Math proof that roulette cannot be beaten

[TurboGenius]

Because he has respect for him, and doesnt for others and his heart is ruling his head on this one. Call it a soft spot, kinda like a murderer helping a cat out of a tree just after he wasted his family in the house...but less serious lol

LOL
I think I'm offended but I'm not sure. (climbs higher up the tree to think about it)

Bayes and others have a great point. Basically -
What If I win or someone wins - have they beaten the game ?.
This is roulette and math.. you have to (HAVE TO) ask yourself -
"Can I do the exact same thing that person did (or is doing) and win the same way ?"
No.. not with almost all systems and methods that have been posted (since forever).
Player A could go and win win win win and Player B will lose on the first try and quit using it.
Player C might win and lose and win and eventually lose.
The total of ALL of their play will be the negative house edge - math says so.
Player A can say all day that it's the Holy Grail, Player B can say it "sucks", Player C will argue
that "hey, sometimes it works - sometimes it doesn't, I ended up losing".
So is this any proof ? No, not unless you look at the "BIG PICTURE" - that is where proof comes from -
it eliminates "luck" (which isn't a real thing anyway).
See ? Everyone should stop thinking as one person who may use something and win - giving it credit when another player can't win using the exact same rules.

[Turner]

@ Bayes

No Blushes, but I always admire how you dont use your knowledge as a battering ram. You have a very open mind.

Knowledge shouldnt stifle your doubt.

I always agree with you...which is no accolade lol

I am similar. When I learn something and become an expert, I feel empowered, but my drive always lies in the feeling that I could be wrong.

No one likes a smart arse...and thats the balance you achieve.

Never becoming one.

[Turner]

LOL
I think I'm offended but I'm not sure. (climbs higher up the tree to think about it)

I didnt mean you lol

[rrbb]

Hi all,

Interesting discussion!

I think it has been proven again and again that spins are independent. Also roulette is a negative expectation game.

i think that the question should be made more specific: "proof that there is no strategy that can overcome the house edge".


I will show my "proof" in words. For anyone versed in the mathematical language: just translate it.



Now lets assume i claim i have a winning strategy. This would mean that i would see a steady increase in my bankroll.

because of this i could define "sessions". A session ends when i'm in the plus. A new session starts after an ended session.

So: a strategy consists of sessions, and sessions consist of "betting decisions"

Now, lets assume that we can proof that any strategy has a finite amount of possible betting decisions. Either by rules, physical boundaries, or inherent features of that strategy.

For example: if the strategy were a simple maringale + FTL, the betting decisions are very limited.

Let's call these possible betting decisions the "template". It just a name i chose.

Let's number these betting decisions from 1 till M. M betting the total amount of possible bets. And lets make a list of this template: we fixed the order. This comes in handy later.

Each session will consist of playing at least one of bets from the template one or multiple times.


Now lets play my "winning" strategy ad infinitum that is, till the end of times,

Also, lets keep track, per session, what the result is per betting decision in the template.

If we would put the template in a row on the lefthand site of a piece of paper, and the make columns to the right of it, we could eadily keep track of what a session does.

Per session we can add the result in the appropriate row.

Now we do this for an infinite amount of sessions.

Because each sessions ends in the plus, we could sum all the results in one session (we sum over a column) and write this down in a row below the sessions (say row M+2).

On the other hand, we could also sum the results per bet in the template!

Well, i used a fixed template, so when we som over a row, i sum over a "constant" bet.

Now, due to the law of large numbers, we know that these sums must be negative.

We get a contradiction! All sums over the rows are negative, and all sums over columns are positive!

This can not be the case, hence my claim must be false!




Now, i claim, there is one HIDDEN assumption that needs to be made to reach this conclusion.
If you can negate this assumption, the "proof" is not valid any more!

Good luck!

[Priyanka]

Atlantis - Very valid thoughts. Probably I should have worded the question as rrbb has done, but neverthless I believe we all get it.

1. All the outcomes are equally likely in every roulette spin.
2. All the spins are independent.
I think the point is are these facts or not? all of the math after is based on the idea that these are facts

Tomla - The question is not about whether these points are facts or not. The question is about what you think about these two hypothesis.

I have a statistical/logical explanation.

That is what is called as FACT also called as EMPIRICAL EVIDENCE.

After all, you can't *prove* independence.

Thanks Bayes. You clearly in your own subtle way established that FACTS are different from PROOFs and what is a FACT can any day be given a second thought by experimenting in an entirely different way.

Your question poses a bit of a dilemma for me, because on the one hand, I'm a "math guy". That means I respect the maths and "believe" it. On the other hand, I'm also a system junkie, and without boasting I claim to have done rather well out of roulette playing my systems.

I didnt mean to though . But as you rightly said, there are certain things which are beyond explanation that we know of and that is why I also believe it is always not a bad thing to question things which has not been proved even though FACT says so.

The total of ALL of their play will be the negative house edge - math says so.

Turbo - You are right. But math says so under two hypothesis as you have seen. Can you give a thought on those hypothesis was my simple request.

So what have we got as people's opinion on these two hypothesis.

Its a FACT.
They are true in Platonic realm not in real world


Independence while cannot be proved, is an aspect that is very hard to be declined as a FACT. How about the other one "Equally likely". Bayes, you pointed out that may be the first aspect will be declined. Is that an explanation that we could give to perhaps why you are winning?

Rather than adhering to the facts, let me turn the attention to a simple experiment/simulation that I showed in cycles of dozens. We saw that the dozen that has defined the previous cycle is more likely (63%) to appear within the next 3 spins than any other dozen that did not define the previous cycles. Does that disprove the FACT that spins are equally likely. Any thoughts here?

[Bayes]

Bayes, you pointed out that may be the first aspect will be declined. Is that an explanation that we could give to perhaps why you are winning?

I think it's more to do with dependence. I do better when taking account of past spins than when I don't.

I think we should define what "bias" means in this context. For me it means the numbers/pockets, not some event which is derived from what is assumed to be an unbiased wheel.

Most events are "biased" in the sense that they're not equally likely. The chance of 2 reds in a row is higher than 3 reds in a row, but I wouldn't call one biased.

Rather than adhering to the facts, let me turn the attention to a simple experiment/simulation that I showed in cycles of dozens. We saw that the dozen that has defined the previous cycle is more likely (63%) to appear within the next 3 spins than any other dozen that did not define the previous cycles. Does that disprove the FACT that spins are equally likely. Any thoughts here?

I think I missed that. Your "random thoughts" thread is long - do you have reply # where you explain it? Thanks.

[The General]

However, how do I explain the fact that the house edge hasn't caught up with me? The general will say it's because I've essentially been lucky (riding a temporary positive variance), but I know enough about probability and statistics to know that it can't be so, because "luck" runs out eventually. I also know a few others who have been similarly "lucky".

The sample that you're playing is not a truly random sample. 
The spins actually played are low/variance.

After all, you can't *prove* independence.

In the random game, yes actually we can and have. However, I suspect you're referring more to the nonrandom game.  Even then it's not that they're dependent as much as it is the gaming device/non random number stream creates a bias effect that makes it appear as though the spins are dependent on previous spins.  Regardless, I notice the careful dance that you're using to tease t the system junkies into believing that there's possibly light at the end of the tunnel when in reality we both know they're looking down the wrong hole.

[The General]

Also, without wishing to deflect from the topic, there's a massive inconsistency going on here between Turbo and the general. I have great respect for both you guys but Turbo ain't no AP. If "math beats a math game" (and I agree, taking a broad view of "math"), how come the general always backs up Turbo when he obviously believes no such thing? The general believes that "Physics beats a physics game", and that *anything* else is fallacious. Yet he apparently indulges *Turbo's* fallacy while trashing everyone else's.

Currently, I don't see any inconsistency.  We both deal with exploiting the wheel, rather than the random game.  And yes, I suspect we both believe that attempting to beat the random game is a fools folly.  I use physics in the forum of defect spotting, coefficient of restitution testing, accoustics, visual observations, and data collection.  Other people that attempt to exploit the gaming device may use strictly data collection in the form of the numbers that have hit.  Both methods can yield an advantage, I simply choose my route because it's the most efficient to out track the casino.

The biggest problem that I see on the forums is that most people don't know how to really think about the game correctly.  They're lost in the numbers and layout, rather than looking at the wheel.  The free modes that many of the online casinos have is like a drug for them because it creates the illusion that they can win.  It fools them,  much like the free mode for slot machines where they're set to pay at break even or above 100% back.

[TurboGenius]

I notice the careful dance that you're using to tease t the system junkies into believing that there's possibly light at the end of the tunnel when in reality we both know they're looking down the wrong hole.

You noticed that too ?   

[Bayes]

The sample that you're playing is not a truly random sample.
The spins actually played are low/variance.

I don't know what this means. You're saying If I'm winning then the sample can't be random by definition. It's a circular argument and gets us nowhere.

Everyone keeps using the word "random" without defining it. It's ambiguous.

Even then it's not that they're dependent as much as it is the gaming device/non random number stream creates a bias effect that makes it appear as though the spins are dependent on previous spins.

The lengths you go to to not let dependence get a foot in the door are quite remarkable.

Regardless, I notice the careful dance that you're using to tease t the system junkies into believing that there's possibly light at the end of the tunnel when in reality we both know they're looking down the wrong hole.

Speak for yourself. I don't know they're looking down the wrong hole. And there is light at the end of the tunnel.

Currently, I don't see any inconsistency.  We both deal with exploiting the wheel, rather than the random game.  And yes, I suspect we both believe that attempting to beat the random game is a fools folly.  I use physics in the forum of defect spotting, coefficient of restitution testing, accoustics, visual observations, and data collection.  Other people that attempt to exploit the gaming device may use strictly data collection in the form of the numbers that have hit.  Both methods can yield an advantage, I simply choose my route because it's the most efficient to out track the casino.

Pull the other one. Turner nailed it, you're letting your heart rule your head here and you know it. That's ok, but why not be honest?

Turbo always claimed to be a winner. Back in the glory days of GG his style of play was completely different from what he advocates now. It was  betting "furthest back" and progressions, and you defended him then just as much as you do now. That isn't meant to be some kind of "gotcha"; it's part of the evolution of most roulette players. From what Turbo has said, he's definitely not an AP because he doesn't look for biased wheels, but just bets on hot numbers. That might be a step in the right direction as far as you're concerned, but as you've pointed out, one SD above the mean doesn't indicate bias, no matter how "clever" the system is.

And yet, I'm "teasing" the sytem junkies and he isn't. Not exactly impartial is it?

[The General]

Speak for yourself. I don't know they're looking down the wrong hole. And there is light at the end of the tunnel.

The lengths you go to to not let dependence get a foot in the door are quite remarkable.

A bit of intellectual dishonesty don't ya think?.

[Bayes]

A bit of intellectual dishonesty don't ya think?.

How so? You'll have to spell it out for me. 

You mentioned that it can be proved that spins are independent. I say we can only assume it, not prove it. Where is the proof?

[The General]

You mentioned that it can be proved that spins are independent. I say we can only assume it, not prove it. Where is the proof?

In the random game of roulette:

1. The number of pockets on the wheel determines the odds of winning.
2. At each spin of the wheel there are 37 pockets.  The ball is equally likely to fall into any one of the pockets.
3. Once a number has hit the dealer does not block a number for hitting again.
4. Since the number of pockets remains the same from one spin to the next, there is no dependence.

Where people are fooled:

The free mode offered by many of the online casinos/cellphones/games sometimes contain program code that's designed to fool people into believing that they can beat the game. 

[Bayes]

C'mon General, you're just pulling out the standard template again! Give me some credit! 

For starters, 1 & 2 are irrelevant to independence/dependence, 3. is true, but your conclusion in 4. doesn't necessarily follow from the fact that the number of pockets remains the same from one spin to the next. Like I said before, there are other ways dependence can arise. Your analysis is too crude.

Also, you're assuming that I'm committing the gambler's fallacy by using past spins as a guide to future spins. I'm not.

The free mode offered by many of the online casinos/cellphones/games sometimes contain program code that's designed to fool people into believing that they can beat the game. 

You may be right. However, not at the casinos I play at.

And this thread is in danger of wandering off course. I think we should let Priyanka have the floor.

[The General]

Whatever floats your boat.

Perhaps you should debate recorded history, rather than me.  I've proven my point.