Betting Systems

Last update: July 29, 2023

“Your 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:

  1. Most betting systems don't increase winning chances in either the short term or the long term.
  2. Some betting systems increase the chances of winning small amounts in the short term, at the risk of losing very large amounts.  They're still short-term losers, because even though most sessions are winners, the losing sessions lose more overall than the winning sessions.
  3. 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).  They can't even put a dent in it.

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.

Hit-and-run systems

A hit-and-run system has the player quitting after a small win.  The player then starts a new session at some later time.  Like all systems, they can be played for fun, but they don't beat the house.

The main reason that hit-and-run can't beat the house should be completely obvious:  you could lose your first bet and be negative for the entire session.  Think you'll just quit when you've hit some stop loss limit and then try again later?  Big deal, the house edge is still there.  Hit-and-run fails for the same reasons that all betting systems fail, as we'll see next.

Why betting systems can’t beat the house

Here are several kinds of evidence for why betting systems can't beat the house.

  1. There has never been any evidence of a winning system.  In all of human history, no one has ever put forth any system that's an overall winner.  And if someone had hit upon a winning system but didn't make it public and simply used it for profit, then 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.  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.
  2. 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 thing 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 (except in hindsight, which is useless), and therefore no way to know the ideal time to sit out or jump in (again, except in hindsight).  Thinking that the outcome of a round influences future rounds is called the Gambler's Fallacy, and I have a whole article on it.
  3. 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 (because of the house edge) 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.
  4. 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 done that kind of programming myself, here's one example.
  5. 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.

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 numbers on a standard roulette wheel.  You bet $1 on 35 numbers ($35).  You've covered 92% of the numbers, you have a whopping 92% chance of winning.  If any of your 35 numbers hits, you'll win $35, plus you get the winning $1 bet back, so you wind up with $36.  With a 92% chance of winning $1 on each spin, you stand to win most spins.

But if you keep playing, sometimes none of your 35 numbers will hit.  One of the three numbers you didn't bet on will hit instead.  When that happens you'll lose all $35 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 be so large it will wipe out all your winnings, and more.

System believers 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 I did 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 few losing sessions wipe out all the wins from the winning sessions.

And even for systems which are likely to win in the short term, that term is usually 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.

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 that first session anyway.

“Bad in the long term” does not mean “good in the short term”

System-believers 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.

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.

The point is, the more rounds we test for, the more confidence we have in the result.  For example:

  • 1 round.  This is the example I used above.  Obviously it's ludicrous to attribute success to a win of a single round.
  • 100 rounds.  If we run a test for 100 rounds and the system shows a profit, we still can't have much confidence in the result.  Anything could happen in a mere hundred rounds, using a system or not.
  • 1000 rounds.  Testing for 1000 rounds, we're more likely to see the mathematically predicted result, and we know this is a better test than 100 rounds, but it's still not enough to have a lot of confidence in the result.
  • 10,000 rounds.  We're increasing our confidence level.  Most systems will fail almost all the time with 10,000 rounds.  But not all of them.  Heck, sometimes flat-betting can return a profit after 10,000 rounds.  So this is a better test, but still not an ideal test.
  • 100,000 rounds.  We can be reasonably certain about results at this level.  But more rounds equals more confidence, so why not test for more rounds?
  • 1,000,000 rounds.  I would trust a test of 1M rounds way more than a test of 100,000 rounds.

For casino games, probability means some results are extremely unlikely, but that doesn't mean they're impossible.  For example, it's extremely unlikely that you'd ever see a hundred Reds in a row in roulette, but it's possible Likewise, even with a monstrously long number of rounds, it's possible that a betting system could show a win out of sheer dumb luck, and look like it was the real deal, even though it's not.

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.

Are math-literate people closed-minded?

Here's an argument (paraphrased) that I've heard about three gazillion times (as on this forum):

“The math boys have closed their minds to the possibilities.  They won't consider that they might be wrong.  They believe what they read in their textbooks without questioning it.  They're sticking their heads in the sand and refuse to consider new ideas, or study them.  But history has shown that people were wrong about things that everyone thought were true.  People used to believe the Earth was flat.  It takes brave people to challenge established orthodoxy, and that's what I'm doing, by standing up to the so-called math experts, whose ideas are good only on paper and not in the real world."

And the reality:

  1. Scientists and mathematicians are not afraid of new ideas.  Indeed, the whole point of science is to discover new things, and to do so by following the evidence.  If newer and better evidence emerges, and is shown to be reliable, then that's where the science goes.  It's not that science and math people willfully ignore new evidence, it's just that there isn't any new good, contrary evidence.  System believers regurgitating some old idea that was debunked centuries ago is not a compelling challenge.  As I say in this article, any believer in betting systems should test it, by learning to write a computer program to model it, so they have actual evidence.  Of course, if they do so, they'll see that their system doesn't work.
  2. The math-literate among us don't trust the principles because we blindly accept what the textbooks say, we trust them because we understand the concepts and see that they actually work.  You don't believe that 2+2=4 because that's what the teacher said, you believe it because you know that if you have two coins and get two more coins then you have four coins, and you know that's true because you can count them.  Similarly, we trust 7th-grade probability for the same reasons:  we understand the concepts, and we can see that they work.  In reality, not just on paper.
  3. This really is 7th-grade math.  If someone tried to convince you that 2+2=5, you wouldn't be very receptive.  You'd continue to be unmoved, even if they followed up with, "Mathematicians have closed their minds to competing ideas.  They're sticking their heads in the sand...."  So, someone trying to convince me that a betting system can beat the house is like someone trying to convince you that 2+2=5.  That's why I'm not receptive to their ideas.  I understand the concepts, I can see that they work, and I write computer programs to prove it.  To beat the house it would have to be the case that the average of a set of negative numbers could be positive, and that future events are more or less likely based on past events.  We know both of those things to be untrue as surely as we know that 2 + 2 ≠ 5.

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 because 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.  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 $200 would do it), or learning how to code it yourself (would probably take a few weeks).  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.  And if you're wary of computer-generated random numbers, you can always use natural random numbers (sourced from background radiation) from


The takeaway

  • 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.

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