
While reaching a definition of a shuffled deck of cards having universal acceptance is impossible the following assertions should be made in determining if or if not a deck is shuffled
  1. The probability of card n being alpha is equal to the probability of card n being equal to beta, for any alpha, beta in the deck of cards.
  2. Given the last known state of the cards, the current state of the cards is different.
  3. No easily recognizable pattern can be found which would allow someone to conclude the value of card n, given a small number of preceeding cards; say three values.
  4. Some random variable is involved in the function which converts the deck at time n to the deck at time n+1.

Shuffling a deck of cards mean to rearrange the order of the cards so that at least 90% of the cards are not in the same position they were in and they are not in the same order. Along with that, the card before and after any cards that is being observed has the potential to be any card in the deck other than that particular card.
I believe that the primary definition for the cards being shuffled is that at least one card has changed position with respect to its original position within the original order of the deck.
A shuffled deck is one that has been assembled in a random manner. This cannot be determined by looking at the order of the cards, but can be determined by what has been done to the cards.
To shuffle a deck means to randomize the order of the cards.
A deck is shuffled when it changes the original order of cards.
As long as any member of a card playing group has foreknowledge of the cards' order or locvation the deck has not been shuffled. In addition if any order can be determined in the placement of cards after the fact, then in all likelihood it was not shuffled.
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