For most players, it won't change the game one bit. After all, very few gamblers have either the bankroll or the desire to make a $5 bet and back it up with $5,000 odds, or anything close to that. And players that don't bet that much but still bet a lot likely already know where to find casinos dealing odds multiples high enough to satisfy their needs. But it's significant when considered from the casino's perspective, in that the Riviera is willing to accept a whole lot of risk for an extremely low tariff.
In just an hour's time with these rules, a gambler who wanted to "take a shot" could get down $100,000 or more in action. This would likely result in a win or loss of thousands of dollars, but generate an expected loss of less than $2! Casinos aren't in the habit of accepting that much risk with such a razor-thin edge, so this is a ballsy move on the part of the Riv any way you look at it. And what is that advantage? Here's how it breaks down.
Since a winning odds bet in craps is paid at true (correct) odds, the casino has no advantage on this wager, a fact that has led many to refer to it as "free odds." But that's a misnomer. Odds are not free, because you can't make an odds without first making a line bet with its attending casino advantage. Used properly, though, the odds bet works to water down the casino edge on your total action; and the more odds you incorporate into your game, the lower the overall house edge becomes.
Specifically, taking single odds on a bet of any amount lowers the 1.4% casino edge on the pass line to .8% (on the average amount wagered on the line and odds combined). Double odds lowers it further to .6%. The edge on a game with 100X odds is just .02%. And the Riv's 1000X has a casino edge on the pass line of just .002%.
Due to this effect, it makes sense for players to incorporate odds into their game. For example, assuming your gambling-stimulation level requires a $10 bet, it's better to wager $5 on the pass line and back it up with $5 odds than to bet the entire $10 on the line. With a line bet only your expected loss is 14¢, but with $5 on the line and $5 behind in odds it's only 7¢, because half the bet is on the odds with no house advantage. Betting $1 on the line and backing it up with $9 would be better yet (an expected loss of 1.4¢), but the Riviera house minimum doesn't allow a $1 initial bet.
The best way to play craps anywhere is to decide how much you want riding on each wager, then bet as little as you have to on the line to get the rest out in odds. With the Riv's policy, that pretty much means you never have to bet more than the minimum. But remember, no matter how much in odds you take, this strategy will never give you the advantage over the casino and you'll essentially be flipping coins for your money.
Note: While this discussion pertains to taking odds on pass and come bets, you can also lay the odds to win 1000X your initial wager on the don't pass and don't come (the casino edge is slightly lower on the don't side).
