Quote from: DeathAndTaxes on July 09, 2014, 04:59:25 AM

I ended up with the following:
TdKh6sAc5s8hJcJs5c6h3s9s7cQsQh4s9h3c4h4c2hTs3hJh9c5hKc2cTc7s4dAh9d2dJdQdAd7hTh5d2s8c7dAsQcKd3d6d6cKs8s8d

Not too bad although there is a big clump of diamonds near the end.

A clump of identical suit or a few cards in a row are to be expected in a truly random shuffle (just like hot streaks and cold streaks are expected in a truly random game).

Exceptionally large clumps might be a concern, but I'd also be a bit concerned about predictable patterns or general movements of cards throughout the deck.

As an example. Imagine an Ace of Diamonds on the bottom of the deck. Now you split the deck in half. The Ace of Diamonds is on the bottom of one of those two halves. You riffle shuffle the deck. Assuming a perfect riffle, there's a 50% chance that Ace is still the bottom card, and a 50% chance it is second from the bottom, right?

Split the deck and shuffle again. There's now a 25% chance that the Ace is still the bottom card, a 25% chance that it is second from the bottom, a 25% chance that it has now moved up to 3rd from bottom, and a 25% chance that it is 4th from bottom.

A third riffle, and we are looking at particularly good chances of it being in the bottom 8 cards.

A fourth riffle, and the chances are that it is in the bottom 16 cards

A fifth riffle, and the chances are that it is in the bottom 32 cards.

And with the sixth riffle, it could be anywhere in the deck.

This all assumes a perfect riffle where the cards exactly alternate right and left sides, and the only random factor is whether the shuffler drops a card from the right side first or the left side. This is probably why it is frequently said that 9 riffle shuffles result in a well shuffled deck.

But if we introduce a human bias and say that the shuffler always holds the bottom half of the deck in their right hand and nearly always drops a card from their right hand first... You could riffle shuffle that deck 100 times, and there'd still be a really good chance that the Ace of Diamonds is the bottom card (or at least very close to the bottom) of the deck. There'd also be a really good chance that the top card hadn't moved very far at all.

It would be interesting to run the test a few hundred times and plot the end position of the cards that start at the bottom and top of the deck. I wonder if you'd see a tendency for those 2 cards to end up in particular areas (or to avoid particular areas) of the deck.

Quote from: DeathAndTaxes on July 09, 2014, 04:59:25 AM

Adding a wash at the beginning and mid sequence cut and additional ripples would probably improve things but I would be pretty confident using this sequence as an entropy seed (well not now that it has been shared).

A wash would probably make a very big difference. Starting with an already used deck would help a lot as well.

Quote from: DeathAndTaxes on July 09, 2014, 04:59:25 AM

One thing that occured to me is if the client asked the user for the actual card sequence it could run a statistical analysis and warn the user of a sequence which may show signs of insufficient shuffling.

Perhaps. On the other hand, identifying a particular person's bias might be difficult. A larger risk would be if a person used this process many times to generate many seeds for various purposes. It might be possible to significantly reduce the search space on all their other seeds if you can get your hands on any one of their sequences.