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Any clarifications, etc. from the wise heads here are welcome.


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You miss a key point and miscontrue the process.

Key point: they do not pick a random deck and deal from it. They deal random cards from a deck, with new randomness injected at each stage where cards are randomly drawn. It's not random decks being chosen; it's random cards.

The Paradise page is a little confusing in that regard. They start by noting that most sites use [ QUOTE ]
either a single-pass full Knuth shuffle, or an incremental Knuth shuffle (which is essentially the same, but does the work as cards get dealt).

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They don't clarify at this point that they use an incremental approach, but their comment at the end makes it clear:
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The updated seed is used for dealing cards during each card dealing round

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As you know, several rounds of cards a dealt in a single hand.

The key here is that there is time for random data to be injected into the seed between rounds of cards. That means that the seed is different when the flop is dealt than when the first two cards are dealt, and it's different again when the turn is dealt.

Party accomplishes the same thing in a different way -- there are central random servers generating streams of random numbers, and tables which need to deal cards pull random numbers from the stream at the time they are needed.

In either case, two critical facts emerge:

1. Because timing and other random factors affect future cards in the very same hand, you can not use the currently dealt cards and knowledge of the random functions in use to determine future cards. I've written about this on this Random Number Generator Wiki page.

2. This also means that you can't tell what "would have happened" if you stayed in a hand vs. folded. If you went back in time and made a different play, the different timings, movements, server delays, etc., would result in a different random card being dealt for the turn and river. This is unlike B&M poker, where the turn and river cards are pre-determined when they shuffling is done. It's also healthier for poker players! I wrote about that on a wiki page called Free Your Mind.

The right way to play poker is to decide based on the current situation (cards on the board, cards held) and all the POSSIBLE next cards. The wrong way to play is to decide whether you were right based on the card that actually came. If you fold JJ against an AK7 board, the fact that a J fell on the turn does NOT mean that you were wrong "this time." You are NOT sure you would have turned a set. If the river comes down a J as well, it does not mean you "would have had quads!" If you had stayed in, the turn card would have been different. The chances that you would have turned a set were about 2 in 47, regardless of the fact that you saw a J come down.