This has come up a number of times in a lot of threads (including the most recent one by Spooky Fanboy). So, to give people a break from thread-diving to find these ideas, I'm going to put them in one thread.

Bidding

As it has been termed a few times, one of the best strategies for Fastlane is to "bid against yourself." Cover the board with your bids. Put half your chips on red, half on black (or half on high, half on low, you get the drift) - then only if a zero comes up will you lose. And the zero is around a 5% chance, or less on the European wheel. If you have an odd number to play, you can always do 3 on the dozens or columns, and then split the remaining even number between the even money bets.

Assuming nobody sees any green, you'll get back exactly as many chips as you put down.

I call this "Playing It Safe." Any deviation from this will net you greater gains if you win, but losses if you fail.

Also note that if you use your style (and get a free chip), this will cover the erosion of facets that happens in the conflict, even if you Play It Safe. In fact, requiring the style to go on the outside ties into this strategy - you are playing it at least a little safe when being stylish.

Spending - Croupier

If a player plays it safe (as above), they can get back exactly the number of chips they put down, and bring them to bear in the conflict. The chances they do not are about the same as rolling a 1 on a d20. Still, you don't want to encourage a player to play it safe all the time - you want to encourage them to take risks. So spending chips equal to what the player is spending means they'll always play it safe (especially since they can see what you spend before they bid).

You have to keep Bank management in mind, as well. You don't want your Bank to dwindle. If your Bank is zero, every conflict will be easy-peasy for a while, because you can't make them any harder! However, if a player Plays It Safe, you will get back slightly more than half of what he bids. This is why I usually recommend setting your difficulties such that you can make the players spend perhaps half of what they can bid. It makes sure that if they do play it safe, they'll probably win, but it encourages risks to get ahead - and in Fastlane, breaking even is just plain boring. If your players are content with breaking even, give them little nudges and pushes in the fiction until it's clear that breaking even won't save them.

General

Roulette is a very weird game when you're not accustomed to it. It takes a while to integrate it into your head. You need to play with it a while before you "get" it. I recommend to the Croupier that they start with small conflicts. Ramp up to large ones. (Or perhaps start with one BIG one, and then a bunch of small ones.) This gives everyone a chance to "get their sea legs" with the wheel and the bidding board. Also it follows how many stories seem to open - mostly small introductory scenes, sometimes following an explosive kicker.

If anyone has any further comments, thoughts, or strategies they wish to share, this thread is open!

Although it's not exactly good strategy, it's also worth noting that you can bid on the zeroes. None of the outside bids cover the green squares, but some inside bids do. Assuming you avoid any straight bids (i.e. putting a chip directly on a zero), here are the other possibilities:

American Wheel
* Split bid (0, 00) : one chip covers both zeroes! Half the payout of a straight bid, but it covers both of them. This has a 5% chance of coming up.
* Street bid (0, 00, 2) : The only "street" bid that isn't on the side of the board, this covers both zeroes and also one "normal" number. I'm not sure why, but this is my favorite. This has a 7.8% chance of coming up.

European Wheel
* Split bids (0,1) (0,2) (0,3) : chip covers one zero and one regular number. 5% chance of any of these coming up.
* Square bid (0, 1, 2, 3): one chip covers the single zero, and an entire row of "normal" numbers. 10.8% chance of coming up roses. The only "square" bid that doesn't make a square on the bidding board. Again, probably my favorite in the Euro model.

I do not recommend bidding on the green. Hell, inside bets in general are somewhat foolhardy, and should be carefully considered (and possibly avoided). After all, "playing it safe" means staying on the outside. But it's nice to know that you can truly bet against yourself. Because the zero means you've lost.