Roulette Ideas

Split from: Negative Extreme Variance Management and Positive Extreme Variance Exploitation

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As a point of reference

Flat betting would have seen the following outcomes on each of the 30 spin samples  -18u, -6u, -2u.

Final balance -26u

Using a simple 1-2-4 progression betting continuously and standing aside on a failure (7u loss) until the losing streak ends with a virtual win.

LLLLL LLLLL LLWLL WLLWL LLLLL WLLWW : 24 LOSSES AND 6 WINS

1-2-4: 4×1u wins - 2×7u losses = -10u

LLWLW LLWLL WWLWL LLLWW LWLLW LWLLW : 18 LOSSES AND 12 WINS

1-2-4: +11×1u wins - 1×7u losses = +4u net

LWLLW WLWLW LLWWL LWLWL WLWWL WLLLW: 16 LOSSES AND 14 WINS

1-2-4: +13×1u wins - 1×7u losses = +6u net

Net zero after 90 spins

Not saying that anyone should do this but it didn't perform badly with the sample provided considering the win loss ratio was rather poor 32W:58L. Certainly more 3+ streaks would not perform as well.

Whilst random can deliver any outcome, probability also provides confidence intervals.

The mean number of wins we expect over 90 spins is 43.78 (90 × 18/37)

The standard deviation for an EC over 90 spins is ± 4.74 √(90×18/37×19/37)

So allowing for 3 standard deviations we cover 99.7% of all possible 90 spin results. This level of confidence means we must accept a range of outcomes from 29 - 58 wins. Only a fraction of 1 percent (0.3%) of 90 spin sessions will have more or less than this range, meaning 0.15% will be lower and 0.15% will be higher.

As we can see only snaring 32 wins is on the very low end as 99.17% of the time we expect 33 or more wins in 90 spins (calculated using the binomial distribution).

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Quote from: Albalaha on Jan 24, 2023, 05:30 PMDo not make a key checking the lock. Make a key that can open most of the locks.

One can open 99.7% + 0.15% = 99.85% of the "locks" if you read the math working withing 3 standard deviations.

The problem with those aggressive negative progressions is that they're so seductive. One of the first things a gambler learns is how dangerous they are because although you might make a profit in 99.85% of your playing sessions, the only thing which matters is how much you lose in the losing sessions, and it doesn't matter that they only occur 0.15% of the time. Looking only at win rates is dangerous, and in fact they are meaningless without taking into account losses. What we're looking for is the sum of:

Probability of win × profit ─ Probability of loss × losses

And this should be greater than zero in order to win long term. It's easy to forget about the 2nd term in this expression. It doesn't matter how it's achieved; you can:

• Increase the probability of a win
• Increase the profit
• Decrease probability of loss
• Decrease losses

Any one of the above will do the trick, so we have multiple possibilities to work on.

Quote from: BlueBuzzard on Jan 25, 2023, 02:54 PMThe problem with those aggressive negative progressions is that they're so seductive. One of the first things a gambler learns is how dangerous they are because although you might make a profit in 99.85% of your playing sessions, the only thing which matters is how much you lose in the losing sessions, and it doesn't matter that they only occur 0.15% of the time. Looking only at win rates is dangerous, and in fact they are meaningless without taking into account losses. What we're looking for is the sum of:

Probability of win × profit ─ Probability of loss × losses

And this should be greater than zero in order to win long term. It's easy to forget about the 2nd term in this expression. It doesn't matter how it's achieved; you can:

• Increase the probability of a win
• Increase the profit
• Decrease probability of loss
• Decrease losses

Any one of the above will do the trick, so we have multiple possibilities to work on.

While there are a few things I agree with here including aggressive negative progressions not being the way forward, there are some things that I view differently..

First a 3 step grand martingale progression requiring just 11 units is not aggressive. I'm not saying it's awesome, but it doesn't dig a huge hole and it handled the "variance from hell" quite well despite the downsides I have detailed already.

I will also say that just because an event is a 0.15% outlier does not mean that when it happens it takes away the gains that have been won the other 99.85% of the time. I think that notion has a built in assumption that you are risking 100% of your bankroll on every coup, which is a bit of a strawman argument IMO.

I tend to think in terms of what you risk.

House edge is paid on what you risk on the felt, the magnitude of the variance is based on both the probability of the wager and the amount you risk.

Survival means managing risk and growth, and one should be figuring out how to steadily increase their bankroll whilst shrinking their session risk in percentage terms vs their overall bankroll, and at the same time increasing their base unit size over time.

May sound confusing, so here is an example.

Let's say you start with $3k overall bankroll and play at $10 units, so your overall bankroll is 300 units. Lets say your method and therfore session risk requires 60 units or $600 to achieve a suitable reliability factor. In effect you have 5 session bankrolls and your session risk is 20% of the overall bankroll.

Let's say you manage to grow your bankroll to $6k and are now playing at $15 units.

Your session risk is still 60 units which means a session bankroll is now 60×$15 = $900 but that is now just 15% of the overall bankroll. So the risk is much smaller in percentage terms but is larger in absolute terms than when you started. A future lost session is paid at a discount in percentage terms vs the percentage gains you received when you won.

Really let that sink in.

When a session represents 1% or less of your bankroll it doesn't matter when the 0.15% event loses a session bankroll, it is paid at a great discount from compounded winnings. In fact once you get things moving your original seed money (and some profits) is withdrawn and is no longer at risk.

The trick is to not try and beat the casino math directly but instead develop a method that has both a low enough failure rate and as low a bankroll requirement as you can achieve so that losses are paid at a discounted rate.

Do what is necessary to enable steady compounding. Ideally one should be aiming for at least 50 session wins for every session you lose (low volatility) and to be able to replace a lost session bankroll in around 5 winning sessions.

Above are many of the reasons why methods that use aggressive negative progressions or require lots of units to force a win vs the profit they generate just don't fit the bill for long term survival.

Quote from: TwoUp on Jan 25, 2023, 05:07 PMI will also say that just because an event is a 0.15% outlier does not mean that when it happens it takes away the gains that have been won the other 99.85% of the time. I think that notion has a built in assumption that you are risking 100% of your bankroll on every coup, which is a bit of a strawman argument IMO.

I didn't mean to imply risking 100% of your bankroll; that would be madness. I agree with the money management strategy you suggest and have been using something similar for many years. It's not sufficient for consistent winning on its own but is an important part of the whole picture.

What I was trying to say was that unless you have an edge, any gains you make from using a negative progression will all be given back at some point.

I've attached a tough sequence of outcomes for an even chance. The second 100 spins (after the dotted line) are what followed the run from hell. I have some software which will generate any number of these sequences for any location. I'll upload it later.

Quote from: BlueBuzzard on Jan 27, 2023, 05:46 PM

Quote from: TwoUp on Jan 25, 2023, 05:07 PMI will also say that just because an event is a 0.15% outlier does not mean that when it happens it takes away the gains that have been won the other 99.85% of the time. I think that notion has a built in assumption that you are risking 100% of your bankroll on every coup, which is a bit of a strawman argument IMO.

I didn't mean to imply risking 100% of your bankroll; that would be madness. I agree with the money management strategy you suggest and have been using something similar for many years. It's not sufficient for consistent winning on its own but is an important part of the whole picture.

What I was trying to say was that unless you have an edge, any gains you make from using a negative progression will all be given back at some point.

I've attached a tough sequence of outcomes for an even chance. The second 100 spins (after the dotted line) are what followed the run from hell. I have some software which will generate any number of these sequences for any location. I'll upload it later.

You may have overlooked a key point of my post.

The gains you make are not all given back.

The key point is that the session risk is shrinking in percentage terms. It is impossible to give it all back when you were originally risking 20% and are now only risking 15%.

The key is to use a method that has enough reliability for compound growth so that whilst the session risk grows in absolute terms it is actually shrinking in percentage terms. The long term is based on percentages not absolutes.

Case in point, the absolute counts of outcomes diverges over time. Most people think it evens up, but quite the opposite.

Which has serious implications for flat betting without an edge. The universe is never fair, the "error" just gets drowned out as a percentage.

That's what standard deviation shows, the results widen as the square root of the number of events we consider. 100 EC results is ±5, 1000 is ± 15, 10000 is ± 50

See how the range gets larger? The thing that does converge to close to zero over time is the percentage.


5/100 = 0.05
15/1000 = 0.015
50/10000 = 0.005

The "mean reversion" is on percentages and also not on the absolutes on your particular random walk that Albalaha believes. There is no evening up.

In fact for most random walks (which is what betting on a random event is), the number of zero crossings is very few meaning you are mostly on either the winning side or the losing side the entire time.

William Feller who was one of the greatest minds in probability theory had this to say in his standard probability textbook:

We shall encounter theoretical conclusions which not only are unexpected but actually come as a shock to intuition and common sense. They will reveal that commonly accepted motions concerning chance fluctuations are without foundation and that the implications of the law of large numbers are widely misconstrued. For example, in various applications it is assumed that observations on an individual coin-tossing game during a long time interval will yield the same statistical characteristics as the observation of the results of a huge number of independent games at one given instant.

This is not so, contrary to popular opinion, it is quite likely that in a long coin-tossing game one of the players remains practically the whole time on the winning side, the other on the losing side


This behaviour is described by the Arcsine law, and zero crossings are proportional to the square root of the number of trials. Mean reversion is not something that you can exploit in session on your singular random walk.

And this is how random coin flips look from the absolute and percentage perspectives:



How many of those lines are crossing back and forth over the zero line? Not many, they generally drift.

 

Quote from: TwoUp on Jan 28, 2023, 01:39 AMYou may have overlooked a key point of my post.

The gains you make are not all given back.

The key point is that the session risk is shrinking in percentage terms. It is impossible to give it all back when you were originally risking 20% and are now only risking 15%.

The key is to use a method that has enough reliability for compound growth so that whilst the session risk grows in absolute terms it is actually shrinking in percentage terms. The long term is based on percentages not absolutes.

I believe I did understand the point of your post, but what do you mean by "a method that has enough reliability"? If by "reliable" you mean the method has an edge, then you have no argument from me, because in my reply I excluded that scenario. But any kind of progression, if used without an edge, only magnifies the variance. In particular, negative progressions magnify the negative variance but not the positive variance, hence you gain many small wins which are offset by a few large losses.

If the betting is essentially random, then it's only luck (positive variance) which will get you to the second stage - ie past the point where your risk was 20% and is now only 15%. And to get beyond this stage to 10% risk (or whatever) will again require luck. If the point of the exercise is to make the most of any positive variance and safeguard the accrued profit, then there is some merit in your strategy, but it seems to me you're putting the cart before the horse; the first order of business is to find a "reliable" method, don't you agree?

Yes, I'm aware that "evening out" is in terms of ratios rather than absolute numbers, but more fundamentally, regression to the mean can't be exploited by waiting for prior losses because (as Albalaha has pointed out) the wheel has no memory. That seems to be a contradiction because at the same time he is saying that virtual losses do make a difference to his bottom line. Albalaha, can you clarify?

Regression to the mean merely says that for each sequence of spins we expect the average outcome. In the case of 100 even chances that means approximately 50 R and 50 B. It has nothing to do with the past, only the statistical expectation. So if the previous 100 spins produced 70 R and 30 B it doesn't mean that the next 100 spins is more likely to result in an evening out because the previous result was extreme. Believing that would be committing the logical fallacy Post hoc ergo propter hoc, to give it its fancy Latin name. It says that since event Y followed event X, event Y must have been caused by event X.

https://www.gamblingsites.org/blog/why-post-hoc-fallacy-causes-bad-gambling-decisions/

Quotebut what do you mean by "a method that has enough reliability"?

I mean that even a method that may lose the session bankroll is ok if the frequency between loss events is sufficient to grow your bankroll such that unit size increases whilst session risk becomes a lower percentage of the overall bankroll. This also goes hand in hand with the session units requirement and profitability.

If say a method requires a lot of units in proportion to the profit it can typically generate, or the profit target cannot be attained on average 50 times for every session loss then it's unlikely to be reliable enough for growth as I have described. I also suggest that 5 winning sessions should recover a lost session bankroll, leaving enough sessions to compound before the next loss event.

The 1 in 50 is the minimum because that is still common enough that you will see clusters of session losses and that significantly harms growth. You see a zero practically every time you play, that's a 1 in 37 event, 1 in 50 is not much better.

The scenario one ideally wants is where your overall bankroll grows, your unit size increases (even just slightly) and your session bankroll as a percentage of the overall bankroll is decreasing.

The "edge" here is not beating the casino math (which is alive and well), it is establishing sufficient distance between failure events, the power of compounding and a shrinking risk footprint. Sessions can absorb some variance and both the bankroll you bring and the method you use can survive a level of variance long enough to catch the wins that make the profit target (or close to it).

However nothing is infallible and in the interests of avoiding "buying the win" through negative progressions it is better to cop the loss, take your lumps and accept defeat. Every trader knows this, you need a stop loss but not too tight that you get stopped out of your trades before they soar, and not too loose that you risk too much to a negative move. A session bankroll is what you are prepared to lose should you get a nemises sequence for your method, what some will call negative variance. In truth no one can make a dollar without risk and that means you can't cover all the numbers, and that means you can therefore lose a bet, and that means you can also lose the next bet and so on. The nemises streak is out there waiting for every method, some methods more than others.

You can think what I am suggesting a bit like how insurance works. The insurance companies have premiums coming in proportional to the assessed risk (they take a bet) and claims going out (losing bets) and they make money between those two events (compounding, a.k.a geometric returns). Insurance is basically a zero sum game. That is why they use delay tactics to increase the time between the money flowing in and the money flowing out so the money can be working, that's where the profit comes from, insurance is just a means to have the use of cash between two events.

I am proposing that the bettor can use a similar tactic, the money you risk/bet today is more (in percentage terms) than the money you risk tomorrow, such that any gains today are worth more in percentage terms than tomorrow's risk (and tomorrow's losses). In order to do that you need enough reliability (I.e. low volatility) in your session returns so that the geometric (compounding) return is increased. If you lose too often then you obviously don't make profit but most importantly you don't grow the bankroll, and then your session risk starts to increase in percentage terms rather than the goal of decreasing (but growing in absolute dollar value terms).

In terms of reliability I benchmark methods using a 1 in a billion failure rate, or 9 nines. 99.9999999% reliability similar to passenger aircraft. Whilst I may be asessing a method that does not have that inherent level of reliability, I will assess how many sessions I could lose in a row where it would be a 1 in a billion event. That makes it obvious which methods are better than others for reliability. The next factor is profit vs the session risk. I prefer methods that require the fewest units possible as the bankroll growth is much quicker and the inevitable losses are quickly recovered.

Hope that explains how I see reliability an important factor for both survivability and growth.