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People who believe in the Law of Averages come up with a vast number of systems that are supposed to "break the bank." None of them work in practice. I'll analyze a few of them here.

The Martingale System - You may have seen flyers or books advertising a "Foolproof Gambling System!" Most often, these are simply the Martingale or Grand Martingale systems, both of which rely on the so-called Law of Averages. The Martingale System is simple: Every time you lose, double your bet. It sounds like a good idea, and it's mathematically sound, in theory - when you win, you'll recoup everything you've lost, plus whatever you started with. However, it doesn't work in practice. Anyone who works with computers knows his binary scale: 1, 2, 4, 8, 16, 32, 64, 128, and so on. After only 8 bets, you're betting \$128 to win \$1. Doesn't sound so good now, does it? There's one other detail that the system doesn't take into account: The House Limit. Most casinos won't let you bet anything you want... There's a minimum and maximum bet at any table you sit down at. The limit is usually calculated to break Martingale players at the 7th or 8th double. One bad streak will put you up to the limit easily... on your eighth bet, you need to bet \$128, but the house will only let you bet \$100. If you ask the Pit Boss to raise the limit for you, when he hears the bet amount he'll smile knowingly and shake his head. And you'll be stuck with two bad choices: Walk away \$127 poorer, or bet \$100 in the hopes of recouping... which will either leave you down \$27 or down \$227.

The Grand Martingale - Based on the Martingale. Every time you lose, you double and add one. In theory, when you win, you'll win one for every bet made, regardless of how many bets it took. The progression looks like this: 1, 3, 7, 15, 31, 63, 127... As you can see, you'll hit the table limit faster with this one.

The Pattern Watcher - This one's a hair smarter... but only a hair. This is someone who understands that the Law of Averages is a fallacy, and is aware that streaks and patterns happen in any sequence of events. This person will bet meagerly, or not even bet at all, while watching the pattern of events, waiting for a streak. When he sees a streak, he'll try to jump on it, and make money riding the streak. Unfortunately, there's no way to know when streaks will happen, or how long they'll last. It's just as likely that a streak will end just as the player's trying to jump on it, taking his bankroll with it. This kind of player is often seen at the Roulette wheel, tracking the results on a piece of paper. Most casinos are happy to provide paper for these players... some even have little pre-printed cards, with a complete Roulette layout on one side, and a long series of boxes on the back, to make it easier for these players to follow trends. Recently, some casinos have even put in electronic tote boards that show the last 40 spins, to make it even easier for these players. Given the Casino mentality of taking a dim view of anything that increases the player's chances (Card counting, handheld computers, etc.), shouldn't you be suspicious of anything the House does that seems to help?

The Reverse Pattern Watcher - This is the dim cousin of the Pattern Watcher. He still believes in the Law of Averages, and waits for patterns to appear, so he can bet against them, expecting them to end. He thinks that the Law of Averages won't let streaks last for very long. He's also fond of the Roulette wheel, and is just as likely to get smacked around by probability.

The Me-Too Gambler - This guy walks around the casino, looking for someone with a big pile of chips or a big-name celebrity. He'll go play what this "high roller" is playing, and bet how the he's betting. The problem here is that appearances can be deceiving. He may be the most competent executive, an oil tycoon or fashion designer - but that doesn't necessarily make him a good gambler. And where celebrities are concerned - many entertainers book return trips to Las Vegas in order to pay off previously-accrued gambling debts... they may well be doing that concert for "free," to get even again.

All of these systems, and many, many more, are music to the ears of casino managers. They're money in the bank for the casino.

Before anyone thinks that I'm sneering at people who use these systems... well, in a way, I am, but I should be candid and say that I have used several of these systems myself, before I undertook a serious study of probability. Unlike most gamblers, I'm willing to admit, both to myself and the world at large, that I have lost far more money gambling than I've ever won. I don't expect this to change, as I know that I don't have the qualities necessary to be a successful professional gambler. But that doesn't mean that I won't occasionally lay a bet here or there.

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