Currently reading: Exotic Betting .
I find in life there are a lot of contrarian positions you can take in which you would be surprised how many times you are correct. It would be mundane as all hell for things to go the way you planned... sprinkle in some volatility for a good time :).
I've been particularly interested in horse racing as of recent. WARNING: Gambling is a losing deal in the long run, but the idea of contrarian (exotic) positions is to catch that rare (and more common than not) spurt of insane upside, resulting in an illustrious sense of accomplishment, or.. just another day at the track.
The house always takes its portion (~15%) during every race. The longer you bet over many races, the more likely you are to lose money. This is rule number one of gambling: the house always wins in the long run. No one can escape the law of large numbers. No one. That's why it's a law.
Keep this pool chart as we progress through some examples:
Exactas / Trifecta / Superfecta Tips & Strategies
- NEVER BOX YOUR BETS / NEVER USE ALL. There is no point making these exotic bets unless you have an opinion. Otherwise, you are diluting the pool of bets (and your win bets) trying to get lucky. We are trying to beat the pool payouts, remember?
- If you're lost on any bets, trifecta is a terrible idea. Trifectas are all about eliminating horses from contention.
- Betting a favorite in any of these exotics, severely depresses the payoffs in that single race, since that's where the pool's money is.
- Exactas to increase win odds without increasing risk. Put your hero (4-1) first, and run the favorite and 2 long shots that you like in second. This avoids the win pool of the favorite, multiplying your odds. Let's avoid following the crowd.
- Exactas to bet contrarian against the 1-1 favorite. Run a variety of exactas (different weights based on odds) with your hero and 2 long shots that you like. When the favorite misses the board, there is a phenomenon where the exact pays more generously than expected.
- Exacta (Contrarian) Situation: Skeptical of favorites but too confused to construct an aggressive play. Key 2 wing-and-a-prayer longshots (2nd to worst odds and 5th to worst) with 4 or 5 others on the field, leaving the favorites out all together.
- Trifecta small boxes: Usually players will play trifecta if they like 3 horses. It's far more likely for 2 to run their usual race and for the third to drop out. To accommodate this contrarian position, require 2 of your horses to hit the board and be loose on the third. Bet 1-2-3, 1-2-4, 1-2-5, and 1-2-6 boxes.
- Trifecta small part-wheels: Focus on 1 horse to place and then wheel the third slot. 1/3,5,7/3,4,5,6,7 and 3,5,7/1/3,4,5,6,7. We sacrifice the third place and gain additional horses.
- Trifecta aggressive punches: Do these every now and then to win big and when you're confident. $1 box 1-2-3, $1 box 1-3-4, $3 part-wheel 1/3/2,4 and $3 part-wheel 1/2,4/3.
- Superfecta: Key one to win and then bet a trifecta underneath.
- Superfecta variation: Key 2 with 4. 1,2/1,2/3,4,5,6/3,4,5,6 - 24 combinations. 1,2/3,4,5,6/1,2/3,4,5,6 and 1,2/3,4,5,6/3,4,5,6/1,2 for 72 total combinations.
Lastly before you make your exotic bets, make sure to bet superfectas in $0.10 amounts and trifectas / exactas in $1 amounts. This is due to another house, the IRS.
IRS rules require that winnings at odds of 300-1 or higher be reported to the government, if they exceed $600 and that the payoffs are subject to withholding if they total $5000 or more. 
Don't worry though, you can always repeat the bet. Think of 2 $333 winning tickets and ducking the $600 tax ;).
Best of luck contrarians.