Query - Poker Odds

[ron8]

Straight forward poker odds do not take into account the cards which the other players are holding, ie: A gut shot on the river is calculated as 4 divided by the 46 cards left in the pack = 11.5 to 1 shot. What I don't understand is this takes no account of the other players cards. For instance when playing a ten player table there would be 18 cards which are counted as being as part of the pack. These 18 cards represent almost a third of the pack and I would think there is a strong probality that one or more of the outs you are looking for are among these cards which would alter the odds drastically.
I would be very grateful for any help with this matter
All the best
Ron