How would you recognize if you had a bet selection that produced lower variance than a random bet selection?

Which parameters would it have to beat? For example, would it need to be able to avoid an x losing streak? Or would it need to avoid an x drawdown from a highest point?

In the search for lower variance, I wonder how you could even be sure when you've got it? Which figures can quantify it?

This is a hypothetical question and it has only hypothetical answers. There can be a bet with lower variance at one point of time but there can be none with no variance or that can stay protected from large variances always.

Monaco, good questions.

Variance can be quantified by mathematical formula, from there you take the square root and ascertain the standard deviation, which is usually more understandable than the variance. I mean, the value means nothing unless it can be interpreted and/or compared to some other benchmark. You are best off using just the SD or even the z-score (how many SDs above the mean), to self-interpret the so-called variance (rather than the variance itself).

There is a z-score excel calculator somewhere here on the forum. An SD or z-score of 3.0 is considered rare, therefore the probability of achieving that result by luck alone is remote. It's worth bearing in mind that I am talking about flat betting here, otherwise the z-score will always fall within normality, whether is it negative or positive. Where there is an edge, the z-score, like your bankroll, should always keep rising.

As ever, much is open to your own criteria. For example, to be sure whatever value is accurate, you really do need to have the results of many many placed bets, or keep testing until you reach a z-score of 3.0+ with level wagers. Also, you cannot trust the results of manual hand testing (if you're doing that). In these cases there is psychological and emotional bias in play, thus the results are open to deadly corruption and a large margin of error which is capable of accounting for a false edge.

If you're looking for your worst losing streak, the results would have to be dissected bit by bit and each trot of variable length to be analysed in order to find the driest area of the system (this might not simply be the most number of consecutive losers). Once you have a z-score for that you will know what your worst variance is. If there's an edge the variance should be negligable and should not so much as even dent the overall return.

The largest drawdown is something else. In that case, you're looking at the volatility of the bet i.e. how adversely the bet's losing streaks affect your bankroll (in short, how much you need to get through the bad times).

Thanks for your replies.




Albalaha - you don't believe any selection can have any impact on variance in any way, shape or form?

Quote from: Number Six on December 17, 2013, 06:11:23 PM

An SD or z-score of 3.0 is considered rare, therefore the probability of achieving that result by luck alone is remote. Where there is an edge, the z-score, like your bankroll, should always keep rising.

Do you think the task of lowering variance (in the sense that you say in your post of lowering the SD's from the mean) has to necessarily be linked to gaining a positive edge? If hypothetically, someone managed to limit the extremes of their bet to between +20 and -20, there would be no increase in their bankroll, but they would be playing a lower variance game than a normal random bet selection.. so in that sense, you would have an edge on the game, but not the edge that allows you to win flatbetting or increase your z-score..

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If you're looking for your worst losing streak, the results would have to be dissected bit by bit and each trot of variable length to be analysed in order to find the driest area of the system (this might not simply be the most number of consecutive losers). Once you have a z-score for that you will know what your worst variance is. If there's an edge the variance should be negligable and should not so much as even dent the overall return.

In this regard, after finding your z-score for this worst part, I wonder if you would expect the driest area of this system to have a lower value than that of a normal random bet selection?
Maybe they wouldn't be comparable.. then again, theoretically, shouldn't all say EC bet selections exhibit the same z-scores for the worst times?

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The largest drawdown is something else. In that case, you're looking at the volatility of the bet i.e. how adversely the bet's losing streaks affect your bankroll (in short, how much you need to get through the bad times).

Lower volatility is probably closer to what I should've said in the beginning, and is probably closer to what i was originally thinking of. The answers help clarify what are the best questions to ask next sometimes.

Thanks Number Six, very helpful & interesting.

Yes, Monaco, these are all interesting questions.

Mostly the answers come down to personal interpretations and definitions. The problem is that if true independence exists between random outcomes then nothing can be defined until after the fact, and so even mathematical values cannot be counted on; they only apply to that single sample you tested (and even then the value applies from only two STATIC single points: A to B, where A and B could both be part of an even larger sample). The key lies in replicating these results time and again using the same logic. If results do not tally, then it can be concluded that there is no difference between that bet and a random selection.

As for lowering the variance in relation to the edge, techincally yes, they are connected of course. Where you play in a state of low variance, you are actually at or reducing the house edge, or even gaining an edge. The bigger the edge, the lower the variance. Unfortunately, mostly any positive variance is simply due to luck. The variance can actually be calculated for each bet and if you can consistently play in that low variance state, yes you could also win long term without an edge while using a soft progression. The drawdowns would still be big though, huge even; you would need a big BR to get through them and be prepared to sit many hours at the wheel to get to a new high. Not everyone has the stones for that. In fact even with a edge, it's still possible to go bust in some circsumstances (due to unforseen volatility). With perfect expectation you should win 1 in every 2 ECs, with a loss every now and then on green. The variance comes into play when the gaps between winners gets longer, and sometimes consistently remain unusually long for hundreds or thousands of spins.

The more you play the more likely you are to encounter worse-than-before variance. There is no low level or high level, you can just never test enough to find them, it's like trying to reach the edge of the universe (if you believe that the universe expands faster than you could ever travel). But if you have an edge or a bet that even reduces the edge in some way then the worst variance would be much lighter than a random selection for sure. All random selections would, on the other hand, be identical.

As a sidenote, nothing can be gained from using fallacious triggers based on previous EC patterns (not saying you're doing that). But if you want my advice and you're still looking for a solution, you're best to look at straight up numbers, that is what the game is after all. All the other bets are just there for convenience. Becoming au fait with the individual numbers may open up a new world where conditional situations can be proved to be effective.

Playing after a particular SD or z- score has no inbuilt advantage. It is only an attempt to get near "virtual limits" of randomness which is a fallacy than reality. Rather, waiting for such variance to occur, we miss winnings of "positive variance" whenever they occur in a session and gets very few opportunities to bet or win.
         For instance, if we are betting an EC and get 1 hit in 9th spin, we have a Z-score of -2.33. If someone feels it advantageous to wait till this happens, statistically, he needs to wait till 250+ spins to get one such opportunity to bet.
            There are a few so-called experts here who mislead all that playing after 3.0 STD has an advantage while there is no such thing, in reality.
               

Thanks again for the replies.

Quote from: Number Six on December 18, 2013, 01:04:44 AM
The problem is that if true independence exists between random outcomes then nothing can be defined until after the fact

Does true independence have to exclude all definitions of knowledge of future facts? Albalaha alludes to regression to the mean - notwithstanding whether it has an advantage or not, but a phenomena like that does give us knowledge of future events. Surely that is undeniable?


If Event A is an extreme event, we can 'depend on that for knowledge' about the following Event B, namely that it is more likely to be closer to the average. I'm not saying we can beat roulette with that information, but it seems undeniable that we have gained some knowledge of future events by looking at past events & there's nothing fallacious going on..
It seems a common enough mundane phenomena, no magic or crystal ball needed, and it doesn't seem to contradict the fact that all spins are still independent and the wheel still has no memory because Event A doesn't cause Event B.


Keynes -
"..there are certain classes of phenomena,
in which, though it is impossible to predict what will happen in each
individual case, there is nevertheless a regularity of occurrence if the
phenomena be considered together in successive sets.."


Is it not an advantage to know that the next set of x spins is more likely to be closer to the average? So future questions could be how to take advantage of it, thinking in terms of 'the next x spins'. 'What is the best value of x?' etc.


(Albalaha - I think your sentiment is that RTM cannot lead to winning more than you lose, and I agree - I've seen experiments with positive progressions, attempts to flatbet after a deviation etc, but I don't see how they fit in at all with regression to the mean. It makes no mention of 'catching-up' so why should you be able to win flatbetting? Similarly, why would a positive progression work any better? They seem to go beyond the information that RTM gives.)

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As for lowering the variance in relation to the edge, techincally yes, they are connected of course. Where you play in a state of low variance, you are actually at or reducing the house edge, or even gaining an edge. The bigger the edge, the lower the variance. Unfortunately, mostly any positive variance is simply due to luck.

In my mind, aiming for lower variance (or I should say lower volatility), this would also imply lowering positive variance, as I don't imagine it would be possible to lower one side of the equation without affecting the other..

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The variance can actually be calculated for each bet and if you can consistently play in that low variance state, yes you could also win long term without an edge while using a soft progression. The drawdowns would still be big though, huge even; you would need a big BR to get through them and be prepared to sit many hours at the wheel to get to a new high. Not everyone has the stones for that. In fact even with a edge, it's still possible to go bust in some circsumstances (due to unforseen volatility). With perfect expectation you should win 1 in every 2 ECs, with a loss every now and then on green. The variance comes into play when the gaps between winners gets longer, and sometimes consistently remain unusually long for hundreds or thousands of spins.

The more you play the more likely you are to encounter worse-than-before variance. There is no low level or high level, you can just never test enough to find them, it's like trying to reach the edge of the universe (if you believe that the universe expands faster than you could ever travel). But if you have an edge or a bet that even reduces the edge in some way then the worst variance would be much lighter than a random selection for sure. All random selections would, on the other hand, be identical.

Thanks for this - I think it helps to have even a vague idea of what you're looking for just in case you happen to bump into it, but wouldn't actually recognize it.

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As a sidenote, nothing can be gained from using fallacious triggers based on previous EC patterns (not saying you're doing that).

Are all triggers naturally fallacious? Are there any types that aren't?

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But if you want my advice and you're still looking for a solution, you're best to look at straight up numbers, that is what the game is after all. All the other bets are just there for convenience. Becoming au fait with the individual numbers may open up a new world where conditional situations can be proved to be effective.

Thanks 

My way to handle "extreme negative variance" is to avoid playing in the stretches where a bet goes above 2x of break even.
LLLLLLLLLLLLLLLLLLLLLLLLWWLWLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL
wwwwwwwllllllllllllllllllllllllllllllllllllllllwwwwwwwwwwwwwwwlllllllllllllllllllllllllllllllllllllllll
lllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
wwwwwwwwwwwwwwwwwwww


you may still lose some bet but not losing  your bankroll.


No money management except this can help.

Quote from: Albalaha on December 18, 2013, 02:15:58 PM
My way to handle "extreme negative variance" is to avoid playing in the stretches where a bet goes above 2x of break even.
LLLLLLLLLLLLLLLLLLLLLLLLWWLWLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL
wwwwwwwllllllllllllllllllllllllllllllllllllllllwwwwwwwwwwwwwwwlllllllllllllllllllllllllllllllllllllllll
lllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
wwwwwwwwwwwwwwwwwwww


you may still lose some bet but not losing your bankroll.


No money management except this can help.

sick variance

Quote from: PratikPokerpop on December 18, 2013, 02:20:30 PM
sick variance

Howsoever sick it may be, it won't kill.

Quote from: monaco on December 18, 2013, 02:07:38 PM
Does true independence have to exclude all definitions of knowledge of future facts?

The thing is, we aren't dealing with facts. They are observations, which lead to some kind of prediction about future events. You can define regression to the mean in your own way, there is no wrong or right answer; but it involves proving the premise beyond all doubt, and in a way that makes it economical to play.

It's not like regression just does not exist. You may have some sucess defining the event after the fact, but what you can't define, though, is its behaviour in real time. It may seem to be happening at a certain point, but how do you know it will continue in that way? The variance is just as likely to get worse at any point as it is to get better. For that reason you can't jump in at -3SDs and begin betting for regression from there. That's a fallacy. The house edge only applies to real money wagers. It's also impossible to bet through that degree of variance from the start. Even flat betting you would go bust in no time.

Which leads us back to a conclusion: regression to the mean is no different from a random selection. You seem to appreciate that; it is fallacious because it involves skipping spins and sitting out a portion of the game until "favourable" conditions appear. Once you step into the game the SD is 0 because you haven't even placed a bet yet. Most triggers are based on that same premise, and they are ineffective.

Quote from: monaco on December 18, 2013, 02:07:38 PM

Is it not an advantage to know that the next set of x spins is more likely to be closer to the average? So future questions could be how to take advantage of it, thinking in terms of 'the next x spins'. 'What is the best value of x?' etc.

For sure, I agree. If you can prove it.

Quote from: monaco on December 18, 2013, 02:07:38 PM

In my mind, aiming for lower variance (or I should say lower volatility), this would also imply lowering positive variance, as I don't imagine it would be possible to lower one side of the equation without affecting the other..

True. The variance would be much tighter than a random selection. You wouldn't even have to worry about that. More likely you would be busy compounding your profits exponentially with some kind of % betting.

Quote from: monaco on December 18, 2013, 02:07:38 PM

Are all triggers naturally fallacious? Are there any types that aren't?

Everything has to be defined and proved, that is the first step in making connections between seemingly random outcomes; past observations and future events. The premise of why a bet is different from a random selection has to be real. For example let's say you play in cycles of 37 spins. The cycle has to be defined and proved to be real rather than an illusion.

But consider: every outcome you record begins a new cycle, ends a cycle and forms part of every cycle in between. Outcome 1 begins Cycle 1, Outcome 2 begins Cycle 2 and is the second outcome of Cycle 1, Outcome 3 begins Cycle 3 and is the second outcome of Cycle 2 and the third outcome of Cycle 1. This goes on for ever and ever, in a constant state of overlapping. For that reason, on the surface, a cycle can only ever consist of one spin: the next spin.

So if you define a cycle of spins, how do you know it's making a difference. How do you know you're in it? Once the illusory nature of the game is past, you can argue that noting you do is a fallacy.

So tracking your worst losing runs to get the average doesn't give you any insight in the variance?

I'm currently working on something, here are the stats. Could you tell me if you think I have the variance under control?

1000 total placed bets
536 wins
Longest losses 8 in a row once
Average losing run is 3.6

This is tested on even chances no zero.  If anyone cares to break it down for me I am not concerned about the 0/00 because I don't play with them.


I remember just recently PA did a post that stated if you can cut your losses to no more then 4 in a row you have an advantage.

As far as z-score and STD I have no idea how to do that, its like a different language to me

Big EZ - nice results. Hopefully others will be able to analyse them better than I could, but I can say they return a z-score of 2.28.
If your next 1000 placed bets return the same numbers, you'd be 3.22.
4000 placed bets & if you can keep the same win ratio, you're looking at 4.55. A score of 3 is rare, so...



I've added an 's' to the thread title from this point on, maybe I should add '& rtm questions' as well... these questions & points are all in the hope of better understanding so I appreciate the responses & hope no-one is banging their head against the screen. I know a lot of people have looked at regression to the mean before and come away believing it not to be usable or useful with regards to roulette, and that may well be true, but in all I've read I haven't really seen it talked about in its pure form – it always seems to be bundled up with the Law of Large Numbers or something like that. So please bear with me!

Quote from: Number Six on December 18, 2013, 04:29:17 PM
The thing is, we aren't dealing with facts. They are observations, which lead to some kind of prediction about future events. You can define regression to the mean in your own way, there is no wrong or right answer; but it involves proving the premise beyond all doubt, and in a way that makes it economical to play.

This second point is a problem I agree, but Regression to the mean is already proven beyond all doubt isn't it?  There aren't any question marks still hanging over it as a real phenomenon are there?

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It's not like regression just does not exist. You may have some sucess defining the event after the fact, but what you can't define, though, is its behaviour in real time. It may seem to be happening at a certain point, but how do you know it will continue in that way?

I agree you can't know for certain it will continue in that way, but you are in position where you know it is more likely to continue in that way. I'm sorry if that sounds like splitting hairs, but I think if there is an advantage to something like rtm, it's going to be in some small details – it won't be something that hits you over the head like a hammer, but even a small advantage might be enough.

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The variance is just as likely to get worse at any point as it is to get better.

Is this not one of the crux's of the matter here – the variance isn't as likely to continue getting worse, it's more likely (those words again) to get closer to the average. That's the heart of rtm.

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For that reason you can't jump in at -3SDs and begin betting for regression from there. That's a fallacy. The house edge only applies to real money wagers. It's also impossible to bet through that degree of variance from the start. Even flat betting you would go bust in no time.

Which leads us back to a conclusion: regression to the mean is no different from a random selection. You seem to appreciate that; it is fallacious because it involves skipping spins and sitting out a portion of the game until "favourable" conditions appear. Once you step into the game the SD is 0 because you haven't even placed a bet yet. Most triggers are based on that same premise, and they are ineffective.

But in this sense, rtm doesn't know if you are making real money wagers or not – it will act itself out whether you are betting or not. At whichever point you enter the game, rtm could be in action, just finishing or about to start, but you need to observe previous spins if you want to take advantage of it because you can only recognize it by looking at successive sets of spins..

Say I've been sitting at the wheel for a few hours, noting down the spins, and the previous 200 were 65 red & 135 black, & then you come & sit down at my spin 201. I know that the next 200 spins are more likely to be closer to the average – you wouldn't know that. Whether I've got the skill to make anything of that knowledge is another matter of course, & I won't know the outcome of any individual spin with any greater accuracy than you, but I have some knowledge of the next set of 200 spins that you don't.

If you decide to play after a strong deviation, then I think what you are trying to do is change the terrain in which you play to one in which extreme events, both positive and negative, are less likely – certainly no positive edge to make you get more right than wrong, & I would also guess that some kind of negative progression would be needed.

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Everything has to be defined and proved, that is the first step in making connections between seemingly random outcomes; past observations and future events. The premise of why a bet is different from a random selection has to be real. For example let's say you play in cycles of 37 spins. The cycle has to be defined and proved to be real rather than an illusion.

But consider: every outcome you record begins a new cycle, ends a cycle and forms part of every cycle in between. Outcome 1 begins Cycle 1, Outcome 2 begins Cycle 2 and is the second outcome of Cycle 1, Outcome 3 begins Cycle 3 and is the second outcome of Cycle 2 and the third outcome of Cycle 1. This goes on for ever and ever, in a constant state of overlapping. For that reason, on the surface, a cycle can only ever consist of one spin: the next spin.

So if you define a cycle of spins, how do you know it's making a difference. How do you know you're in it? Once the illusory nature of the game is past, you can argue that noting you do is a fallacy.

Here are 2 things – outcomes & cycles – different descriptions that can be applied to the same game. So you can look at individual outcomes, and you can look at individual outcomes as sets of individual outcomes - light described as both a wave and particle type premise; so does looking at the cycles, or sets, have any less validity than the individual outcomes?


(I hope this isn't coming across as just word games or semantics, it really is an attempt to understand something and see if it has any advantage...)

Quote from: monaco
Regression to the mean is already proven beyond all doubt isn't it?  There aren't any question marks still hanging over it as a real phenomenon are there?

Yes, it is a normal behaviour of statistics, we know the outcomes will slide up and down from the mean all the time. I'm not so much saying RTM has to be defined, but rather, it has to be put into context so you can predict it more accurately in real time. Going back to the example of cycles of outomes constantly overlapping, by that logic, RTM has to be measured from constantly moving points in time. Analysing 100,000 spins is pretty pointless for RTM, we know it will happen, and even begin all over again in such a long sample. But how is RTM behaving between spin 20 and spin 250? What is happening between spin 5000 and spin 5729? There is a "trot" within a trot, and a trot within that, and a trot within that, there are as many or as few trots as you want, the shortest trot being one outcome. Does this make any difference to the bigger picture? The bigger the picture, the more diluted the premise becomes, until such a point that using it makes no difference to a random selection.

Quote from: monaco
but you are in position where you know it is more likely to continue in that way

Yes, but only if you have kept betting through everything, even negative variance. Only then do things like probability and standard deviation apply to your wagers. If there are no bets there is no expected value, and thus there can be no variance. You can't jump in and out of random outcomes and expect to ride the big upswings and avoid the downswings. The variance just stops when your wagers stop, and begins again when your wagers do. At that point, on the ECs, variance has a 1 in 2 chance of going either up or down. For example if you reached -2.0 SDs you might choose to stop betting, and begin again when the "virtual" SD is -3.0. The virtual SD is exactly that: an illusion. When you jump back in at -3.0 and expect it to regress, the real SD is still only -2.0.

Quote from: monaco
Is this not one of the crux's of the matter here – the variance isn't as likely to continue getting worse, it's more likely (those words again) to get closer to the average. That's the heart of rtm.

Same principle applies, you have to continue betting through everything, every spin, only then does "likely" and "unlikely" really mean anything. The problem then becomes, do you have a big enough bankroll to last through these dry patches?

Quote from: monaco
But in this sense, rtm doesn't know if you are making real money wagers or not – it will act itself out whether you are betting or not.

No it doesn't. But we can agree to disagree. The casino certainly knows, though, when you stop paying them tax. And where there is no wager, there is no probability of winning or losing, and hence no expected value. That skipped outcome can have no impact on you or your future. Bear in mind that mostly RTM is observed after the fact, in real time you can't really tell what is happening unless you have defined all parameters and proved them to yourself. I mean, there may be cases where you reach a scenario in which you're confident some regression will happen over, say, the next 50 spins, which will allow you to profit nicely. This is where putting things into context matters, including other popular ideas like hot numbers.

Quote from: monaco
I know that the next 200 spins are more likely to be closer to the average

Are they? Regression can happen over thousands and thousands of spins in total. And that is the one biggest problem with it, and what mainly makes it uneconomical in terms of both time and money. Plus, when you jump in at spin 201 and begin betting, there is no SD. Virtual tracking in this form is a fallacy.

Quote from: monaco
I would also guess that some kind of negative progression would be needed.

If you know when to play, positive would be better, do you think? It would keep you in the game longer and give a better chance of reaching the upswing. When you are losing, it's probably best to lose as little as possible.

Quote from: monaco
Here are 2 things – outcomes & cycles – different descriptions that can be applied to the same game. So you can look at individual outcomes, and you can look at individual outcomes as sets of individual outcomes - light described as both a wave and particle type premise; so does looking at the cycles, or sets, have any less validity than the individual outcomes?

Yes, it's pretty much spot on. As for validity, I couldn't possibly go into that. The concept of cycles of outcomes constantly overlapping suggests it is not valid at all, since the implication is that every outcome is totally independent. With that in mind, everything you do can only ever be defined as being random, unless is can be proved to make an actual difference.

Quote from: Big EZ on December 19, 2013, 01:33:33 PM
So tracking your worst losing runs to get the average doesn't give you any insight in the variance?

I'm currently working on something, here are the stats. Could you tell me if you think I have the variance under control?

1000 total placed bets
536 wins
Longest losses 8 in a row once
Average losing run is 3.6

If you look at an average, you can only ever get an average picture that ends up halfway between best and worst; that can still lead to ruin. It's best to know the single instance of the worst possible variance and how long it lasts, then you can make sure you have enough money to outlast it. 8 losses is OK, but if it's 8 losses, 1 winner, then another 8 losses, that's something else. They are nice results, probably you should test another 1000 and see if you can match them.