I'm not sure if I'm posting this on the correct sub-forum.

If the deck of cards are poorly shuffled, but nobody has any information of the deck's arrangement, nobody should have any advantage right?

But, I'm wondering when the same deck of cards is played multiple times, poorly shuffled, in a live poker game, is it true that some outcome would be less likely? For example, some combination of starting hands would less likely happen?

I'm thinking this is true because when the outcome is not as random, the outcomes would not be evenly spread in the long-run.

Do you think there are degrees of random?

I'm not sure, I have close to zero knowledge about randomness.

I do. It's the focus of a field of mathematics, information theory.

And it's usually exploitable, for example a lot of cryptographic attacks take advantage of insufficient randomness in hashing and encryption algorithms.

In the case of an improperly shuffled deck, consider the easiest case. Let's say that someone opens a fresh deck and does a shuffle that is very bad, like you can see that there are big clumps of cards that are sticking together. In a case like this, if your hand has the 6s, then you should expect that it's more likely than usual that the guy to your right has the 5s and the guy to his right has he 4s and so forth.

In practice, it's going to be difficult, because even if the shuffle isn't perfect, you'll be starting with (usually) an unknown deck, and there will be multiple imperfect shuffles. Your initial state is unknown, the transform is unknown. A computer monitoring the situation might be able to gain an advantage, but a person probably won't.

Not that I recommend cheating, but as a practical example, in a home game where amateurs are hand-shuffling, it's common for a card that starts at the bottom of the deck to remain in the last few cards, because of how riffle shuffling works, especially if there are no cuts in between riffle shuffles. Now, once someone cuts the deck, the bottom portion will go into the middle. If it's a deep or shallow cut you can reason to yourself that this card will be more or less likely to be in play during the hand. It's a tiny advantage, but it *is* an advantage.

There's a (fictitious, but possibly based in reality) anecdote in the book "The Cryptonomicon", a fiction book by Neal Stephenson (which I recommend, it's quite good).

In WWII much cryptography was done using "1 time pads", where basically a random sequence is generated and given to 2 parties. One party can encode a message with the pad, and the other party can read it. After using once, it's thrown away. If the pads are not compromised, then it's a completely unattackable form of encryption.

Unless... the pads are not properly generated. In the anecdote, there was a building full of women pulling, I don't remember, bingo balls or something, and using those to make pads. But some women didn't like certain sequences or preferred other ones, so sometimes they would write a different number than what they pulled. A cryptanalyst realised this and was able to decrypt some messages by exploiting this weakness.

I may be mixing up more than one anecdote. Here's a brief summary that doesn't exactly match my recollection
http://derekbruff.org/blogs/fywscrypto/tag/onetime-pad/

Wouldn't this be a case of not actually being random?

Random isn't really what I'd call a binary situation. In information theory, the term "entropy" defines how much "randomness" or "how random" something is.

Also consider that random has a colloquial usage, and within that usage there are definitely degrees of randomness. If I ask you to choose a random number, your choice will not be as random as if I asked you to roll a die, and that probably wouldn't be as random as if I sampled white noise or something.

Consider degrees of randomness in the sense of "could I guess the outcome more often than probability suggests I would be able to, if it were completely random" which, I admit, is not an airtight/technical definition. But say, if there's an algorithm that generates a "random" number from 1-10, my odds of guessing the next number should be 1/10. If I can guess the next number at a higher frequency than that, it's not perfectly random.

@RustyBrooks, so, I'm assuming the answer to my question is yes?

The answer is "yes, but probably not in a way you can exploit"

Very interesting posts, Rusty. Thanks. Makes a lot of sense.

There are books written about beating various shuffles in games like blackjack. It is definitely possible to exploit weak shuffles, although not easy.

I expect it is possible to do in poker as well, especially with dealers who have either poor shuffles or extremely precise shuffles.