Say you are playing a 6 max holdem game and you have a flush draw on the flop. Say you have 10 J diamond and your opponent has 2 black AA. Flop is 2d 7d kh. the calculation says you have 9 diamonds left to hit (13 diamonds - 2 diamonds your holding - 2 diamonds on the flop). Now wouldnt a more conservative and accurate estimate be that you have 7 diamonds left to hit? If you are playing with 5 other players (10 cards) and 1 out of 4 cards is a diamond, that means that a conservative estimate would be that there were atleast 2 diamonds in the other players hands. So instead of 9 diamonds left, there would more likely be 7 left.

thoughts?

No, with diamonds showing in known cards, it just means that opponents who are mucking will have fewer diamonds on average.

There is one interesting way to get some extra information with regards to FDs. Lets say several players get to the flop and you have a FD on the button. EP player bets and you see 3 quick folds. It's pretty clear none of the three had a FD themselves so you can assume at least one card in each hand wasn't your suit. This means you can reduce the stub by 3 when calculating odds for your FD.

This topic is covered in the sticky. Basically the fact that there are non-diamond cards also mucked/dealt means that on average the ratio of diamonds to non diamonds is equivalent to assuming no other cards have been dealt from the deck.

The 9/unknowns calculation gives you the correct frequency that the flush will complete in the long run. Unknowns in the muck or in other hands are no different than unknowns on the bottom of the deck. They are still randomly distributed.

A similar explanation is the burn card. If the dealer did not burn a card do you think the probability of hitting changes? What if he burned two cards?

If he burns a card, yes, it could have been a flush card, so the hit probability will in fact decrease. BUT, he could have burned a non-flush card so the hit probability increases. We don’t know what he burned but it can be mathematically shown that the two possibilities balance so we can just act as if there was no burn card or, as NewOldGuy said, we can think of the burn card being in the bottom of the deck.

I'm sick of these threads over and over again. Someone should sticky the burn card solution. It's quite fascinating to see different thread titles all the time though, they always manage to intrigue me to click the link.

This is well covered in the FAQ, so closing it up