http://en.wikipedia.org/wiki/Labouch%C3%A8re_system straight from wikipedia
The Labouchere system:
An obvious downfall to the system is bankroll, because the more losses sustained by the player, the greater the amount being bet on each turn (as well as the greater the amount lost overall) is.
Occasionally, a player following this system will come to a point where he can no longer make the next bet as demanded by the system due to table limits. One work-around for this problem is simply to move to a higher limit table, or a player can take the next number that should be bet, divide it by two and simply add it to the list twice. The problem with the latter option is that every time a player commits such a play, it will infinitesimally increase the percentage of spins a player must win to complete the system. The reason this is so is because the player is adding two numbers (which both will be crossed out in the event of wins) where only one loss was sustained.
To prove this, if a player were to play the Labouchère System the same way with the exception being that the player always added half of the wager lost to the bottom of the list twice for every wager lost where:
x = Number of Wins y = Number of Losses Z = Numbers Originally on the ListWhen:
y + (z/2) ≤ xThe result is the list being completed.
The player would actually have to win in excess of 50% of the time (the actual percentage of wins necessary, given x and y, being dependent on z) in order to complete the list, or more than the player could actually be expected to win.