Random or sequence does the math change?

Most poker is played from a deck of cards in sequence from the top down. If we used a fanned deck and drew at random would the probabilities or math change? Like in Holdem, we would draw three cards at random from the fanned deck and turn them over for the flop, ect.

[SheetWise]

Wouldn't change a thing.

SheetWise

[AaronBrown]

I agree with SheetWise if the deck is perfectly shuffled. If not, it would make a difference.

[SheetWise]

I have some wonderous equations and simulations pondering the randomness of a shuffle, and attempting to track shuffles ... but these days I simply take randomness as a given, without cause to think otherwise.

SheetWise

[llamaoo7]

This is an important point to bring up on a misdeal at a home game where someone deals to the wrong person first or only one person gets one card. I always say if you don't accept taking the first card off the deck as your second card, then you are pretty much accusing the dealer of stacking the deck or not randomily shuffling it.

[AaronBrown]

That's a valid point, but the rule uses the opposite logic. In draw poker, if a card is exposed in the draw, the dealer is required to continue giving every player the card he would have received without the exposed card; then the exposed card is replaced at the end. This prevents a dealer from perserving a stacked deck with a deliberate exposure when a player draws an unexpected number of cards.