The Short Term and Long Run in Gambling

Last update: May 6, 2025

Why it matters

It actually doesn’t matter, for most people.  Most of us understand these basic concepts:

1. No betting system can beat the house.  (I have an entire article on that topic.)
2. It’s possible to win in the short term but not in the long run.

But people who believe in betting systems don’t get that.  They believe, mistakenly:

1. It’s possible to devise a betting system that can beat the casino.
2. Even if a betting system fails in the long run, that’s okay, because they’ll play only in the short term.
3. Mathematicians can’t give a precise number for “long run”, which is proof that mathematicians don’t know what they’re talking about. (example)

All of those are 100% false.  And in fact, if you understand that, then you don’t need the rest of the article, you can read something more interesting, like my coverage of slot machine returns, which is pretty popular.

And for those who suffer from the misconcptions above, I don’t actually hope to change their mind.  People believe what they want to believe, despite all available evidence.  Rather, this article exists so that the math-literate among us can cite it when debating system-believers in the forums.

With that out of the way, let’s get on with the good stuff.

How the short term is different from the long run

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.

This means that even systems that win most of the time, are still overall losers.  What matters isn’t what percentage of sessions you win, it’s that plus how much you win or lose in those sessions.  For example, let’s take the Martingale system, where you’ll win mos of your short sessions, but still be an overall loser:

This is so important it bears repeating:  even systems that usually win, are still overall losers.  The Martingale wins a whopping 82% of one-hour sessions.  On the surface that looks fantastic.  But in reality, it’s still a loser, and just as worthless as every other betting system.

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, or the Martingale right after that.  What proponents can't do is come up with a system that has an overall average dollar win, because the reality is that the few losing sessions wipe out all the wins from the winning sessions, and then some

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 that method isn't foolproof:  Although you're a favorite to win your one session, you could get unlucky and lose that first session anyway.

Myth #1:  A betting system can beat the house.

FACT:  No betting system can beat the house.  I have an entire article on that subject, but here’s a summary:

1. No one has ever come up with one.
2. Past results don’t predict future results.
3. The average of any combination of negative-expectation bets is negative.
4. These ideas have been well-understood for centuries.
   
5. No one has taken me up on my $30,000 Betting System Challenge.

Myth #2:  It’s okay if a betting system fails in the long run, because I’ll play my system only in the short term.

System-believers argue that their systems will work in the casino because real people play way fewer rounds than in a computer simulation.  This is 100% wrong.  “Bad in the long run” does not mean “good in the short term”.  If it's bad in the long run, 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.  We’d really be testing short-term efficacy directly.  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.

We typically run a single-long-session sim rather than lots-of-short-sessions sims because a single-long session truly tells 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, and we get the same result if we test lots of short sessions instead of a single long session.  Long-run losers are also short-term losers.

Myth 3:  Mathematicians can’t give a precise number of rounds for “long term”, which is evidence that they don’t know what they’re talking about.

Before I debunk this one, let me show that people really spout this B.S.:

“AP [advantage players] parrot the mathematicians’ mantra that you will lose ‘in the long run’ but cannot tell how long the long run is.  No one can so it is only a ‘theory’ or ‘hypothesis’. (RouletteLife) 

(Groan.)

The reason that mathematicians don’t give a precise number is because long term is a  general concept, just like “far”, “tall”, and “expensive”.  You can’t tell me precisely at how many miles away something becomes “far”.  That doesn’t mean there’s no such concept as far.  Certainly, 1 inch is typically not far, and 5000 miles usually is far, but nailing down the exact number for when a distance crosses over from not far to far is impossible.  But certainly far is a thing even if we can’t pin it down to a specific distance.

Let’s take an example.  Your friend Bob believes he’s more likely to win if he snaps his fingers after placing a bet (pass line bet in craps).  In each scenario below, he’s ahead at the end.  What were the odds that he would do so, and does this count as the long run?

• 1 round.  Bob won his round.  But he had a 49.2% chance of winning this bet whether he snapped his fingers or not, so we’re unconvinced.

• 100 rounds.  Is Bob’s win here conclusive proof that he’s on to something?  Hardly.  Anyone betting pass line has a 40% chance of being ahead after 100 rounds, so while Bob beat expectations, it’s far from proof that his method works.
• 1000 rounds.  You or I would have a 30% chance of being ahead at this point without doing anything special, from pure dumb luck.  So, even with 1000 rounds, we can’t distinguish Bob’s system from pure dumb luck.
• 10,000 rounds.  Bob’s win here is impressive, because he had only a 5% chance of being ahead after 10,000 rounds.  But 5% is 1 out of 20.  If he played twenty times, 10,000 rounds each, we’d expect him to win one of those times.  Maybe the winning session we observed was his 1 in 20.  So, this is still far from long-term.
• 100,000 rounds.  The chances he’d be ahead after 100k rounds is about 1 in 4 million, so those are extremely long odds.  Is this the long run yet?  That’s a judgement call.  Certainly 10k rounds was not, and one million rounds would be, but here in between, it’s a gray area.  Yes, the 1 in 4 million odds to be ahead after 100k rounds are really long, but the odds on the Powerball lottery are even longer (1 in 300 million), and people win that regularly.  Still, if someone came out a winner in craps after 100k rounds, I’d take notice.  Not that I’d already be automatically convinced, but I’d want to explore further.
• 1,000,000 rounds.  The chances of being ahead after 1M rounds is about 1 in 10⁵⁸.  That 10⁵⁸ is more than the number of atoms on Earth.  Is that long term?  For this test, hell yeah.  This does not mean that anything less than 1M rounds is short term.  As we’ve seen, we can’t define long term precisely, just like we can’t precisely define “far”.  Also, for a different betting system (like the Martingale, or betting two columns in roulette), the long term could be larger or smaller than it was in this particular test.

I hope what you saw is that as the number of rounds grows, so do the chances of failure, but those chances are never zero.  It’s always possible for someone to win, no matter how long the odds.  The way it works is that larger the number of rounds, the more confidence we have in the result.  That’s true even if we don’t have a specific number of rounds in mind.

The takeaways

1. No betting system can beat the house.
2. Short-term wins don’t prove that a betting system works.  It’s trivial to create a betting system that usually wins in the short term, but is still an overall loser.  That’s because the amount lost in the losing sessions outweighs the amount won in the winning sessions.
3. Any system that seems to win in the short term simply hasn’t been tested enough.  Run a few thousand short sessions through a computer simulation, it’ll lose.
4. “Long term” isn’t a specific number of rounds, just like “far” isn’t a specific distance, and “expensive” isn’t a specific price.  The idea of long term is simply that the more rounds we test, the more confident we are about the result.

Related articles:

• Martingale betting system
• Martingale System Tester
• Halfies Betting System
• Betting System Tests
• $30,000 Betting System Challenge
• How to win $1 million