The Martingale gambling system is the grand-daddy of all modern gambling systems. The strategy is to double your bet after a loss when betting on a 1:1 payout. If you bet $1 and lose, your next bet would be $2. If you lose again, your next bet would be $4. Following the progression, your next bets would be $8, $16, and $32. If you win your $32 bet, you would’ve spent $63 in total and won $64 for a profit of $1 between all 6 bets. This sounds great on paper – just double your bet until you eventually win! This strategy can do well in the short term, but it is not a long-term winning strategy. Streaks happen, and they happen both ways. If you hit a winning streak of 10 bets, then you would’ve won $10, but if you hit a losing streak of 10 bets, then you would’ve lost $1023, and casinos have a minimum bet and a maximum bet for all games. If you play a game with a minimum bet of $5 and a maximum bet of $10,000, then you would be able to make 11 full bets with the 11th bet being $5120. You may win this bet, but you’ve just spent $10,235 to make a $5 profit.
The Stearn gambling system is basically a modified version of the Martingale, but instead of trying to recover your money with one winning bet, you’re trying to recover your money by winning two bets in a row. Instead of doubling after every loss, you would double after two losses, so the progression would go as follows – 1, 1, 2, 2, 4, 4, 8, 8, 16, 16, 32, 32. After a win, you would bet the same amount, and if you win twice in a row, you would start from the beginning, but if you lose, you would keep on with the progression. With the Stearn method, you’re betting half as much as the Martingale, but you’re trying to win twice as often, and you’re not guaranteed two wins in a row. Just like the Martingale, this strategy can do well in the short term, but it is not a good long-term strategy because you will eventually hit a losing streak that you cannot recover from.
These two betting systems rely on something called “the gambler’s fallacy.” The gambler’s fallacy is the belief that a particular occurrence is more likely to happen or less likely to happen based on previous outcomes in a game of random chance. If black was spun ten times in a row, someone may think that red is due to hit. In actuality, red has the same chance of coming up on every single spin – 18 chances to hit out of 38 possible outcomes or 47.36% on every spin. Someone could also think the opposite way – black was spun 10 times in a row, so black is more likely to hit because it’s on a streak. Streaks do happen, but black still has 18 chances to hit out of 38 possible outcomes on every single spin. All of the betting systems that I will list in this article rely on the gambler’s fallacy as opposed to relying on having a mathematical advantage against the casino by having an expected value over 100%.
The Martingale and Stearn methods are negative progression betting systems, meaning that bet sizes are increased after losses, but the Paroli gambling system is a positive progression betting system, meaning that bet sizes are increased after a win. With the Paroli, you actually double your bet after a win and keep doubling until you collect your winnings because you are trying to catch a streak. Typically you would try to win three or four times in a row. This is just another betting system that relies on the gambler’s fallacy. If you use this strategy, then you are relying on past occurrences to determine future outcomes in a game based on random chances. You may win in the short term, but there is no way to guarantee getting three wins in a row.
The strategy behind the D’alembert gambling system is to only add 1 unit to your bet after a loss and subtract 1 unit after a win. When wins and losses are both at a 50% rate, you would actually turn a profit because each winning bet will always be 1 unit larger than your previous losing bet. Besides having a basis in the gambler’s fallacy, you can already see the problem here – each session will not have exactly 50% wins and 50% losses. I’ve seen baccarat shoes with over 70% player outcomes and other shoes with over 70% banker outcomes, and we can’t know which session will have the next set of 70% player outcomes or 70% banker outcomes.
The Labouchere gambling system – also called the cancellation system – is a strategy where the player usually writes 10 numbers on a piece of paper and bets the first number plus the last number combined. After a win, we would erase those 2 numbers from the list and bet the new first and last numbers, and after a loss, we would add the amount lost to the end of the list and then bet the first number plus the new last number. If I write 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, I would start out by betting $2, since the first and last numbers add up to 2. If I win, my list would now be 1, 1, 1, 1, 1, 1, 1, 1. I now have 8 numbers on the list instead of 10 numbers. If I lose, I would add the number 2 to the end, and my next bet would be $3 since the first and last numbers now add up to 3. The theory behind this strategy is that because we’re adding 1 number after a loss and erasing 2 numbers after a win, we only have to win one third of the time. Again, this can do well in the short term, but coming from my own personal experience with this betting system, I can tell you that the numbers can add up extremely quickly when you hit a losing streak even if you have a few wins dispersed between the losses. When you win, not only do you erase the last number, but you also erase the first number, so the first number will not stay at the original betting unit. If you hit a losing streak, the last numbers on the list will eventually become the new first numbers on the list, and those numbers will automatically be larger than the numbers on your original list.
The Fibonacci gambling system is a modification of both the Stearn system and the Labouchere system. We’re making lists and crossing off numbers like the Labouchere method, and we’re attempting to recover our money using the Fibonacci sequence, which goes 0, 1, 1, 2, 3, 5, 8, 13, etc. The Fibonacci sequence adds the previous two numbers in the sequence to calculate the next number in the sequence. When you win a bet, you would recover the previous two bets. If you win after betting $13, then your next bet would be $3 since you have just recovered the $5 bet and the $8 bet. The “golden ratio” is derived from the Fibonacci sequence, and we see many examples of the golden ratio in nature, but when applied to gambling, we are still relying on the gambler’s fallacy. There is no way to determine the results in advance, and the amounts can become very large very quickly.
Now for all of the people who are positive that there must be some winning system out there, I can point you to Parrondo’s Paradox. The physics professor Juan Parrondo discovered a way to have a positive expected value when gambling, but it wouldn’t be very feasible because it would require a very particular order of alternating back and forth between two games. Juan Parrondo explained the Parrondo’s Paradox using a hypothetical biased coin since most casino games are automatically biased towards the casino. He explained two sets of gambling games each with their own rules, and if you were to play each game individually, then you would would have a negative expected value, but if you alternated back and forth between the two games in a very specific order, then you would actually have a positive expected value. Kevin from Vsauce2 made a great YouTube video explaining how Parrondo’s Paradox works, but there is also a flaw in the video since he explains it using roulette wheels and includes 0 and 00 as winning outcomes.
If you must use a gambling system, I would say that the Paroli method has the least amount of risk since you only have a net loss of one unit whenever you lose. If you’re betting $1 at a time and have a losing streak of 10 bets, then you’ve lost $10. If you hit the same losing streak playing the Martingale, then you would’ve lost $1023. Playing the Stearn system you would’ve lost $62, playing the D’alembert system you would’ve lost $55, playing the Labouchere system you would’ve lost $65, and playing the Fibonacci sequence you would’ve lost $143. Most casinos have a $5 to $10 minimum bet, so we can see just how large these losses can eventually become. These systems are based on the gambler’s fallacy. They are not based on having a mathematical advantage over the casino by having an expected value over 100%. If you would like to learn how to have an expected value over 100%, you can sign up for a membership and learn about advantage playing by using casino loopholes. Regular advantage playing takes advantage of statistics, but loophole gambling takes advantage of game flaws and house rules. We’ll see you inside!