Blackjack Side bet - does it matter full table or one-on-one with the dealer

I was recently down in Las Vegas. Lots of the blackjack tables down there were 21+3Xtreme! We all know that the side bets are sucker bets, but some places had a $1 min on them, so we freerolled with some little ones from blackjack payouts.

The idea is pretty standard for side bets, your two starting cards plus the dealer's up card.

It had the following payout structure:
Straight Flush: 30:1
Trips: 20:1
Straight: 10:1
Flush: 5:1

Let's just talk about the chances of hitting the Flush. Does it make a difference to the odds if you are HU vs the dealer (i.e. to payout 3 cards in a row need to be all the same suit) or if there is a full table?

Assumptions:
- 6 deck shoe (or infinite shuffle machine with 6 decks)
- doesn't matter which position you are sitting in

Makes no difference.

Why? Does distribution have no effect?

We tried to break it down like this ...

Have 8 cards total, two of each suit. Give one card to you and one to the dealer. So regardless of what suit you get, dealer has a 1/7 chance of getting the same one.

With another player, you get the spade; Second player has a 6/7 chance of not getting the other spade. Does that increase the odds of the dealer getting the other spade? Or is it still always 1/7?

It makes no difference because while having additional players at the table could have the cards you need, they could also be dealt the cards you don't need. It makes no difference whether the cards are dealt to other players or remaining unused in the deck, only your cards combined with the dealers cards result in a winner. Similar to the reason that it makes no difference in blackjack how other people play their cards as they could help you just as easily as they may hurt you. What the other players will be dealt is irrelevant when you make your bet, but after betting and having the cards dealt, if you are dealt two diamonds and no one else at the table is dealt a diamond, obviously your odds of the dealer turning a diamond are higher as more diamonds remain in the deck. But at the point of you placing your bet on the table (which you cannot do after the cards are dealt), it makes no difference how many people are playing.

It's still 1/7.

Imagine dealing all 8 cards out to 7 players and the dealer. The probability that you and the dealer have the same suit is still 1/7 - it doesn't matter about the other players at all.