Not sure how it works elsewhere but horse betting in the US is almost always parimutuel, meaning that everybody gets the post odds, regardless of when they bought their ticket. In other words, betting early doesn't give any advantage and in fact the later you can wait, the more accurate an idea you have of the actual payout odds of your bet. Thus, having access to a private betting machine, and not having to elbow other gamblers to buy a ticket at the last minute, is a real advantage.
That said, the state's take-out is so high in most states that you need a massive edge to actually make money. The slight edge a private betting machine would bring probably isn't enough.
If you bet at 10-1 here, your bet is 10-1 on your receipt, and your odds are 10-1. Your bet at that price may change the odds for everyone who comes later, but that doesn't affect yours. It is quite possible to arbitrage odds between bookmakers. Or it would be, if they didn't do such a good job of conferring and mutually underwriting their risk themselves.
It must be crazy having the odds change on you after your bet.
Yeah the whole idea of parimutuel betting is that there is no "bookie" and that you are betting against the other gamblers. No central entity is taking a side in the bets. This makes sense when you realize that the central entity is, for example, the State of Kentucky. Do you want a bureaucrat making millions of dollars in bets on behalf of taxpayers? Probably not. Instead, let's just collect all the bets from race fans, take out say 5% for the state, and then pay out to the fans holding tickets for the winning horse (forget about exotics like exactas and trifectas to keep things simple, but the idea is the same). That way, we don't need to have handicapping experts set odds in order to ensure the state makes money. Instead, it's all simple math that can easily be audited and still guarantees a profit. The side-effect of this is obviously that you can't know the final odds until the last ticket has been sold at post time.
For Swedish harness racing there is only one bookie. The state has had monopoly on betting in general for a long time and is very strictly regulated also today.
So, there won't be any arbitrage across bookies for these races at least.
Everyone in the US can bet using his or her smartphone, with the current odds shown up the second the gate is opened. There's no advantage in a private betting machine. Some online betting tools even let you set parameters that place your bet automatically if and only if certain odds are reached, so you don't have to stand there and watch it. Of course, for casual bettors, that's half the fun.
That said, the state's take-out is so high in most states that you need a massive edge to actually make money. The slight edge a private betting machine would bring probably isn't enough.