Oh boy. Bad math for the fail…
Wizard of Odds is awesome and anybody with a slight interest in gambling should read thoroughly. If you don’t both to read that, let me try to break it down.
First of all, what you are describing is a progressive betting system and is perfectly acceptable and, in fact, pretty much encouraged by casinos. Why is it encouraged? Because in the long run, it will make them more money.
If you play a negative expectation game (such as roulette), where the house has the edge, the house will ALWAYS win in the long run. There is no way around that. Betting systems can only change how much and in what increments you put your money on the table, they can do nothing about the odds. If the odds are against you, you will lose in the long run.
The problem with a progressive betting system, such as the one you describe, is that you are exposing yourself to an incredible amount of risk for a relatively low payoff. Let’s say you bet $100 increments because I don’t think there’s a casino in the world who would take a $100,000 roulette bet.
The odds of hitting a bet on “black” are 18/38, or about .474. Thus, the probability of losing that bet is .526. The probablity of losing twice in a row, then becomes .277. The probability of losing 4 times in a row is .076 and the probability of losing 8 times in a row is .005 or roughly once in every 170 times.
Here’s your bet amounts: (1) $100, (2) $100, (3) $200, (4) $400, (5) $800, (6) $1600, (7) $3200, (8) $6400.
So you can see that, with this strategy, you have a very high probability of a single session win of $100. If you have a $10,000 bankroll, you can expect to win $100 over 99% of the time. However, you can also expect to lose your entire bankroll about 0.5% of the time, which is an incredible risk compared to the potential profit.
If you don’t like math, then just use common sense. This is not a complicated strategy and a lot of people use it. Then why are casino still incredibly profitable businesses? Because no betting strategy can change house odds which are, for the vast majority of games, including roulette, stacked against the player.
Very good analysis. And as someone earlier alluded to, at some point you will run up against maximum table stakes - you cannot continue to double your bet without limit. At some point during a losing streak, you will max the table limit and you will not have the ability to recover your entire loss in one spin. There is no way to “beat” a house game over the long term. Every single house game has a built in edge.