Absolutely correct in many many aspects.  Most will never understand the simplicity of it.

Gambling Science: Why the house will always win in the long run

Undoubtedly you have heard the phrase "the house always wins" when it comes to casino gambling. But what does that actually mean?  And why is that said?

After all, people do hit jackpots, people have great runs at table games, people win repeatedly in the sport books, people win at the other games.  And casino games are supposed to be fair – so what guarantees the casino still comes out ahead?

The answer lies in a simple but powerful mathematical idea called "the house edge": a small, systematic statistical advantage built into every single casino game. It's the invisible force that ensures the numbers will always tilt toward the house in the long run.

So, let's unpack and quickly take apart the science behind that edge: how it's constructed, and how it plays out over repeated bets.

Roulette: the clearest place to see the house edge at work

Roulette looks like one of the fairest games in the casino. A spinning wheel with numbered pockets, half colored red and half colored black, and a single ball sent spinning around the outside to eventually land in one pocket at random. If you bet the ball will land in a red pocket (or a black one), it feels like a 50–50 gamble.

But the real odds are a little bit different. In most Australian casinos you'll find 38 pockets on the roulette wheel: 18 red, 18 black, and two "zero" pockets marked 0 and 00. (In Europe roulette wheels have 37 pockets, with only a single 0.)

The zero pockets are what creates the house edge. The casino pays out as if the odds were 50–50, however if you get the color right, you get back the same amount you bet. Which most believe that is a 50-50 chance, but in reality, on a wheel with two zero pockets your chance of winning is 47.37%.

When you bet on a color, the house has a 5.26% edge – meaning gamblers lose about five cents per dollar on average. A single-zero wheel is slightly kinder to the gambler at 2.7%.

You don't see the house edge in the course of a few spins, one-two or three shoes of cards, a few hours at a slot machine, etc. But casinos don't rely on a few spins, a few shoes or a few hours at a machine. Over thousands of bets, the law of large numbers takes over. This is a fundamental idea in probability that implies the more times you repeat a game with fixed odds, the closer your results get to the true mathematical average. The short-term ups and downs flatten out, and the house edge asserts itself with near certainty.

The law of large numbers is why casinos aren't bothered by who wins this spin or that shoe of cards, or even tonight, or win for several nights or even more. They care about what happens over the next million bets. They don't care about the winners (unless they are obviously cheating), they only care that there are enough losers.  Please read the Wiki for a great detailed run down of 'the law of large numbers', that will help you understand this super important info as to what I just mentioned. 

CLICK ON THE WIKI:
https://en.wikipedia.org/wiki/Law_of_large_numbers

Simply a great detailed explanation.  OPENING:  "In probability theory, the law of large numbers is a mathematical law that states that the average of the results obtained from a large number of independent random samples converges to the true value, if it exists. More formally, the law of large numbers states that given a sample of independent and identically distributed values, the sample mean converges to the true mean."

And once you understand that, you will be able to adjust your play, gain advantages and use a Money Management Method that benefits you whether you are winning or losing. 

The Gamblers' Ruin problem

Another way to see why the house always wins is through the so-called Gambler's Ruin problem.

The problem asks what happens if a player with a limited bankroll keeps betting against an opponent with effectively unlimited money (even in a fair game).  Say baccarat with 50-50 banker-player wagering with no commission or side bets. 

The mathematical answer is blunt: the gambler will eventually go broke if he continually wagers every hand or a large number of hands per shoe, plays everyday or nearly everyday.  Period, with absolute certainty. 

In other words, even if the odds are perfectly even, the side with finite resources loses in the long run simply because random fluctuations will push them to zero at some point. Once you hit zero, the game stops, while the house is still standing.

You have to fully understand the following without any doubts, "In statistics, gambler's ruin is the fact that a gambler playing a game with non-positive expected value will eventually go bankrupt, regardless of their betting system.  The concept was initially stated: A persistent gambler who raises his bet to a fixed fraction of the gambler's bankroll after a win, but does not reduce it after a loss, will eventually and inevitably go broke, even if each bet has a positive expected value."

Casinos, of course, stack the odds even further by giving themselves a small edge on every bet. That tiny disadvantage, combined with the fact the house never runs out of money, makes ruin mathematically inevitable.

The more bets you make, the worse your chances

Say you walk into a casino with a simple goal. You want to win $100, and you plan to quit as soon as you hit that target.

Your approach is to play roulette, betting $1 at a time on either red or black.

How much money do you need to bring to have a decent chance of reaching your $100 goal? A thousand dollars? A million? A billion?

Here's the surprising truth: no amount of money is enough.

If you keep making $1 bets in a game with a house edge, you are practically certain to go broke before getting $100 ahead of where you started, even if you arrive with a fortune.

In fact, the probability of gaining $100 before losing $100 million with this strategy is less than 1 in 37,000.

You could walk in with life-changing wealth and still almost certainly never hit your modest $100 goal. (The full mathematical explanation is spelled out in, 'the law of large numbers', I referred to above.

Betting bigger may give you a fighting chance

So how do you create a real chance of success? You must either lower your target or change your strategy entirely.

If your target were only $10, you'd suddenly have over a 50% chance of going home happy, even if you started with just $25. A smaller goal means fewer bets, which means less opportunity for the house edge to grind you down.

Or you can flip the logic of Gambler's Ruin: instead of making hundreds of small, disadvantageous bets, you can make one big bet.  Or several depending on your knowledge and bankroll in regards to what you are attempting. 

If you put $100 on red all at once, your chance of success jumps to roughly 47%. This is far higher than the near-zero chance of trying to grind your way up with $1 bets.

The long-run strategy is mathematically doomed, while the short-run strategy at least gives you a fighting chance.

A small house edge adds up

Roulette is the clearest place to see the house edge, but the same structure runs through every casino game. Each one builds in a varying degree of statistical tilt or bias.

Some games, like roulette, have fixed, rule-based house edges that don't change from one player to the next. But others, like blackjack, have a variable house edge that depends on how the game is played. But no game is exempt from the underlying structure.

Small edges don't stay small when you expose yourself to hundreds or thousands of bets. In the long run, the variance fades, and the outcome converges to the house's advantage with almost certainty.  Again, maybe not in a session or two or three or even five.  But the house's advantage will always outweigh yours, always.

That's why the house always wins. Because mathematics never takes a night off.  Never ever.

Win you win, there is no charge to color up and leave.  By the way, you can opt-out anytime.

A few details about what was written and pending, it's not over yet:

A new tax law goes into effect on Thursday that is likely to have massive ramifications for gamblers.

Starting on Jan. 1, 2026, only 90% of gambling losses will be able to be deducted on taxes at the end of each year.

Meanwhile, 100% of winnings will still be taxed as income, meaning that even if you break even while gambling, you could still be on the hook for a significant tax bill.

For example, if you record $100,000 in gambling losses throughout 2026, but also record $100,000 in gambling winnings, you would still owe $10,000 in taxable income, despite earning no net income.

Those with modest annual net income gains could also see their gambling winnings completely erased in taxes if a significant amount of offsetting losing wagers are placed throughout the year.

The change comes as part of the Big Beautiful Bill, which was signed into law in July. All 50 states will be affected, and the changes will apply to all sports bets and casino games that are played, both online and in person.

However, the change will not affect previous wagers placed throughout 2025, with old tax rules still applicable for the last time this spring as tax season gets underway.

Only federal taxes to the IRS will be impacted. State tax rules on gambling winnings and losses will not be affected.

Already, the new tax rule is generating significant backlash among the gambling community, with some warning that wagers placed on sports bets and in casinos are likely to decrease as a result of the change.

A push is underway to repeal the provision of the bill, led by Las Vegas-area Rep. Dina Titus of Nevada. However, the bill, titled the Fair Bet Act, was introduced in July, and has not progressed in the House since.

Regarding your second question, KFB:

It depends.
For example a shoe per shoe registration will make plenty of opportunities to exploit an expectation/actual deviation ratio especially at the very first pattern happening at each shoe as being complete randomly determined.

Suppose we're constantly betting that the very first pattern will be an asymmetrical pattern (so not followed by a same quality second pattern and according to the guidelines decribed in my pages).
Obviously we'll expect a fair amount of AS first patterns or, at least, that S counterparts will be somewhat restricted in their back-to-back appearance. The AS/S pattern ratio (utilizing a 0.75 p) is 3:1 but even though it could be slight lesser than that (2,92:1 or so), itlr such ratio will approach the expected value, especially after having assessed the consecutiveness of the results.

But more importantly and besides the real numbers, it's the quality of such first patterns as single S or double S-S will be easily followed by an AS pattern and of course ranges of AS clusters will be particularly probable.
Obviously this first-pattern distribution translates into a permutation issue more insensitive of a possible symmetrical distribution bias of the entire shoe.

To get a better idea of that, let's try to adopt the reverse strategy, that is wagering toward first S patterns and everyone will see very soon that it's impractical to say the least.

Once we want to bet into an entire shoe, things will change a lot because the boundary between expectation and actual distribution becomes more subtle (yet more profitable with some experience).
I'm sorry but by now I have no time, see you next time.

as.

Hi KFB!

Q: Approximately how many events(i.e., Betting Spots) do you consider in most shoes?

This depends a lot about the actual texture of the shoe, sometimes we need a lot of hands before approximating at best the prediction.
So if the shoe is getting too many weird situations (mainly from an 'hand results' point of view) we prefer to stay put or wagering very few spots.
We think that it's slight more likely to cross a WW situation by diluting the betting than getting the same WW by a consecutive betting approach.
More or less the same about a LL sequence,  anyway those considerations are strongly linked to our specific approach.
Recently we have implemented a kind of additional (very diluted) strategy based just on this: so betting the very next hand toward a L after a single W and betting the very next hand toward a L after a single L.

Once WW and LL patterns had formed we take care of the actual and expected deviations basically by running two different lines:

1) W and L patterns (so "events") seem to get a 1-2 distribution (1 or 2 gaps);

2) W and L patterns seem to provide 3/3+ streaks and few 1 or 2 gaps.

Notice that I'm talking about W/L sub sequences coming out from a selected plan and not necessarily about B/P hands.
If we implement the asym/sym factor on such sub successions, more often than not we are not going to face 'many' symmetrical situations, meaning that WWW/LLL or WW/LL, etc won't be common findings.

It's now that "expected" values will help us to define whether the 1 or 2 line will be predominant at which level of apparition and the idea that per every shoe dealt a perfect balancement between two opposite situation patterns widely intended is out of order.

Q:What is your typical deviation-from-expectation requirement for betting into that spot? For example do you look for events that lets say occur four times per shoe. Then after say 60% penetration (with -0- occurrence) in the shoe you start wagering for that event to occur  after the first stages of said event have shown?
    OR
Are you more likely to only wager on events that lets say only occur every 3.5 shoes?

I'll answer this later.

as.

Hi Asym.

"...Obviously when in doubt betting towards the deviations will be a minor mistake than wagering to have that deviation to stop..."

    I think this is the optimum approach for most events. 


Q: Approximately how many events(i.e., Betting Spots) do you consider in most shoes?


Q:What is your typical deviation-from-expectation requirement for betting into that spot? For example do you look for events that lets say occur four times per shoe. Then after say 60% penetration (with -0- occurrence) in the shoe you start wagering for that event to occur  after the first stages of said event have shown?
    OR 
Are you more likely to only wager on events that lets say only occur every 3.5 shoes?


Thx in advance.

Hopefully they will fix this(i.e., revert back to previous rules).

Good news for slot players is the $1200 cutoff(for jackpot payouts generating a form) has been raised to $2000 >1/1/26. This change doesn't affect me as I don't play slots (or if I do its only when required for free play).


https://cdcgaming.com/brief/house-rules-committee-blocks-fair-bet-act-leaving-2026-gambling-tax-reform-uncertain/




Continued Success,
Continued Success,

@whatwhats

Basically only a large number of complex approximate algorithms working together will get the best EV+ situations, where some of them ascertain the relative unrandomness (or real randomness) of consecutive shoes and the other part will take care of the "more likely" deviations every shoe is entitled to produce.
Mostly common bac successions we're destined to face are 'biased' in the sense that they seem to get a bit greater  number of univocal deviations than expected, yet the problem remains to understand if such deviations will come out from "natural" fluctuations (sd values) or artificially endorsed by the bias.

Obviously when in doubt betting towards the deviations will be a minor mistake than wagering to have that deviation to stop.
Anyway a steady betting plan directed to get deviations or moderate/strong deviations around any corner is destined to fail unless the asym/sym factor is implemented in the approach.

So any strict mechanical plan (unless suggesting over selected situations) will surely lose because we have no means to know if the shoe is randomly or unrandomly distributed.
I mean that even the 2nd bet could endure long consecutive losing situations, so waiting for a moderate/long fictional 2nd bet losing succession to show up before real betting won't make the job. Actually it should tell us that that shoe is either following a natural deviation or that it wasn't properly shuffled. So no hints.

What you call as "reverse" strategy is an interesting point, providing you'll put in a proper balance what is theorically more likely to happen with what is really happening and that is often best determined by the asym/sym patterns shape and lenght considered by each relative step.

For example, we've tested several thousands of real shoes dealt by a perfect "random" shuffle and we got no one complete asymmetrical pattern succession (that is up to 21 patterns had featured at least one symmetrical pattern per shoe) but in the real world the almost same sample got two shoes without any symmetrical pattern.
Conversely, the longest symmetrical consecutive sequence in our random sample was 6, but in the real world we've accounted a 7 and a 10 long sym succession, supporting the idea that actual real shoes are not properly shuffled.

Conclusion is that nowadays at most (say the entirety) of shoes dealt, the asym/sym feature considered by each step will be less likely to provide specular (so symmetrical) patterns than the opposite situation.

as.

Excellent!

Those were great!!

I'm the one in the blue pants when we have our annual "Fun Shoot" at the range.

Team Waffle House!!

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Quote from: alrelax on January 07, 2026, 03:54:58 PMChime in here if it's okay please.

Finding and defining advantages from fallacy to tangible;

Applying a rock solid Money Management Method that works and you religiously abide by regardless of loss or win;

The ability to take uncertainty out of the picture.  Not easy but you have to. Taking uncertainty out of your conscious will allow a crucial skill for minimizing emotional chaos and allowing you an advantage to distinguish more between what is actually happening and presentments that have a much greater negativity of advantaged play.

The above 3 have proven themselves as great advantages IMO, in my actual brick & mortar play experience and allowing myself the ability to win far greater than what I lose. 

That's a very good list, indeed.

From fallacy to tangible:

That's the theorical key part of what we're talking about.
One thinks to play with an advantage: good, yet the advantage must be measured by running the same situations "infinite" times, thus B bets and P bets must get an EV+ return capable to overcome strong negative variance fluctuations, otherwise the advantage is fake or simply being the by product of unlikely positive volatility lasting for long.

Applying a rock solid Money Management Method that works and you religiously abide by regardless of loss or win;

In that regard we only trust the simplest MM: flat betting. Or, maybe, a very slow multilayered plan where the standard bet is increased by small percentages of it.

The ability to take uncertainty out of the picture.  Not easy but you have to. Taking uncertainty out of your conscious will allow a crucial skill for minimizing emotional chaos and allowing you an advantage to distinguish more between what is actually happening and presentments that have a much greater negativity of advantaged play.

That's the key practical part to consistently win at this game.
A sophisticated and long term successful plan must be always related with what is happening at the table we're playing at. Especially when we have strong reasons to doubt that actual shoes are real randomly shuffled (so not completely fitting those shoes we utilized in our tests).

@whatswhats
I'll answer you later

as.