In Texas Hold'em there exists certain situations where a big draw is favoured over a hand like top pair on the flop. These situations generally arise when one player has 13 or more outs and his opponent has limited or no re-draws.

Consider the following:

Poker Stars
No Limit Holdem Ring game
Blinds: $1/$2
6 players
Converter

Stack sizes:
Hero: $123.90
UTG+1: $208.70
CO: $159.05
Villain: $373.60
SB: $107
BB: $129.55

Pre-flop: (6 players) Hero is UTG with 4♦ 5♦
Hero calls $2 (pot was $3), UTG+1 calls $2 (pot was $5), CO folds, Villain raises to $10, 2 folds, Hero calls $8 (pot was $17), UTG+1 calls $8 (pot was $25).

Flop: A♦ 5♠ J♦ ($33, 3 players)
Hero checks, UTG+1 checks, Villain bets $30, Hero raises all-in $113.9, UTG+1 folds, Villain calls $83.9 (pot was $176.9).

Turn: Q♣ ($260.8, 1 player + 1 all-in - Main pot: $260.8)

River: 7♥ ($260.8, 1 player + 1 all-in - Main pot: $260.8)

Results:
Final pot: $260.80
Villain shows Ah Kc and wins $257.80 with a pair of Aces

First of all, let's address the pre-flop play. Our hero initially limped in, under the gun, with a weak suited connector. This is not a fantastic play, but in a short-handed game assuming the table is not too aggressive it may be worth seeing a flop with this type of hand every now and then. Also, people tend to be suspicious of an under the gun limper, so they're less likely to raise with junk. After the villain raises to 10$, the hero decides to call and see a flop. Again, this is not fantastic, but not horrible either. The idea being that the villain has a lot of chips and if the hero can hit the flop hard, he may be able to double through.

When the flop comes, it's not really the hard-hitting board our hero was hoping for, but there is some potential. The check is pretty standard as our hero is out of position in a 3-way pot and someone else has taken the lead pre-flop. When the villain bets 30$ on the flop, he is basically representing an Ace. With bottom pair, the most sensible thing to do would often be to fold. So, why would our hero go all in? Well, if he is correcting in believing that his opponent has the Ace, then our hero has 14 outs to best his opponent (two fives, three fours, and nine diamonds). He is about 28% to hit one of these outs on the turn, so the pot is not really giving him the correct odds to call. However; with 2 cards to come our hero is slightly better than fifty-fifty to outdraw his opponent. Therefore, if he goes all in and gets called he will be mathematically ahead and have a positive EV. Here are the numbers to back it up:

http://twodimes.net/h/?z=1664280
pokenum  -h 4d 5d  - ah kc  -- ad jd 5c
Holdem Hi: 990 enumerated boards containing 5c Ad Jd
cards  win   %win  lose  %lose  tie  %tie     EV
5d 4d  505  51.01   485  48.99    0  0.00  0.510
Kc Ah  485  48.99   505  51.01    0  0.00  0.490

($257.80 * 0.510) - ($113.90 * 0.490) = +EV $75.67

So, since the math supports it, going all in is certainly the best move right? Not necessarily. Here's the problem with this kind of situation; the math only supports this play after our hero has commited a considerable amount of money in order to create a situation where he has a slight edge. In effect, one could say he has created an "Artificial Edge" by throwing a whole lot of money into a pot he should probably not have been involved in to begin with. The only redeeming quality of this type of play is the folding equity that it carries. But, your average online 1/2 player with a fat stack isn't going anywhere with top pair and a strong kicker and that's what makes this play so weak.

Consider the same hand only instead of having 4♦ 5♦ preflop, our hero actually has pocket fives. Now he would be in a position to double through the villain since the villain has shown a willingness to put a lot of chips in the middle with only top pair. In essence, with pocket fives, our hero would have risked a small amount of money to gain a huge advantage. So, if you know that you will have a much better opportunity to make money off your opponent down the road, then there is no need to manufacture these small edges by putting your whole stack in jeapordy. If you look at the numbers, there is just no comparison:

http://twodimes.net/h/?z=1664327
pokenum  -h 5s 5d  - ah kc  -- ad jd 5c
Holdem Hi: 990 enumerated boards containing 5c Ad Jd
cards  win   %win  lose  %lose  tie  %tie     EV
5s 5d  956  96.57    34   3.43    0  0.00  0.966
Kc Ah   34   3.43   956  96.57    0  0.00  0.034

($257.80 * 0.966) - ($113.90 * 0.034) = +EV $245.16

From now on, our hero should reserve this type of "move" for a situation where his opponent is an extremely solid player who can lay down his/her top pair-top kicker to a big bet, and who will not pay off our hero's good hands as easily. The bottom line is, against your average player, there is no need to be a hero because basic poker is the only edge you need. Conversely against the top players, you need to be aware of these more advanced plays so that you can make a profit.