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Mike

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Why Progressions Fail
« on: November 22, 2016, 07:05:12 AM »
Very good article which shows that all progressions are ultimately equivalent to flat betting and therefore can't give you an edge by themselves.

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I was chatting with my friend Garrett last week about using progressions in a negative expectancy game such as baccarat, and I thought our discussion would make an interesting post.

In this post, I will explain why in the long run, any progression, no matter how mild or aggressive, must fail when used to bet in a negative expectancy game such as baccarat. I’ve mentioned this fact in many of my previous posts (e.g. Transcendental Baccaratology), but I haven’t yet devoted an entire post to explaining why.

First, here is a reminder about the three basic elements of any method of play:

1. Bet Placement: where to place your bet, for example, in baccarat, whether to bet Banker or Player.

2. Bet Selection: how much to bet for each of your bet placements. Flat betting (always betting 1 unit) and progressions (increasing your bet beyond your base bet in some manner as you win or lose the last bet) are examples of bet selection methods.

3. Money Management: when to start, pause, or stop betting. Some call this “discipline.”

Boiled down to their essences, all baccarat approaches (methods, systems, etc.,) consist of at least one of these three elements, usually, all three. Developers, players, and enthusiasts spend countless hours researching and discussing each or any of their combinations in their search for the holy grail, a system that can consistently win in the long run. However, each of the three elements can be rigorously shown to fail in the long run for negative expectancy games such as baccarat.

Here, I will explain why any type of progression (an example of 2. Bet Selection) must fail for negative expectancy games in the long run. No matter how mild or aggressive, simple or complex the progression is, it will not be able to make a long term negative expectancy method positive. Not only do my computational results clearly demonstrate this, but the rationale for why this must be true can be easily and intuitively grasped.

The key is simply this:

In the long run, any progression is simply a set of many different levels of flat bets.

So, if flat betting is long term negative, then progressions must be, too.

Another way to say the same thing:

Since the underlying odds per decision never change, a large bet has just as much chance to lose as a small bet, so the actual amount of the bet doesn’t matter in the long run; the wins and losses will all cancel out anyway.

An example may help.

Let’s skip right to the top to the king of kings of progressions, the most aggressive progression possible, the revered and feared standard Martingale, which doubles the size of the bet upon each loss.

The Martingale goes like this:

Start betting at 1 unit (1u).

If you win, keeping betting 1u.
If you lose, double your bet to 2u.

If you win, you win back your -1u lost in the previous bet, plus you gain 1u, so you’re ahead by +1u.
If you lose again, double your bet to 4u.

If you win, you win back the -3u lost in the last two bets (1u and 2u) and gain an additional unit (+1u).
If you lose, double again.

And keep doubling until you finally win.

So, the Martingale progression is 1u, 2u, 4u, 8u, 16u, 32u, etc … as long as your bankroll lasts and you don’t hit the table limits.

In the Martingale, every time you win, you gain +1u, and every time you lose, you double the amount of your last bet. With bottomless pockets and no table limits, the Martingale is the most effective way to stay ahead of your losses in the long run. All other progressions can be regarded as some dilution of the Martingale.

Now, let’s pretend we’ve played a million decisions of a perfectly fair, 50/50 coin-flip game, and we’ve thus placed a million bets using the Martingale.

The following table summarizes the number of wins and losses per bet amount level:
Bet Amount    Number of Wins    Number of Losses
1u    250,000    250,000
2u    125,000    125,000
4u    62,500    62,500
8u    31,250    31,250
16u    15,625    15,625
32u    7,813    7,812
etc.    etc.    etc.

Of course, in reality, the actual results won’t be so nice, neat, and exact, but I use these rounded off, whole numbers to facilitate discussion and to emphasize the main conceptual point. The important feature about the results is that for each level of bet amount, the number of times you won will be roughly the same as the number of times you lost. In the limit of an infinite number of bets, the number of wins and losses will approach exact equality for a perfectly fair, 50/50 game (a zero expectancy game), while for a negative expectancy game, the losses (net after any commissions, as in baccarat) will always outweigh the wins.

Presenting the total results in the above table should help you see the key point: Even though you were using a progression of many different bet amounts, you were effectively simply flat betting at various amounts. That is, there’s no mathematical difference between the following:

1) Using a Martingale progression over 1,000,000 decisions, or

2) Flat betting 1u over 500,000 decisions, flat betting 2u over 250,000 decisions, flat betting 4u over 125,000 decisions, etc.  For each of those bet amounts, the wins and losses will cancel each other out at best, just as would have happened had you simply flat bet the same amount throughout.

Moreover, it’s easy to generalize the above to any kind of progression, no matter how mild or aggressive, simple or complex (convoluted?), because in the final analysis, tabulating all of the bets of any progression in the same manner as above will show the same thing in the long run:  the number of wins essentially cancel the losses at each and every bet amount level.

So, if you can’t stay ahead flat betting at any single amount, how can flat betting at various amounts (which is what a progression really is) be any better? It can’t!

comparing 3 progressions

Comparing 3 progressions:
Blue: Flat betting
Red: U1D2M2
Green: Martingale
From Series 14 Results

My computational results consistently show that in the long run, progressions either 1) maintain or 2) worsen the flat bet expectancies.  For example, in baccarat, the flat bet expectancies are roughly -1%ish.  That is, for every \$100 you bet, you expect to lose about \$1 in the long run.  Applying a progression, the long term expectancies can still remain -1%ish, or drop to -2% to -4%ish, (lose on average \$2-\$4 per \$100 bet), or in some cases, depending on when the simulation is stopped, be much worse, exceeding -10%.

To understand this more intuitively, consider a capped Martingale, where a maximum sized bet is set, for example 1u, 2u, 4u, 8u, 16u, 32u, and no more.  If you lose the 32u, start the progression over at 1u for your next bet.  The capping makes the Martingale more practical, because it lengthens your bankroll’s lifetime, as well as respects the casino’s table limits.  Just as we had discussed previously, in the long run, the number of wins and losses of each bet amount will be equal. But realize this: Every time the peak bet of 32u wins, your bankroll gains only +1u, but every time the peak bet of 32u loses, your bankroll suffers a huge -63u drop! And then you have to go back to betting only 1u to start the progression over.  The figure below illustrates this quite dramatically.

Another way to see the same result: Statistically, winning 6 in-a-row will occur just as often as losing 6 in-a-row. When you win 6 in-a-row, your bankroll gains only +6u, but when you lose 6 in-a-row, your bankroll crashes -63u! So clearly, because the expected losses are so much greater than the expected wins, the long term expectancies will be worse than simply flat betting.  This is likewise true for any other progression capped at a peak bet limit.
Characteristic "stair step" pattern of bankroll balance when peak bet of capped Martingale is lost.From Series 16 Results

Characteristic “stair step” pattern of bankroll balance when peak bet of capped Martingale is lost.
From Series 16 Results

You might try to be clever and think, if my long term expectancies are significantly worse than expected for a nearly break-even game, I’ll just reverse the bet placements which had yielded -2% to -4% to become +1% to +3% (pivoting around the expected -1%). Why that won’t work is due to the progression. If a certain bet placement method yielded -4% flat betting, then, yes, reversing the bets would indeed yield +3% (and it will be a Holy-of-Holy-Grails!). But using a progression, reversing the bets won’t change the final answer. Why? Simply because everything reverses symmetrically. That is, while reversing your bets will change a 6 in-a-row loss of -63u into a 6 in-a-row win of +6u, it will symmetrically change your previous 6 in-a-row win of +6u into a 6 in-a-row loss of -63u!

(Incidentally, traders often make the same error in reasoning, thinking they can make a winning trading method out of a losing one by simply reversing the entry/exit logic!)

Gambling gurus often teach progressions as essential to stay ahead in a game such as baccarat.  By doing so, they are acknowledging the underlying negative expectancy of the game.  But their advice would be valid only in the short term.  This is because in the short term, luck may favor you and winning that larger bet can more quickly erase a host of smaller losses which you’ve suffered up to that point.

So, if your objective is to leave the casino once you’re profitable and never return to the tables again, then you would be wise to use a progression, if you can afford to, a Martingale, and pray to your lucky stars you win before your bankroll dries up.   In the short term, progressions are double-edged swords:  When you win, you dig yourself out of the hole faster, but when you lose, the hole becomes your grave.

If your intention is to keep playing (and thus dwell within the realm of the long term), understand that using any kind of progression can be much worse than flat betting, and it will never flip the polarity of the underlying expectancies.
Disclaimer: The betting strategies and results presented are for educational and entertainment purposes only. Gambling involves substantial risks, and the odds are not in the player’s favor by design. The author does not state nor imply any system, method, or approach offers users any advantage, and he shall not be held liable under any circumstances for any losses whatsoever.

« Last Edit: November 22, 2016, 11:33:11 AM by kav »

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Trilobite

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Re: Why Progressions Fail
« Reply #1 on: November 22, 2016, 09:35:17 AM »
I've always said that progressions are the same as flat betting, but no one ever agreed.
Here is my “flat betting” money management.

1) up as you lose, 1.2.3 from 8 to 15 layout positions

2) up as you lose, 1.2.3 from 9 to 18 layout positions

3) funky d'alembert up & down as you win/lose, 1.2.3.4 from 8 to 15 layout positions

4) funky d'alembert up & down as you win/lose, 1.2.3.4 from 9 to 18 layout positions

5) up as you lose, 2.4.6 from 12 to 15 layout positions

6) up as you lose, 2.4.6 from 13 to 18 layout positions

7) funky d'alembert up & down as you win/lose, 2.4.6.8 from 12 to 15 layout positions

8  ) funky d'alembert up & down as you win/lose, 2.4.6.8 from 13 to 18 layout positions

9) up as you lose, 3.6.9 from 12 to 15 layout positions

10) up as you lose, 3.6.9 from 13 to 18 layout positions

11) funky d'alembert up & down as you win/lose, 3.6.9.12 from 12 to 15 layout positions

12) funky d'alembert up & down as you win/lose, 3.6.9.12 from 13 to 18 layout positions

13) up as you lose, 4.8.12 from 12 to 15 layout positions

14) up as you lose, 4.8.12 from 13 to 18 layout positions

15) funky d'alembert up & down as you win/lose, 4.8.12.16 from 12 to 15 layout positions

16) funky d'alembert up & down as you win/lose, 4.8.12.16 from 13 to 18 layout positions

17) up as you lose, 5.10.15 >15 layout positions

18) up as you lose, 5.10.15 >15 to 18 layout positions

19) funky d'alembert up & down as you win/lose, 5.10.15.20 >15 layout positions

20) funky d'alembert up & down as you win/lose, 5.10.15.20 >15 to 18 layout positions

+12 units overall back to step 1)
+12 units at any stage but losing overall back to previous step.
Step 20) completed and still losing back to step 1)

« Last Edit: November 22, 2016, 10:40:29 AM by Trilobite »

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Mike

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Re: Why Progressions Fail
« Reply #2 on: November 22, 2016, 09:56:08 AM »
Trilobite,

Your system is a good effort and will probably make you some dough. In the short term of course.

When you say 8 to 15 and 9 to 18 "layout positions" what do you mean? Is it referring to the number of numbers bet?

And what is a "funky" D'Alembert? Is this a reverse D'Alembert in which you raise after a win and lower after a loss?

Trilobite

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Re: Why Progressions Fail
« Reply #3 on: November 22, 2016, 10:39:18 AM »
I bet a mix of numbers, sixlines, dozens/columns, and EC's.

When playing 1 unit only numbers and sixlines.
When playing 2 or more units dozens and columns are added.
When playing 5 or more units EC's are added.

The mix is generally from 8 to 12 positions, but can get up to 15 positions, in the first instance.

The final 3 possible positions that can take it to 18 are the EC's, which are introduced further into the cycle.

The mix is such that every number on the wheel is represented with every bet, which means every spin returns some units at the very least.

My d'alembert goes up or down as you win or lose according to the Lw registry, depending which is in front. It also holds the previous bet whenever the Lw is equal.
« Last Edit: November 22, 2016, 10:50:38 AM by Trilobite »

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Mike

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Re: Why Progressions Fail
« Reply #4 on: November 22, 2016, 11:21:30 AM »
Thanks. So how's it working out for you?

I suppose if you're going to use a progression then including many levels and steps + bets is the optimum way to go, because it follows that if all progressions amount to flat bets in the long run, then your strategy lengthens the long run (it's going to take longer for the long run to manifest using 10 steps rather than say 3).

kav

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Re: Why Progressions Fail
« Reply #5 on: November 22, 2016, 11:37:15 AM »
Great post.
My question would be this:
Considering various progressions, positive or negative and stepped in-between (Oscar's grind), would you prefer flat bet over progressions?
I mean when we say progressions fail, we should have a reference and presumably the reference is flat betting. Well in my opinion progression is a better way to bet than flat betting.

The logic behind negative progressions

And there is also some kind of
Mathematical Proof that Progressions cannot overcome Expectation
and the counterargoument:
Martingale progressions and Kelly
« Last Edit: November 22, 2016, 12:03:50 PM by kav »

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Mike

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Re: Why Progressions Fail
« Reply #6 on: November 22, 2016, 12:17:12 PM »
Kav,

I think you're missing the point, which is that there is no essential difference between flat bet and progressions. If they are the same then the question of which to prefer makes no sense. The problem is that progression junkies believe that their progressions take advantage of the order of the outcomes, but in fact they don't. For positive progressions to be effective the outcomes have to be bunched together or at least you need a good run where wins outnumber losses. For negative progressions you don't need bunched wins but a long losing run will be disastrous.

In either case you need to be able to predict what's going to happen (bunched wins or no "run from hell"), which can't be done. And because it can't, all progressions amount to arbitrarily increasing staking amounts at different times, which obviously can't increase your profits in the long term.

kav

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Re: Why Progressions Fail
« Reply #7 on: November 22, 2016, 12:34:56 PM »
Ok Mike, let's get practical.
Would you dismiss this info here as useless:
Re: Does A Series Of Short Sessions Combine To Make A Long Series?
Isn't it possible to use progressions in any ingenious way to gain any sort of "advantage" (term used in a lose way)?
No study of roulette or wagering plans can offer any "benefit" over throwing your chips randomly on the roulette table?

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MrPerfect.

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Re: Why Progressions Fail
« Reply #8 on: November 22, 2016, 01:36:58 PM »
Ok Mike, let's get practical.
Would you dismiss this info here as useless:
Re: Does A Series Of Short Sessions Combine To Make A Long Series?
Isn't it possible to use progressions in any ingenious way to gain any sort of "advantage" (term used in a lose way)?
No study of roulette or wagering plans can offer any "benefit" over throwing your chips randomly on the roulette table?
Progressions may work if you bet positive expectation numbers only. Progressions are multiplier of edge. If edge is negative- expected result is negative, if edge is positive- expected result is positive. Best results with progressions are achieved with medium to long run. Best progressions are positive ones, where you make your bet higher as you win. They offer best value for money invested.

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Reyth

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Re: Why Progressions Fail
« Reply #9 on: November 22, 2016, 02:52:03 PM »
Obviously progressions outperform flat betting but like Mr. Perfect says, its about creating an edge; progressions can help you get closer to that edge but based on my exprience, they are not enough by themselves to create that edge.

Randomness has patterns and I see no reason why they cannot be exploited to create an edge.  Roulette is not as simple as "do the math's house edge must always win rofl".  In all projections of house edge, winning bets can also be projected to exceed that house edge.  The question will always be the spin samples used.

Vociferous system critics have closed their minds to possibility and have embraced a negative roulette world view for whatever personal reasons; e.g. losing, sale of roulette related products, ego aggrandizement, to discourage those that would attempt to successfully employ systems, etc.
« Last Edit: November 22, 2016, 03:00:18 PM by Reyth »

Mike

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Re: Why Progressions Fail
« Reply #10 on: November 22, 2016, 03:16:07 PM »
Would you dismiss this info here as useless:
Re: Does A Series Of Short Sessions Combine To Make A Long Series?

Yes, useless. No matter how many statistics you generate how does it help you to predict the next winning number or series of numbers? Please be specific in your answer.

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Isn't it possible to use progressions in any ingenious way to gain any sort of "advantage" (term used in a lose way)?
No study of roulette or wagering plans can offer any "benefit" over throwing your chips randomly on the roulette table?

What do you mean by "ingenious"? No matter how clever any progression is, as Mr Perfect rightly points out, money management and progressions merely amplify whatever edge you have. No or negative edge means no or negative profit. Using a progression + negative edge means you just lose more than if you had been flat betting.

Mike

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Re: Why Progressions Fail
« Reply #11 on: November 22, 2016, 03:28:44 PM »
Obviously progressions outperform flat betting...

Er no Reyth, they don't. What does "outperform" mean? If it means that using a progression will garner more units in the short term that flat betting would have, then yes SOMETIMES progressions do outperform flat bets. They only consistently outperform flat bets in the sense that you lose MORE when you don't have an edge and win MORE when you do. The edge isn't an afterthought; it's essential.

Quote
Vociferous system critics have closed their minds to possibility and have embraced a negative roulette world view for whatever personal reasons; e.g. losing, sale of roulette related products, ego aggrandizement, to discourage those that would attempt to successfully employ systems, etc.

Oh good grief. So on your view, it's a personal thing; us "vociferous system critics" are critical for PERSONAL reasons. Nothing to do with math, logic, or anything objective like that. Not to mention the 100's of years of failure of any system advocate to demonstrate even one consistently winning system.

kav

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Re: Why Progressions Fail
« Reply #12 on: November 22, 2016, 04:58:23 PM »
Flat bet is a bad wagering plan, or no plan.

Your rational is analogous to this line of thinking: Just because the enemy has a stronger army (advantage) there is no point in devising a strategy/tactics for our attack.

If these tables can not convince you that different wagering plans have different bankroll fluctuation characteristics and can produce different results, then I don't know what can.

« Last Edit: November 22, 2016, 05:00:41 PM by kav »

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Reyth

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Re: Why Progressions Fail
« Reply #13 on: November 22, 2016, 06:39:06 PM »
Oh good grief. So on your view, it's a personal thing; us "vociferous system critics" are critical for PERSONAL reasons. Nothing to do with math, logic, or anything objective like that. Not to mention the 100's of years of failure of any system advocate to demonstrate even one consistently winning system.

No, I am talking about how certain people across the web incessantly pursue an anti-system crusade to the point of becoming obnoxious.

MrPerfect.

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Re: Why Progressions Fail
« Reply #14 on: November 22, 2016, 11:42:53 PM »
@Cavouras.
Nice table posted, Mr Cavouras. But what about other side of the coin? When progressions win, it's obviously good, what happens when they repeat losses? Would be fair to include that part of stats as well.
Like how many trials ended with the loss , Wighted average loss egeinst Wighted average win... ets.