My advice for betting on horseracing's Triple Crown hasn't changed in 20 years and should be familiar to readers of this site. I support the strategy that over time one should make bets of good value more than grinding out as many wins with poor return as might be available. The Kentucky Derby has way too many horses running for me to feel comfortable with any favorite so I try to find a couple of horses about which I feel positive whose betting line is in the 15/1 to 30/1 range. At the Preakness I bet the Derby winner if their betting line is greater than 6 to 1 or if I won money on them at the Kentucky Derby. I also take a serious look at local horses to show. At the Belmont I'm all about the longshot, particularly if one did inexplicably well at a track and/or distance similar to what you're seeing at that event.
And that's about it. Wear a hat. Have a cocktail. Enjoy the day. Horse racing is for those who think baseball has too much going on. I'm not a good gambler but I'm an enthusiastic amateur and I'm way, way up on a lifetime of occasional hunch bets. The most important thing is to have fun. Bet to direct your cheering and potentially upgrade your dinner plans, not to make cab fare home or to make enough money to afford dinner. If you're at the Kentucky Derby itself, bet an Oaks/Derby ticket and sing "My Old Kentucky Home" at full volume. That's a fun song to sing full volume.
Update: A pair of readers have pointed out the ugly past of "My Old Kentucky Home."