You have better odds if you play 500$ to get 630$ in one bet
It may be less fun because you will play less but mathematically speaking your expected loss is lower
There was an phrase for simple casinos in Old Las Vegas. They were called
"grind houses" because people were said to grind away their money by making repeated bets, where the house edge works it magic on the entire group of players. But I think many people understand that. The Wizard of Odds describes the house edge as a kind of entertainment tax. He encourages people that if they are paying an entertainment tax, to look for games where the tax rate is low. It doesn't get any lower than Just Dice.
If you enjoy Martingale, then by all means play it. It doesn't increase the house edge, but it's danger is that you break up your goal (for example doubling your money) into smaller and smaller units. The more units of betting you have, the more the house edge grinds away your money.
And there is a an average number of plays before you get a streak of length k.
Any discussion of Martingale without mentioning this average is woefully inadequate. For coin tosses (no house edge) with even money payback the average is 2^(k+1)-2. So for 6 losses in a row, it is 126 plays. If you add a house edge that average is lower. For
JD it only drops to 120. There is a lot of variation on that average in real life, but if you are playing 6 loss Martingale, and you've won 200 cycles, then you have beaten the odds.
If you need to see a simulation then here is a simple one on a spreadsheet for two losses in a row for a coin
https://docs.google.com/spreadsheet/ccc?key=0Aor7l039-pqHdDR1SXNONV9KQW1Id3F6cGQ0bUdPblE&usp=drive_web#gid=0Theoretically the average number of plays for a streak of
two losses should be 6 (=2^3-2).
Personally, I think
JD compared to "boxcars" in craps is a good bet. Throwing boxcars in a craps games has odds of you winning 1/36=2.77778% . The payout is 31X. In comparison in
JD you can play odds of winning of 3% and have a payout of 33X. In most casino games if you want a jackpot, then you must play a bigger house edge (i.e. bigger thrill, bigger tax). But not in JD.