The house has a definite edge in every casino game (except against card-counters in blackjack); no willing bet on the long-term break-even system, much less a profit exposure.
For any casino game, every betting system will eventually reflect the inherent casino advantage for that game; therefore, there is no betting system any better, or any worse, than all the other betting systems, although the systems with the broad betting ranges can lose faster.
While it is true that the house must continue to play indefinitely and covers all bets within its stated minimum and maximum, the player does not derive benefit from the option of varying their bets, or to quit after a win / loss total specifications, except the diffusion of their game over a longer period of time.
Since betting in every casino game has a house edge (except for free-chance bets at craps), no combination of bets will show a profit for the player. It is impossible to put together a series of negative-expectant wagers and get a positive result.
Since the casino advantage works on every bet, you have the best chance of doubling your money if you put your entire stake on the first wager and then quit. The greater the number of bets you make, the safer you are to lose your stake and the less chance you have of doubling it.
Law of averages:
Much of the childlike faith of the gambler in their latest “infallible betting system” is determined by a misunderstanding of the law of large numbers, misnamed the law of averages and is believed to mean that all things finally balance out, or “even on”. For example, if you cast an impartial coin long enough, an equal number of heads and tails is bound to appear.
That is, if you throw a silver dollar 100 times, the probability theory tells us that 95% of the time heads appear between 45 and 55 times, 5 more or 5 less than the 50 expected, or a deviation of 10 %. The same theory however, for example that in 10,000 tests, 95% of the time, will show between 4,950 and 5,050 times, 50 more or 50 less than the predicted 5,000, but only a deviation of 1%. Furthermore, if you launch a million times, the heads will turn out 500 more or 500 less than expected half-million, or just a tenth of 1% off.
It is important to understand that the longer you toss the coin, the larger the number of times it will vary from a uniform slits, but closer you will be percentage-wise. Remember that just the percentage difference tends even up and then only after a tremendous number of tests, while at the same time the fluctuations in the result get bigger and bigger.