In determining the odds of making your hand on the flop, most players simply calculate the odds of the scenario and compare these odds to the pot odds. This indicates what the "mathematically" correct move is. If your pot odds are higher than odds of completing your draw, you call. If the drawing odds are higher than the pot odds, you fold.
However, many players mistakenly calculate the drawing odds on the flop on the presumption that they will have 2 chances (the turn and the river) to complete their draw. The truth is that, in many situations, it can be mathematically correct to call on the flop, but fold on the turn if you miss your draw. In these situations, you must re-evaluate your odds on the flop and re-calculate them on the basis that you will not see the river card.
Failing to re-evaluate your flop odds when you intend to fold if the turn doesn't complete your draw can be the difference between a winning and a losing decision.
The MathematicsLet's start with a basic example: heads up with a draw
1) You are in a $20-$40 game.
2) You are in the big blind.
3) Everyone folds around to the small blind.
4) The small blind calls.
5) Therefore, before the flop, there is $40 in the pot.
6) You flop a flush draw (four diamonds).
7) On the flop, your opponent bets into you.
A person with an understanding of hold'em and mathematics/odds would look at this situation and indicate that a call is 'technically' correct. On the flop, there is $40 + the small blind's $20 bet = $60. Therefore, you are being asked to call $20 to win the $60 in the pot. Since you are getting 3-1 pot odds on the flop, it is therefore profitable to call because you are 2-1 against making your flush.
The mathematics is wrongWhile the mathematics "theoretically" appears to support a call on the flop, you should fold. You are actually taking the worst of it. In mathematical terms, the odds of making your flush on the turn are approximately 4-1 against. Similarly, the odds of making your flush on the river (if the turn card is not a diamond) are approximately 4-1. In other words, you have 2 shots at winning when you are 4-1 against. This means that OVERALL you are approximately 2-1 to make your flush on either the turn or river.
So how is the mathematics wrong? To put it simply, the method of calculating the odds used above assumes that you have two chances (the turn and the river) to make your flush.
If you do not make your flush on the turn and your opponent bets into you again, you would be taking the worst of it by calling. Look carefully: if miss the turn, you are a 4-1 underdog of making your flush on the river. If you called the flop, the pot on the turn would be $80 + the $40 bet from the small blind. Therefore, you need to call $40 on the turn to win $120. In other words, you are getting pot odds of 3-1 while you are a 4-1 underdog. This is an automatic fold.
Here is the key: if it is always mathematically correct to call on the flop but always correct to fold on the turn, you must re-evaluate your odds on the flop. You must recalculate your odds on the flop on the presumption that you will not call the turn if it doesn't complete your draw. In other words, you calculate your odds pretending that no river card will be dealt.
As a result, your drawing odds on the flop and essentially the odds of making a flush on the turn ONLY. If you flop a flush draw, the odds of improving to a flush on the turn is approximately 4-1. In the above example, you are getting pot odds of 3-1 on the flop. This is a clear fold, rather than a call.
While the example above is a flush draw, this method of thinking can apply to any situation where you will either hit your draw on the turn or fold if you miss. Whenever this arises, re-evaluate your odds to take account of the fact that you will not see a river card with your hand (ie. Calculate it on the basis that you have only one shot at making your draw).
Implied oddsSome professionals may disagree with my advice on the basis that the implied odds will make up for the shortfall in odds on the turn. However, I think you need to be realistic about the prospects of attracting a lot of action if you make your draw. For example, if you call the flop and the turn is the flush card, your opponent will be very careful if you start betting or raising. They are not going to throw you a lot of action in a small pot without the nuts. Further, they may even fold when you raise.
As such, the implied odds argument would, at best, result in an even money proposition on the flop and, at worst, not improve your pot odds on the flop whatsoever. In either case, it is still not worth pursuing unless you are up against an extremely loose aggressive player who will give you mountains of action if you hit the flush.
Exception 1: Opponent routinely bets the flop and checks the turnThis involves observations of the opponent in question. Some players have a habit of always betting the flop with a reasonably good hand, but always checking the turn, even if the turn card does not appear to have helped anyone. This sort of player is commonly described as 'weak' or 'weak tight.'
Against this sort of player, always call the flop with a flush draw, even if you are in one of those situations where you couldn't call a bet on the turn if the turn card doesn't help you. This is because your opponent, in all likeliness, is going to give you a free look at the river if you call the flop.
Exception 2: Over cardsThis is more of a friendly reminder! If you have 7d-8d and the flop is Kd-Jd-3s, it would seem that only a diamond will give you the winning hand. However, if you have Ad-Qd and the flop is 4d-7d-10s, any diamond, an ace or a queen may give you the winning hand. With these additional six outs in the latter situation, your odds of winning are much better and you need to take account of that. In this situation, you may even be correct in calling the turn, even if the turn card doesn't help you.