In this thread there was a mention of a thing called the Martingale sequence which is effectively doubling numbers in a sequence ie: 1,2,4,8,16 etc. A WARNING here, dont ever apply this blindly to any gambling, it can have some success but it also can lose you a huge amount of money very quickly if you are foolish enough to use it blindly. The thread explains its own controls so you dont blow everything you have but I dont think those controls are practical or simple enough relative to the amount one might bet. It talks about betting only 5% of your "bank" (bank being your betting account total) but that can give you strange amounts to bet like $3.74 and when you start applying the sequence multiplier (I will explain soon) it all gets messy and Im not that flash at maths.
However I did start out using this system as described, I hadnt yet seen or worked out the pitfalls and very quickly my balance rose from $110 to about $250. I thought I was on to a winner.
So here is how it works. You only ever bet on the favourite. For example start with a $ bet on a favourite to win. if it loses double your bet for the next race favourite and so on till one finally comes in. The idea here being that over the last 70 years statistics show that the favourites win about 34% of the time.
But there are some serious flaws. What if no favourite wins in a 10 race meeting?. The betting sequence would be $1, $2, $4, $8, $16, $32, $64, $128, $256, $512. Those bets are accumulative so your total loss would be $1023. What if you just happened to strike 2 race meetings where no favourite won?. This website http://www.adrianmassey.com/fav/fav0.php has a set of stats for horse racing and at the bottom of the page it has some stats showing the sequence of no win results. Those numbers are pretty sobering.
Probability and statistics can be your friend if you want but they can also trip you up.