Lets break this right down.
1 - If they have an automatic shuffler, it does not slow the game down at all. You just place the cards in the chute at the back of the shuffler and it processes them in automatically.
2 - Yes you do have the same chances of red and black, no matter what the previous outcome. But of course none of them will come in 1,000,000x red in a row. Its possible, but improbable.
3 - People do play 1,2,3,4,5,6. According to lottery statistics, over 10,000 people in the UK each week play those numbers. And why is it more unlikely? Each ball has the same chance of coming out. The odds of hitting any 6 numbers from a 49 number draw is jut over 14million.
4 - I talk about poker math as it is definitive.
5 - If I see 100 hands to the river in a row, I will hit a flush 6.4 times.
6 - If i hold 2 cards of a suit, and 2 more are on the flop, I will hit a flush 36% of the time generally. And this is entirely true. It might be 1% up or down over a life time, but not by a significant number.
7 - Technically you can miss every draw you have. But thats almost impossible too. Im not saying it IS impossible, as mathematically speaking there is a chance of that, just like there is a chance you are winning this arguament, but I would bet that I will hit my flush draw at least once in a life time from here on our. In fact, maybe twice!
Much love