Last update: May 2021
article debunking betting strategies on your website is the most
comprehensive and practical I've found so far. Well done.”
— Wizard of Vegas forum user
A betting system is a recipe for which bets to make, how much to bet, and when to place the bets. It's usually based on what happened in previous rounds. Proponents think it makes them more likely to win. Here's the truth:
- Most betting systems don't increase winning chances in either the short term or the long term.
- Some betting systems increase the chances of winning small amounts in the short term, at the risk of losing very large amounts.
- No betting system can achieve a long-term advantage over the house. They can't overcome the house edge (the casino's built-in mathematical advantage on every game), or even reduce it a little bit.
Example: The Martingale
One of the oldest betting systems is the Martingale. The idea is that you keep doubling your bet until you win. Once you do win, your profit will be the amount of your first bet. For example, you bet $5 (and lose), then $10 (lose again), then $20 (lose), then $40 (lose), then $80 (win, finally). You made $75 in bets and won $80, for a profit of $5. If you could always double your bet you'd be a guaranteed winner, but at some point you won't be able to afford to double. Lose 12 bets in a row (it happens) and you'll have the privilege of coughing up $20,480 for your next bet—to try to make a mere $5 profit. With the Martingale, in most short sessions you'll have a small net win, but every once in a while you'll suffer a devastating loss. For more, see my full article on the Martingale, or try my Martingale System Tester.
Less Risky Systems
Of course, not all systems are as risky as the Martingale. They're also less likely to make you a short-term winner, but that's the tradeoff.
The Martingale is called a negative progression system because you bet more when you're losing. Think of this as digging yourself into a deeper hole. By contrast, positive progression systems have you bet more when you're winning. By ramping up your bets during winning streaks you can take advantage of the streak and win more than you would had you been flat-betting. This doesn't overcome the house edge (no betting system can do that), but if you are lucky enough to hit a winning streak you'll wind up with a little more money in your pocket then you would have otherwise.
Here's a simple positive progression system you can use. Every time you win, just add 50% to your bet. For example, start with an $8 bet. If you win then you'll add half of that, which is $4, so you'll be betting $12. If you win your $12 bet you'll add another half, so you'll bet $18. Whenever you lose, start over again with $8. I used this system while playing with a friend once and she remarked how cool it was when the stack of chips grew to be dozens of chips high.
With this system your bets go up only when you're winning. If you're on a losing streak, you'll lose only one unit each time. But if you're on a winning streak, you'll have the extra money to increase your bets with. However, if the pattern is very choppy (win, loss, win, loss), you'll lose more than if you were flat betting, because you'll be winning the small bets and losing the bigger ones.
Another system is to bet 1/4th of your total chips on every round. This way you're automatically betting more when you're winning (exploiting winning streaks), and scaling back your bets when you're losing (limiting your losses). A fun goal with this kind of system is to try to either double the amount of money you started with, or go bust trying. I've done this one many times as well. I succeed slightly less than half the time, and fail slightly more than half the time, which is what you'd expect.
Finally see my own special Halfies System, which gives you a good chance of winning in the short term.
Why betting systems can't beat the house
I'll give four kinds of evidence for why betting systems don't beat the house.
First, past results have no bearing on future results. Getting several heads in a row on coin flips doesn't make tails more likely. The same is true in casino games. Making bets based on past results is futile, because past results absolutely don't matter. This means there's no way to identify hot or cold streaks, and no ideal time to sit out or jump in. Thinking that the outcome of a round influences future rounds is called the Gambler's Fallacy, and I have a whole article on it.
Second, any combination of negative expectation bets is always negative. If I let you choose any number of nickels from a bag, drawing them out in any method, the average of your nickels will never be 13¢. Similarly, the average of any set of negative numbers can never be positive. For example, the average of -6, -5, -8, -2, -3 is clearly negative. Casino bets are negative-expectation bets, and no combination of negative bets can ever be greater than zero, which means no combination of negative bets can ever show a long-term profit.
Third, this has been studied to death. Mathematicians have understood probability as applied to games since 1654 (source), and in the modern era, they write up formal proofs of why betting systems don't work,(source) as well as run computer simulations which show that systems return the exact same house take as flat-betting without a betting system. I've modeled one such system myself, and you can see the results here. (There might be even more systems tested there by the time you read this.)
Fourth, for over a decade I've offered $30,000 to anyone who could prove a winning betting system. Skeptics think that anyone with a winning system wouldn't take my challenge, because they could just use the system to make money in the casino, but consider that a winning system might win only $10 an hour. It would take a year and a half to win $30k in a casino, so anyone who actually created a system to win even a piddling $10/hr. should have been falling all over themselves to take my $30k, but no one ever has, because no system can win even a penny an hour overall.
Incidentally, while my $30k challenge is no longer available to the general public, it's still available to system sellers. I aim to show that any system that's being sold is bogus, because no system seller has ever taken my challenge. Anyone who wants your $29.95 should be enthusiastic about getting my $30,000, but they won't put their system to the test, which is telling.
Bottom line: If the house edge on a given bet is 1.4%, it's 1.4% no matter what pattern or method you apply to bet it.
How the short term can be different from the long term
Here's an example of how the longer you play, the more likely you are to lose. Let's say I have a hundred shoe boxes with a hole cut out on the side so you can stick your hand inside to grab the contents. In 99 of these shoe boxes there's a hundred-dollar bill. But in one of them there's a rattlesnake. The game is that you pick a box and put your hand in to try to get a $100 bill. Of course you don't know which box contains the snake. Every time you successfully get a $100 bill the box is removed. You can play as many times as you want. Obviously, the odds are always in your favor for getting a $100 bill, unless there are only one or two boxes left. The fewer times you play, the greater your chances of walking away with money instead of getting bitten. The longer you play, the more likely you are to lose. And when you do lose you'll lose big.
This is analogous to the Martingale system mentioned above. Your chances are good in the short term, but if you play long enough, you'll suffer a catastrophic loss..
in the long term” does not mean “good in the short term”
Some fans of systems argue that while systems can't win in
the long term, that's okay because nobody plays into the long term
(thousands to millions of rounds). They maintain
that their systems will work in the casino because real people play
way fewer rounds than in a computer simulation. This reasoning
is just 100% wrong. “Bad in the long term” does not
automatically mean “good in the short term”.
The idea that a system will fail only if it's played for the long term comes from misunderstanding how we normally disprove betting systems. We typically debunk a system by writing a computer simulation ("sim") and running it for millions of rounds. Some people therefore conclude that a system will fail only if it's played for millions of rounds. But that's the wrong conclusion. Systems are actually both long-term and short-term losers. Instead of testing a single long session, we could test a few thousand short sessions. And if we do so, we find that the system is still an overall loser even in the short term. It'll win some short-term sessions, but overall, it'll be a loser.
The single-long-session sims are more common than lots-of-short-sessions sims because they truly tell us what we need to know, to anyone who understands the math. We typically don't test lots of short sessions because the math-literate among us know that if a system fails in a single long-term session, it'll fail overall in a bunch of short-term sessions too. It's only those who don't understand the significance of the single long session who think that their system will win in the short term. It won't. Long-session losers are also short-session losers.
The only difference between long- and short-terms for systems is that a betting system will always fail to show a profit in the long term while it will usually fail in the short term. But just because a system ever wins in the short term doesn't mean that it's an overall winner. The overall short-term results (adding the results of all the short sessions) shows that every system is an overall loser.
Most systems actually don't increase your chances of winning in either the long *or* the short term. Those systems are no better than flat-betting (betting the same amount every round).
For those systems that do increase your chances of winning in the short term, the short term in question is really short. With a $1000 bankroll and $5 bets on the pass in craps, the Martingale has an 82% chance of coming out ahead after an hour, but only 37% after eight hours. And again, when the system loses, it loses big. If we test such a system by running a sim of lots of short sessions, adding up the profit on the winning sessions and subtracting the losses on the losing sessions, we'll see that the system is an overall loser for short sessions. That's true for all betting systems, including all the ones that people have thought of before now, and all the new ones they'll think of in the future.
Why we look to the long term
This example shows why long-term results matter. Your friend Jack tells you he has a winning roulette system, he just used it in the casino and he won. You ask for the details, and he tells you: He went to the roulette table, waited for Black to come up two times in a row, then he bet on Red, and he won.
Of course this is not amazing. That's extremely short-term, and anything can happen in the short term. His win had nothing to do with any power of his system idea, and everything to do with blind luck. Intuitively we know that if he keeps playing, he'll eventually lose—not just a single round, but all of the profits he's made previously and then some.
Similarly, anyone who thinks he's got a winning betting system has simply gotten lucky in the short term. If he keeps playing it, he'll eventually lose. The longer he keeps playing, the more certain the loss. That's why we typically test systems by looking at longer terms, even though all systems are also overall short-term losers as well. (See above.)
A common question is, "Okay, so how many rounds do you need to be in the 'long-term'?" It's not a precise number, and here's why: It's extremely unlikely that you'd ever see one million Reds in a row in roulette, but it's possible. So even with a monstrously long number of rounds, you could never be 100% certain that a system were a loser. To put it another way a system might have:
- A 53% chance of losing after 1 round
- A 60% chance of losing after 10 rounds
- A 67% chance of losing after 100 rounds
- A 75% chance of losing after 1000 rounds
- An 85% chance of losing after 5000 rounds
- A 99% chance of losing after 10,000 rounds
- A 99.99999999% chance of losing after 100,000 rounds
Those numbers are just examples, not actual figures for any particular system. The point is, there's not an exact number for long term. Rather, it's just that the more rounds you have, the more confidence you have in the result (though you never get to 100% confidence). This is why we test betting systems in computer simulations for millions or billions of rounds. But, to repeat myself, modeling a whole bunch of short-term sessions shows that betting systems are overall short-term losers, also.
Anyway, you can see that in my previous explanations, I fudged a bit. I said that systems always lose in the long term, but in fact, after 100,000 rounds a system might lose "only" 99.99999999% of the time, which isn't quite "always". That's probably close enough for most people, but you know I like to be accurate.
How to test betting system ideas
There is no hope of creating a winning betting system, for the reasons outlined above. We've known for centuries not only that systems don't work, but more importantly, why. Nevertheless, if you're determined to try to test your betting system idea, despite all evidence, here's the wrong way and right way to do it.
The wrong way to do it is to gather random roulette spins, baccarat rounds, or craps rolls and then apply your system to it using a pen and paper. It's wrong because you can't practically check thousands and thousands of rounds by hand. And if you did invest all that time, you'd be pretty upset at the end when you found that your system didn't work anyway. Want to tweak the system and have another go? That means checking the thousands and thousands of spin results by hand again, starting from square one. (No pun intended.) (Okay, maybe a little.) So, forget the idea of hand-checking round results against your system.
The only way to do test a system properly is to run a computer simulation. And you don't have to run a single simulation of millions of rounds, you can test the short term instead, by running a simulation of thousands of short sessions. Running a computer simulation means either hiring someone to write the program (probably $100 would do it), or learning how to code it yourself (would probably take about a week or two). To hire someone, try Fiverr or Upwork. To learn programming, try Udemy, Code Academy, or Learn Python.
By the way, computer-generated results are just as good as live (real-world) results. There's a myth that some systems fail against computers but will work in a casino, which is just wrong. If it fails on a computer, it'll fail in the casino, too. Here's an analysis showing that both live and computer-generated baccarat shoes have proper random distributions.
- Betting systems can be fun, but no betting system can reduce the house edge, much less overcome it completely. You don't gain an advantage just because you're using a betting system.
- "Fails in the long term" does not mean "wins in the short term". Betting systems fail in both terms.
- If you want to use a betting system for fun, try adding 50% to each winning bet, or bet 1/4th of your total chips each round.
- Don't use risky systems like the Martingale unless you've read my separate article about it and you're prepared for the chance of a catastrophic loss.
- Never pay good money for a system when I've just given you three decent systems for free.