I picked up Longshot at Gencon this year. My girlfriend trains eventing horses so it was a way to get her interested in my gaming hobby, and it worked.
Longshot is a ton of fun, it is fairly quick and exciting and the system it uses for betting is great.
On your turn you have to decide between playing a card, buying a horse, or placing a bet. cards have all kinds of abilities that either give you cash or move horses, or sometimes give you free bets, but the balance between changing the race and placing a bet is built in and works very well.
I would definitely recommend it.
Also the game says it supports a minimum of three players but we play it two player quite a bit and it works without any modification, the horses just spread out a little differently.
Once you play the very nasty horseracing game all othr racing games with betting pale in comparison. That is of course if you a just a bit meanspirited.
I bought Longshot at GenCon as well. We've played it a few times and it is a fun game. The problem we seem to run into is that certain horses don't get moving very much, even after people have bought them. When I play it two player, each player covers two owners. I do like how they balance betting with buying horses or playing a card. It is a nice tight system.
Turf Horse Racing
is a great little fun game by Knizia from the 90s, recommend it for a 45-60min fix.
Then there's the already mentioned
Really Nasty Horse Racing Game
and
Totopoly
, both games I own but both unplayed due to the 'family' nature of them making it hard to get them to the table against the hundreds of other games my limited opponents (and me) want to play.
And then there's the established
Win, Place, and Show
.
A vote here for WIN PLACE & SHOW. Probably the best 6p gaming experience I've had. Assuming you don't play with dicks and can skip all the "Foul" rules for people pulling their horses up short (to make bets), it's awesome.
WP&S is awful; from what I remember you have two race 'decisions' to make, the type of jockey and something else, and it's obvious which is best. I've also been repelled by it due to encountering someone who recorded every single game in order to gain some 'insight'! And if an APer is present it sucks even more mightily. (Yes, I now have an unreasoning hatred of it.)
I was really underwhelmed with Longshot the few times I played it. It was decent enough that it made me want to play a really good racing game, but it clearly wasn't it.
Lots of Euros seem to be thinly-disguised racing games. The victory point track is basically a racetrack, and players are betting resources on various strategies.
REALLY NASTY HORSE RACING GAME and WIN, PLACE & SHOW are very similar except in one you have cards in your hand during the race and use them to cheat to the win and in the other you have cards in your hand that you play when you suspect someone is cheating their way to the loss.
I like Manila for the large number of things you can bet on. You can bet on which smugglers will finish the race and in what order. You can speculate on the goods they carry. You can even gamble on the long odds of piracy. It's pretty Euro in it's presentation but don't let that fool you.