Last update: October 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, almost always 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. That is, the overall result for a whole bunch of sessions will be negative, whether using a betting system or not. Betting systems simply 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
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.
Fifth, if it were as easy to beat the house with something as ludicrously simple as varying bets, someone would have figured out how to do it successfully decades ago. And the casinos would not be standing. Yet there they are, because trying to beat a random game is as fruitless as trying to predict the next result of a coin flip.
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 systems to the test, because they know they don't work.
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 you can be likely to win in the short term, but more likely to lose the longer you play: There are 38 slots on a standard roulette wheel. You bet $1 on 36 slots. You've covered 36 of 38 slots, so you have a 94.7% chance of winning. If any of your 36 numbers hits, you'll lose 35 of your bets, or $35. You'll get paid $35 on your winning hit, plus you'll get your dollar back on the winning bet, so you'll have $36 total. So, you profited by $1.
But if you keep playing, sometimes none of your 36 numbers will hit. One of the two numbers you didn't bet on will hit instead. When that happens you'll lose all $36 that you wagered. In the long run, this will cancel out all the rounds where you won $1, and then some.
The Martingale system mentioned above is similar: you're a favorite to win a small amount in any particular short session, but the longer you play, the more likely you are to have a loss, and that loss will wipe out all your winnings, and more.
System proponents think they've done something special when they devise some system that wins most sessions. Big deal. It's child's play to come up with a system that wins most sessions, as shown in the roulette example above. What proponents can't do is come up with a system that has an average win across all sessions, because the minority of losing sessions wipes out all the wins from the majority of winning sessions.
The only real way to try to exploit the likelihood of winning in the short term is to quit as soon as you're ahead, and never play again. After all, the more you play, the more likely you are to lose. And even this method isn't foolproof: Although you're a favorite to win your one session, you could get unlucky and lose than session anyway.
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 mean “good in the short term”. If it's bad in the long term, it's bad in the short term as well. Let's see why.
Your friend tells you he's got a winning system and wants to show you. He walks up to the roulette table, bets on red, and holds his breath. He wins. He tells you that holding his breath was the key to winning. His evidence is that he won.
Of course this is ridiculous. He won because he got lucky, not because he held his breath. You suggest he play for a few hours to see how he does. You do that because you instinctively know that the longer he plays, the more likely he is to lose. The longer playing time will prove that his "system" doesn't really work.
That's precisely why we typically computer-test systems for millions of rounds. We have to get into the long term to definitively show that any short-term wins were just dumb luck.
This does not mean that systems fail only when tested for the long term. If a system is a long-term loser, it's actually an overall short-term loser as well. Instead of running one test for millions of spins, we could instead simulate thousands of short-term sessions of, say, 100 rounds each. And all betting systems fail the thousands-of-short-term tests as readily as they do the single-long-term test. Sure, some of those short sessions will be winners, but overall, the systems are assuredly short-term losers
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 overall in the short term. It won't. Long-term losers are also short-term losers.
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 tradeoff is that when you do lose, you lose big, which more than wipes out your wins from the winning sessions. The Martingale, explained above, is an example. You might win $15 for each of ten short sessions, but then lose $240 in the eleventh session. You won most sessions, but you still lost overall.
Also, for these kinds of systems, 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.
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.
What exactly is the long-term?
"Long-term" isn't a precise number of rounds. A single round is obviously short-term and a billion rounds is obviously long-term, but in between those extremes, we can't say at exactly what number rounds we move from short-term to long-term. However, we don't have to, because trying to pin down a precise number misses the point. 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, what we see is that the more rounds we have, the more confidence we have in the result (though we 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 I'm noting the difference to satisfy the pedants.
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 you do have to check at least thousands of rounds, to verify that your winning results didn't happen just becuase of dumb luck). And if you did invest all that time to check thousands of results with pen and paper, 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 properly test a system is to run a computer simulation, because it's the only practical way to test thousands to millions of rounds. 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.