I'm really confused by this question.
If you're asking about probability of making a draw, then it doesn't really matter if the hand is dealt HU or 10 handed (as our opponent's cards are an unknown entity, just like cards in the deck). The only major difference is that in a full ring environment, we can make more educated guesses as to our opponent's holdings to add or subtract equity from our own (ex: you bet turn with the nut flush draw and get raised, a 3rd player calls two cold, we can say that our opponent has two of our "outs" a reasonable amount of time, while if everyone folds, it's more likely that our equity is slightly higher than pure random). DougL addresses this general idea well.
As far as betting, I'm also confused? The math behind betting has to do with your hands versus the range of your opponents, while the math behind calling is an equity calculation (as in, you bet into a 3.25 bet pot on the river because your opponent is folding > 23.5% and it is immediately profitable, or you call this bet in a now 4.25 bet pot because you're winning > 19% of the time). As far as chasing your draw goes, you should always just default to dividing the number of "non-outs" you have by # of "outs" to get your needed pot odds (in the case of a flush, you're 37:9 on the river to make it, close to 4:1). So if there's 4 bets in the pot for every 1 you have to call, you should call absent a compelling reason (like you suspect you have a dominated draw w/ RIO).
If the pot is simply too small to chase (ex: 4 way limped, flops checks through, guy bets turn w/ his top pair, you're getting 3:1 not accounting for rake), then you should feel happy that these guys aren't charging you to make hands. You can always splash the pot before the hand, then you'll be guaranteed to have profitable calls with your flush draw on later streets
. Of course, this makes no sense, because we don't like putting money in with the worst of it. We'd much rather see another card for free.