First, thanks for offering this game. I've enjoyed playing it the couple times that I've given it a try and I've enjoyed the minuscule payouts that I've received made. In fact, I'm going to go ahead and share my strategy but, be forewarned, you may want to modify your service to prevent this type of statistical "abuse". If enough people (with enough bank roll) played this strategy, you could end up losing a lot of coin.
One quick note, I'm not sure what this strategy is called but I do know if you are caught using it in a near 50/50 chance game like Blackjack in Vegas, they'll kick you out and never let you back in (or so I've heard.)
Here's how it works. Each turn, bet a minimum bid that is significantly less than your available bank roll. If you loose, take the sum of all your losses and double it for your next bet. I see that with bitcoindouble.com, you can bet a minimum of .01BTC. The betting progression could therefore follow .01, .02, .06 ((.01 +.02) *2)
, .18, .54, 1.62, 4.86, 14.58... Well, you get the picture. The odds are exceptionally low that you will lose the game 4, 5, 6... 10... times in a row. Following the double-your-loses progression will yield a payout average of 33% of all lost bets once you finally break a losing streak (well, it's better than that if you win on the first or second round.)
Starting out at .01 won't accumulate much but .10 or even 1.00BTC as an initial bet can yield significant returns with enough game play, assuming you have the freedom to set your bet.
I played your game a couple nights ago and at that time you allowed betters to specify any bet between .01 and 100 BTC. After a few rounds, I managed to cash out with a profit of around .30BTC. I know, not much, but I don't have that many BTC so I was starting at the .01btc as my initial bid for each streak. I did manage to get a total gain of 1.5, or so, before I managed to get into a loosing streak that was a bit over my head (Eek, I was down about 2 BTC!) After I won, I played a few more rounds of my strategy and cashed out while I was ahead.
Today, I logged into your site and I noticed that you had changed the betting system to a series of 8, fixed bets. This is a fair house improvement but someone can still implement my strategy... sort of... and clear out your coffers.
Significant payout could still be achieved if a player bets the minimum bid, and if the lose simply bet the next highest bid increment that you offer assuming, they had the bank role. I don't have that kind of cash, so I, personally, wouldn't even try. It is worth mentioning that if a player had a horrendous loosing streak, and lost, say, 7 or 8 times in a row, they'd call you a cheater! Just kidding, they would lose their entire betting "investment" for that round of bets because they can't double their bet after the eighth bet. This is the key to protecting your house balance.
If you are worried about someone sweeping in and cleaning you out what you can do to fix the problem is lower the maximum bid (or raise the minimum bid) so that there isn't a wide swing of betting options. I, personally wouldn't offer bets above 5 BTC. Also, I would offer only 3 or 4 betting tiers (maybe .05, .5, 1 and 5.) There is only 7.3% chance that someone will make it to a fourth round and lose-- 3.8% chance that they will make it to a 5 round and lose.
Players who know their statistics would know that after multiple rounds their strategy would break down under such constraints, and they would avoid playing this method all together.
I hope that helps. It never hurts to double-check your statistics when playing a game a chance... even if you're the house.