Suppose you want to calculate the equity for a hand 4 and 8 (the color does not matter). The cards on the flop are A,2,3. To calculate the probability to have a straight you first consider the outs for a 5. Here the outs are 4. With the usual methods you multiply by 2 to get the probablity to get a four at the turn and by 4 to get it at the the river. However what I am considering is that on a table of 9 players, there are 5 known cards on the flop (your hand and the 3 on the floop). There are 16 cards of the total 47 unknown cards that are on the players hand (8 players x 2). Therefore the probability that the card that you need, 5 in this case, only has a probablity of 31/47 to be on the "remaining cards yet to be played" at the table (since 16 of 47 cards are on the players' hands). Therefore when you you multiply the outs for a Gutshot straight by four and get 16% shouldnt you also multiply by 31/46 considering the possibility that this card could be on the players' hand ?
Consider an extreme case which there are 22 other players and only one card remains to be played your odds in this case to get that one card you need is obviously very small. How does multiplying by 2 and 4 considers the fact that as the number of players increase your odds decrease