Archive for flat bet

Why Any Progression Must Fail For Negative Expectancy Games In the Long Run

Posted in Life with tags , , , , , , , , , , , , on December 16, 2012 by virtuoid

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.

Baccarat Advantage: A Bogus Black Box

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on May 4, 2011 by virtuoid

A friend sent me a computer application Baccarat Advantage (baccaratadvantage.com), a black box which outputs bet placement instructions based on inputted Banker and Player hand total values.

The creator of Baccarat Advantage calls himself “Dr. Jacob Steinberg,” and claims to have achieved a positive expectation after running 1 million live shoes through his program.  Because a user of the program only accesses the program’s interface, where he enters the total hand values and receives the outputted betting instructions, the actual method of determining the bet placement is never revealed, and he can only use the application to play at online casinos, never at physical, brick-and-mortar casinos.   In addition to the purchase price, Dr. Steinberg also requires his customers to share a percentage of their winnings from using the program, and the exact purchase price depends on what percentage the customer agrees to pay.  In this way, he justifies selling the program, since he can in principle exponentially increase his income through his customers’ winnings while never actually revealing to them the exact method of his supposed holy grail.

Despite what Dr. Steinberg claims, my tests of his Baccarat Advantage objectively demonstrate that it quickly yields negative expectancies, and if he really did win a million live shoes with the method in his program, those shoes must have been unbelievably favorably biased to it.  On the surface, his procedure appears to utilize information from hand totals and not just the (mathematically doomed to fail) pattern of P/B wins.  Thus, there is a faint glimmer of card-counting potential, though the program does not fully account for the values of each card.  However, whatever his method is, my tests show that it consistently yields negative expectancies and can no better win at baccarat than any other method tested to date.

A picture of the Baccarat Advantage user interface:

Upon activating the program, a brief splash window encourages the player with an affirmative tagline, Because winning feels so good.  Play commences as follows:  At the beginning of each shoe, the user enters the first four hand totals of the first two decisions in the “Second-to-Last Hand” and “Last Hand” rows.  The program then outputs a bet placement instruction in the “Now Bet” row.  The user then presses the “Won,” “Tie,” or “Lost” button according to the result of the bet, upon which the values in the “Last Hand” row moves up to the “Second-to-Last Hand” row, clearing  the “Last Hand” row and making it available for fresh input.  He then enters the next set of hand totals in the now emptied “Last Hand” row and repeats the process.  After the end of each shoe, the “Reset” button is pressed, all the input boxes clear, and the process begins again for the next shoe.

There are two money management options: 1) Flat Betting and 2) Progression Betting.  Based on $1 units, flat betting requires a $50 bankroll, while progression betting requires a $164 bankroll.  The progression (as seen in the picture above) is a simple 7-level Martingale, padded at certain levels to cover Banker commissions.  Flat betting is described as a “slow winner,” but requiring “lower bankroll,” while progressive betting is touted as an “infallible, quick winner,” but requiring “higher bankroll.”  Either way, Dr. Steinberg claims his method consistently beats the house edge and is the only true (and easy) way to win baccarat.

For the most part, the program consistently outputs the same bet placement instructions per set of inputs.  I write, “for the most part,” because there were some minor glitches which would sometimes result in the same set of inputs resulting in different bet placement instructions.  The apparent glitches may occur when one changes an inputted value, and then back to the original value again, whereupon the opposite bet placement instruction would sometimes appear.  This is clearly an operational bug on the part of the programmer, assuming there is supposed to be a one-to-one correspondence between unique input values and output bet placement instructions.  Otherwise, the program appeared to be consistent enough for the most part to be tested against data sets of baccarat shoes.

To examine the long term performance of Dr. Steinberg’s baccarat black box, I created a script to automate the inputting and reading of the outputted bet placement instructions for 12,100 baccarat shoes.  Roughly 3-4 shoes per minute could thus be accurately inputted and analyzed, and the entire testing took place over several days and nights.  My automation script performs exactly what a human would do, entering the total hand values decision by decision, reading the outputted bet placement instructions, pressing the “Won,” Tie,” or “Lost” button according to the result of the bet, and pressing “Reset” after the end of the shoe before starting the next one.  For the testing, I used the Flat Bet mode, since no progression will be able to consistently help a method which cannot win flat betting.  For verification, I sent the data output to my friend, who double-checked and confirmed he was getting the same outputted bet placements from the program.

A sample of the data output follows:

1st column: shoe number
2nd column: decision number
3rd column: Banker hand total
4th column: Player hand total
5th column: decision P/B/T winner
6th column: Baccarat Advantage outputted bet placement

1  1 5 2 B -
1  2 1 3 P -
1  3 9 5 B P
1  4 3 8 P P
1  5 6 2 B B
1  6 5 5 T B
1  7 0 9 P -
1  8 8 7 B B
1  9 9 5 B B
1 10 0 6 P P
1 11 5 9 P B
1 12 6 6 T P
1 13 9 2 B -
1 14 6 7 P P
1 15 9 3 B P
1 16 0 5 P P
1 17 0 0 T P
1 18 2 1 B -
1 19 0 9 P P
1 20 5 8 P B
1 21 6 8 P P
1 22 7 9 P P
1 23 0 9 P P
1 24 8 1 B B
1 25 9 5 B B
1 26 8 6 B B
1 27 6 9 P B
1 28 1 9 P B
1 29 6 5 B B
1 30 3 8 P B
1 31 0 5 P B
1 32 3 9 P B
1 33 0 9 P B
1 34 8 4 B B
1 35 3 7 P B
1 36 8 6 B P
1 37 9 7 B B
1 38 3 8 P B
1 39 5 9 P B
1 40 4 6 P P
1 41 8 8 T P
1 42 3 9 P B
1 43 9 2 B B
1 44 7 5 B P
1 45 9 6 B B
1 46 0 2 P P
1 47 1 7 P P
1 48 9 0 B B
1 49 9 6 B P
1 50 8 0 B B
1 51 2 2 T P
1 52 4 7 P B
1 53 8 8 T B
1 54 9 5 B B
1 55 5 6 P P
1 56 9 6 B P
1 57 5 8 P P
1 58 4 4 T B
1 59 7 6 B B
1 60 6 5 B P
1 61 0 9 P P
1 62 1 7 P B
1 63 0 8 P P
1 64 1 6 P B
1 65 0 9 P P
1 66 8 6 B B
1 67 6 6 T B
1 68 4 6 P P
1 69 4 3 B B
1 70 0 9 P B
1 71 5 1 B B
1 72 3 4 P B
1 73 4 2 B P
1 74 4 8 P P
1 75 8 7 B B
1 76 7 8 P B
1 77 2 2 T P
1 78 9 4 B P
1 79 8 6 B P
1 80 6 6 T B
1 81 6 4 B P
1 82 3 7 P P

Notice that sometimes the program does not bet after a Tie, and sometimes it does.

The numerical and graphical results of the testing are presented in Simulation Series 31 Results.  Three sets of data were examined, each one consisting of slightly different Banker (B) and Player (P) compositions.  As the following plots show, the qualitative behavior of the Baccarat Advantage Player’s Advantages (P.A.’s, the net units won after commissions divided by the total amount bet) depend on the B/P compositions of the data set, though all are consistently negative.

Data Set 1 had a slightly lower-than-average numbers of Bankers, 50.61% Bs and 49.39% Ps (not counting Ties).  In this set, the P.A.’s of the Baccarat Advantage bet placements are always consistently worse than the expectancies for B, while the P.A.’s of the opposite of the Baccarat Advantage bet placements are always consistently better than those of P.  (Because of the lower-than-average numbers of Bs in Set 1, the expectancies for B is always more negative than that of P.)  The following plot which graphs the evolution of the P.A.’s over the numbers of shoes tested shows that in Set 1, Baccarat Advantage P.A.’s (blue for the program’s output, and red for the opposite of the program’s output) mostly lie to the outside of the Banker and Player P.A.s (yellow for B, and green for P).

Data Set 2 has slightly more Bs overall than Data Set 1, 50.69% Bs and 49.31% Ps (not counting Ties), which is closer to what are the “average” proportions.  As the following plot shows, the blue and red Baccarat Advantage P.A. lines begin to fall in-between the yellow and green Banker and Player P.A. lines.

Data Set 3 has 50.83% Bs and 49.17% Ps (not counting Ties), which is more Bs than “average,” and for the most part, the Baccarat Advantage P.A.’s are always comparable to or no better than the standard B/P expectancies.  Thus, in the plot below, the blue and red lines are mostly contained within the yellow and green lines.  In various, brief stretches, the Baccarat Advantage P.A’s became slightly more positive that that of B, and the opposite bet placement’s P.A.’s correspondingly became slightly worse than P, which is the opposite of what occurred in Data Set 1.

Notice that the line of symmetry between the opposing pairs in the above P.A. graphs is about half way between -1.0 and -1.5. This line of symmetry is due to the built-in tilt of the game in the house’s favor, and the fact that it is negative is the reason why “just bet opposite” a losing method does not win either. In a perfectly fair 50/50 game, the line of symmetry would be at exactly P.A.=0, meaning in such a zero-expectancy game in the long run, you always have equal chances of being net positive or negative, and on average, break-even. However, in baccarat, the house’s edge skews everything in the house’s favor, and you expect to always be net negative in the long run, no matter how you play. In other words, if you can’t consistently win a perfectly fair 50/50, zero-expectancy game in the long run, you have even less mathematical hope of winning a negative expectancy game in the long run.

Despite the above qualitative differences due to B and P compositions in the shoe, the resulting P.A.s are always negative, and the Baccarat Advantage method itself loses all data sets quite unceremoniously, as the following plots of the net score versus shoe clearly show:


I did not test Baccarat Advantage’s progression mode systematically, but I compared a few shoes to demonstrate that the bet placement output from the program in progression mode is exactly the same as in flat bet mode; only the bet amount differs according to a win or loss, and the progression is the straightforward 7-level Martingale.

Just for fun, I let my automation script run through a small data set in the progression betting mode.  In these runs, the required bet amounts would bust past the 7 levels of the progression every few dozen shoes, and a rather sad pop-up box would announce, “Sorry, you have lost.  Start over.”  Tracking the exact results of the 7-level progression over my testing results would have been a routine exercise, but completely not worth the time or effort.

In conclusion, my tests show that Dr. Steinberg’s Baccarat Advantage yields standard negative expectations and is quantitatively no different than any other baccarat method I have tested, except that in certain situations when the B/P compositions are above or below average, the P.A.’s of the Baccarat Advantage bet placements or its opposite are slightly more positive than expected when always betting B or P.  Unfortunately, the slight improvements in odds in these situations are not enough to be profitably exploited.

Baccarat Advantage is a black box that is at best broken and at worst bogus.

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.

Baccarat Simulation Series 31 Results: Baccarat Advantage

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on May 4, 2011 by virtuoid

Results from Baccarat Simulations Series 31 are presented below.

In this series, I entered sets of 12,100; 4,100;  and 2,100 shoes (each set varying in B/P compositions) into the black-box Baccarat Advantage application and analyzed the results.

Read a full discussion of these results at the following post:
Baccarat Advantage: A Bogus Black Box.

Set 1: 12,100 Shoes (B: 50.61%, P: 49.39%)
PBT Stats:

Count % (w/T) % (only PB) Expectancy
B 451,428 45.80% 50.61% -0.013162
P 440,597 44.70% 49.39% -0.012142
T 93,623 9.50%

Simulation Results:

Method Net Score Total Bet P.A.
BaccAdv -11,870.20 858,946 -1.38%
BaccAdv R -9,862.25 858,946 -1.15%
B only -11,740.40 892,025 -1.32%
P only -10,831.00 892,025 -1.21%

Set 2: 4,100 Shoes (B: 50.69%, P: 49.31%)
PBT Stats:

Count % (w/T) % (only PB) Expectancy
B 153,433 45.90% 50.69% -0.011454
P 149,228 44.64% 49.31% -0.013893
T 31,599 9.45%

Simulation Results:

Method Net Score Total Bet P.A.
BaccAdv -3,360.05 291,442 -1.15%
BaccAdv R -3,725.80 291,442 -1.28%
B only -3,466.65 302,661 -1.15%
P only -4,205.00 302,661 -1.39%

Set 3: 2,100 Shoes (B: 50.83%, P: 49.17%)
PBT Stats:

Count % (w/T) % (only PB) Expectancy
B 78,750 46.01% 50.83% -0.008731
P 76,165 44.50% 49.17% -0.016687
T 16,242 9.49%

Simulation Results:

Method Net Score Total Bet P.A.
BaccAdv -1,578.05 149,191 -1.06%
BaccAdv R -2,212.85 149,191 -1.48%
B only -1,352.50 154,915 -0.87%
P only -2,585.00 154,915 -1.67%

Data Set: 12,100 baccarat shoes used (ref. My Baccarat Shoe Factory).

Player’s Advantage is the net units won after commissions divided by the total units bet.

BaccAdv = Baccarat Advantage bet placement (output from black-box)

BaccAdv R = Baccarat Advantage reversed bet placement (opposite of output from black-box)

B only = always betting B every decision
P only = always betting P every decision

% (w/T) = percentage of decision counting ties
% (only PB) = percentage of decision not counting ties

Always flat-betting 1 unit per betting opportunity.  (No bets on ties, and bets occurring on ties are pushed and not tallied into the total number of bets.)

__________________________________________________________

Graphs of P.A. and Net Units Won (after commissions) per Shoe:

Set 1: 12,100 Shoes (B: 50.61%, P: 49.39%):


Set 2: 4,100 Shoes (B: 50.69%, P: 49.31%):


Set 3: 2,100 Shoes (B: 50.83%, P: 49.17%):

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.

System 40 Advanced?

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on October 25, 2010 by virtuoid

More like, “System 40 Declined.”

System 40S (“Advanced System 40″) is Ellis’ latest attempt to design an all-around baccarat system which does not require table selection and adapts profitably to any shoe condition.

System 40S consists of 3 of Ellis’ methods, and it uses the CS and SAP counts as switching indicators:

1.  System 40
(ref. System 40: Ellis’ Crown Jewel)

2. RD1
(ref. Squeaky Parts)

3. F2/F3
(ref. Squeaky Parts)

The CS (Chop-Streak) count assigns +1  for every opposite decision and -1 for every repeat decision.  For example, if the shoe decisions had been PPPBPBBPP, the CS count at the end of that sequence would have canceled out to be 0 (-1-1+1+1+1-1+1-1).

For positive CS counts which indicates choppy shoe conditions, System 40 is used, and the SAP determines the culprit.

For negative CS counts which indicates streaky shoe conditions, RD1 and F2/F3 are used, and the SAP determines which one to use, F2/F3 when 1s are more than expected, and RD1 when 1s are fewer than expected.

For neutral CS counts, System 40 is net bet, also called System 40N.

The SAP count was explained in System 40: Ellis’ Crown Jewel.  In System 40S, the SAP count is used as a secondary indicator.  For choppy conditions, the SAP count determines whether to use the 2s, 3s, or 4s as the culprit in System 40.  For streaky conditions, the SAP count is used to decide whether to use RD1 or F2/F3.

As explored in System 40: Ellis’ Crown Jewel and Squeaky Parts, the three basic methods System 40, RD1, and F2/F3 played straight through the shoes yield Player’s Advantages no better than single-side betting.  Since System 40 is primarily a chop method and RD1/F2/F3 are strong streak methods, Ellis’ rationale in combining the three together into a single system is to maximize their strengths under the appropriate shoe conditions.  When to use witch?  Ellis proposes using the CS and SAP counts as indicators to switch between the three, as explained above.

All of this sounds reasonable and rational, and in fact, Ellis’ use of RD1 and F2/F3 seems to be borrowed out of Mark’s Maverick manual.

However, as my Series 9 results show, Advanced System 40 does no better than the original System 40, RD1, or F2/F3 alone, and all perform comparably with simple single-sided betting (ref. Series 1).  Money management and U1D2M2 do not offer any significant improvement, a recurring theme for overall negative methods.  Using Advanced System 40 on the R/A basis does not make a difference, another recurring theme.

Thus, complexity does not appear to outperform simplicity in the long run.  A shoe which a simple system would lose, a complex one may win.  But the converse is also true:  a shoe which a complex system would lose due to unnecessary switching, a simple one may win.  Indeed, complex systems which involve switching merely transfer the decision-making process from deciding between Player and Banker to deciding between System 1 and System 2.  When you’re right, you win; when you’re wrong, you lose.  In the long run, all washes out to yield effectively what is mathematically expected from simply single-side betting Player or Banker, the simplest of all systems.

It is not too surprising that combining System 40, RD1, and F2/F3 fail when used together:  Three wrongs a right does not make!

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.

Baccarat Simulation Series 9 Results: System 40S (Advanced System 40)

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on October 25, 2010 by virtuoid

Results from Baccarat Simulations Series 9 are presented below.

In this series, I examined Ellis’ newest System 40S, also known as “Advanced System 40.”

A discussion of the results can be found here:  System 40 Advanced?

Player’s Advantage (Flat Bet) Player’s Advantage (U1D2M2) % Shoes Win % Shoes Loss % Shoes Broke Even Best Score Worst Score
PB S40S A -1.27% -1.26% 58.50% 39.82% 1.68% 71 -449
PB S40S C -1.18% -1.19% 64.41% 33.96% 1.62% 63 -27
RA S40S A -1.29% -1.28% 58.15% 40.21% 1.64% 70 -465
RA S40S C -1.31% -1.29% 64.38% 34.02% 1.61% 57 -27

Data Set: 102,600 baccarat shoes used, including Zumma 600, Zumma 1000, Wizard of Odds 1000, and Virtuoid 100,000 (ref. My Baccarat Shoe Factory).

Player’s Advantage is the net units won after commissions divided by the total units bet.

A, C refer to Money Management Procedures (ref. Money Matters).

Flat betting and U1D2M2 betting progression (ref. Money Matters).

P = Player
B = Banker
R = a derivative of PB
A = a derivative of PB

S40S = System 40S (“Advanced System 40″)

% Shoes Won, Lost, Broke Even, and Best and Worst Scores are from shoes using U1D2M2.

__________________________________________________________

Graphs of Net Units Won (after commissions) per Shoe:

P/B Results:

System 40S Strategy (with MM and without MM, flat bet and U1D2M2):

R/A Results:

System 40S Strategy (with MM and without MM, flat bet and U1D2M2):

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.

The Ties That Bind

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on October 21, 2010 by virtuoid

Claiming that most pattern based baccarat strategies are based on temporary (and thus inconsistent) biases and thus do not offer a true mathematical edge, Michael Brannan proposed a card counting method which supposedly indicates when conditions favor ties.

His reasoning is simple:  remove all of the odd valued cards from the shoe, and since the remaining even valued cards can only add up to even sums, the chances that ties occur drops from 1-in-10 to 1-in-5, effectively doubling the probability for ties to occur.  Since ties pay 8-to-1, betting ties when the odds become 1-in-5 seems like a sure way to consistently beat the casino!

His advanced tie count assigns positive counts to the odd valued cards and negative counts to the even valued cards, with the exception of 2 and 8, which are assigned positive counts.  If odd valued cards are coming out of the shoe more often than negative valued cards, the count becomes positive.  Once the tie count reaches a certain positive threshold, the strike count, the shoe is relatively rich in even valued cards, conditions favoring ties, according to Brannan.  So, after the strike count, start betting ties.  The more positive, the better for ties.  In fact, Brannan uses a negative betting progression (increasing his bet as he loses), since he believes the chances of getting a tie increases the more positive the count becomes.

However, my statistical and experimental evidence in Baccarat Simulations Series 8 on data from 100,000 baccarat shoes (ref. My Baccarat Shoe Factory) contradict Brannan’s claims.

1.  Frequency of Ties vs. MB Tie Count

First, I examined how frequently ties occur in relation to Brannan’s advanced tie count.  If Brannan was right, ties would occur significantly more frequently for positive counts than negative.  However, I found that they show a completely symmetric distribution about a count of zero.  That is, ties occur just as frequently for every negative count as it does its corresponding positive count, as seen in the following graph:

2.  Percentage of Ties per Hands vs. MB Tie Count:

Next, I recorded the tie count for every hand, which allowed me to calculate the percentage of hands that ties would occur for each of Brannan’s advanced tie count.  As the following graph shows, the percentage of ties per hand for each tie count is around 9.5%, practically identical to the theoretical tie percentage 9.5156%.  So, contrary to Brannan’s claims, a more positive tie count is not associated with a greater percentage of ties.  (The spike for the most positive bin is due to insufficient statistics at that extremely high count.)

3.  Both of the above statistical findings in and of themselves already doom Brannan’s method to fail.  For sake of completeness, I performed full baccarat simulations over the 100,000 shoes, betting for ties after strike counts of +30, +40, +50, and +60.  In every case, the player’s advantage was found to be practically the same as the theoretically expected -14.3596%.  That is, Brannan’s method does no better than simply always betting tie every decision.

If Brannan is actually winning with his method, he is probably doing so by inadvertently taking advantage of the same kind of temporary (and unreliable) biases which he identified as a weakness for pattern based methods.  If that is true, Brannan’s method would still be relatively inefficient, since I found that betting opportunities where the tie count exceeds +30 arise less than 3.5% of the time.  That is, on average for every 100 decisions, less than 4 offer betting opportunities where the tie count exceeds +30.

In the long run, such patience is not rewarded, and it makes no difference whether you use Brannan’s method or bet ties every decision.  The latter is a lot easier and faster, and just as ineffective.

Related topic: Frequency of Ties in 1M Baccarat Shoes.

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.

Baccarat Simulations Series 8: MB Advanced Tie Count

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on October 20, 2010 by virtuoid

Results from Baccarat Simulations Series 8 are presented below.

In this series, I examined the Michael Brannan’s Advanced Tie Count Method.  Read a discussion of the results in the following post, The Ties That Bind.

Strike +30 Strike +40 Strike +50 Strike +60
Total Units Won 219,736 60,480 13,272 2,416
Total Units Lost 259,623 70,761 15,854 2,944
Total Units Bet 287,090 78,321 17,513 3,246
Player’s Advantage -13.8936% -13.1267% -14.7433% -16.2662%
Percentage of Bets Won 9.5674% 9.6526% 9.4730% 9.3038%
Percentage Bet Opportunity 3.4268% 0.9349% 0.2090% 0.0387%

Data Set: 100,000 baccarat shoes (ref. My Baccarat Shoe Factory).

For this set of 100,000 shoes, the frequency of Player, Banker, and Ties were as follows:

Player Wins 3,738,456 (44.6232%)
Banker Wins 3,840,209 (45.8377%)
Tie Wins 799,170 (9.5391%)
Total 8,377,835

Player’s Advantage is the net units won after commissions divided by the total units bet.  The theoretical player’s expectancy for the tie is -14.3596%.

Flat betting only.

Strike +30, +40, +50, +60 = MB Advanced Tie Count after which to bet tie

Percentage of Bets Won = Percentage of all bets won for tie, where the theoretical expectancy for winning the tie is 9.5156%.

Percentage Bet Opportunity = Percentage of all betting opportunities available to bet, determined by the strike count.

__________________________________________________________

Graphs of Net Units Won per Shoe:

Strike +30, +40, +50, and +60 (full view):

Strike +30, +40, +50, and +60 (close up):

__________________________________________________________

Other Statistics:

Percentage of Ties and Hands per Count:

Advanced Tie Count Bins Frequency of Ties per Count Frequency of Hands per Count Percentage Ties per Hands
-71 to -80 31 265 11.6981%
-61 to -70 180 1,923 9.3604%
-51 to -60 1,100 11,511 9.5561%
-41 to -50 5,018 52,522 9.5541%
-31 to -40 17,581 184,004 9.5547%
-21 to -30 49,516 519,538 9.5308%
-11 to -20 111,411 1,172,155 9.5048%
-1 to -10 200,952 2,113,769 9.5068%
1 to 10 202,404 2,111,641 9.5852%
11 to 20 111,902 1,171,674 9.5506%
21 to 30 49,663 521,043 9.5315%
31 to 40 17,866 186,878 9.5602%
41 to 50 5,111 53,178 9.6111%
51 to 60 1,143 12,079 9.4627%
61 to 70 215 2,296 9.3641%
71 to 80 39 404 9.6535%
81 to 90 5 67 7.4627%
91 to 100 1 2 50.0000%

Frequency of Ties and Hands per Count:

Advanced Tie Count Bins Frequency of Ties per Count Percentage of Total
-71 to -80 31 0.0040%
-61 to -70 180 0.0233%
-51 to -60 1,100 0.1421%
-41 to -50 5,018 0.6482%
-31 to -40 17,581 2.2710%
-21 to -30 49,516 6.3963%
-11 to -20 111,411 14.3916%
-1 to -10 200,952 25.9582%
1 to 10 202,404 26.1457%
11 to 20 111,902 14.4550%
21 to 30 49,663 6.4153%
31 to 40 17,866 2.3079%
41 to 50 5,111 0.6602%
51 to 60 1,143 0.1476%
61 to 70 215 0.0278%
71 to 80 39 0.0050%
81 to 90 5 0.0006%
91 to 100 1 0.0001%
Total 774,138
Advanced Tie Count Bins Frequency of Hands per Count Percentage of Total
-71 to -80 265 0.0033%
-61 to -70 1,923 0.0237%
-51 to -60 11,511 0.1418%
-41 to -50 52,522 0.6472%
-31 to -40 184,004 2.2675%
-21 to -30 519,538 6.4022%
-11 to -20 1,172,155 14.4444%
-1 to -10 2,113,769 26.0478%
1 to 10 2,111,641 26.0216%
11 to 20 1,171,674 14.4385%
21 to 30 521,043 6.4208%
31 to 40 186,878 2.3029%
41 to 50 53,178 0.6553%
51 to 60 12,079 0.1488%
61 to 70 2,296 0.0283%
71 to 80 404 0.0050%
81 to 90 67 0.0008%
91 to 100 2 0.0000%
Total 8,114,949

Advanced Tie Count Bins = bins of 10 tie counts

Frequency of Ties per Count = how often ties occur for each count

Frequency of Hands per Count = how often a hand has a count

__________________________________________________________

Graphs of Other Statistics:

Frequency of Ties vs. MB Tie Count (log scale):

Percentage of Ties per Hands vs. MB Tie Count:

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.

Baccarat Simulation Series 7 Results: Scott’s (eirescott) Grail

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on October 16, 2010 by virtuoid

Results from Baccarat Simulations Series 7 are presented below.

In this series, I examined Scott’s (eirescott) Grail (Final, October 8, 2010).

Read a discussion of the results in Can Betting on Birthdays Make You Rich?

Player’s Advantage (Flat Bet) Player’s Advantage (U1D2M2) % Shoes Win % Shoes Loss % Shoes Broke Even Best Score Worst Score
SG A -1.23% -1.29% 59.97% 33.26% 6.77% 13 -105
SG C -1.28% -1.24% 56.33% 31.87% 11.79% 7 -26
SG A Z600 -3.48% -2.98% 57.50% 34.67% 7.83% 10 -53
SG A Z1000 -0.74% 0.19% 59.90% 32.60% 7.50% 12 -45

Data Set: 102,600 baccarat shoes used, including Zumma 600, Zumma 1000, Wizard of Odds 1000, and Virtuoid 100,000 (ref. My Baccarat Shoe Factory).

Player’s Advantage is the net units won after commissions divided by the total units bet.

A, C refer to Money Management Procedures (ref. Money Matters).

Flat betting and U1D2M2 betting progression (ref. Money Matters).

P = Player
B = Banker
R = a derivative of PB
A = a derivative of PB

SG = Scott’s (eirescott) Grail (Final, October 8, 2010), based on the birthday paradox theory with pre-fabricated, random sets.  No LLMx bets.

Z600 = Zumma 600
Z1000 = Zumma 1000

% Shoes Won, Lost, Broke Even, and Best and Worst Scores are from shoes using U1D2M2.

__________________________________________________________

Graphs of Net Units Won (after commissions) per Shoe:

P/B  Results:

Scott’s (eirescott) Grail (flat bet and U1D2M2), Full Data Set:

Scott’s (eirescott) Grail (flat bet and U1D2M2), Zumma 600 & 1000:


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.

Baccarat Simulation Series 6 Results: System 40

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , on October 15, 2010 by virtuoid

Results from Baccarat Simulations Series 6 are presented below.

In this series, I examined Ellis’ System 40.

Read a discussion of the results in System 40: Ellis’ Crown Jewel.

Player’s Advantage (Flat Bet) Player’s Advantage (U1D2M2) % Shoes Win % Shoes Loss % Shoes Broke Even Best Score Worst Score
PB S40E A -1.22% -1.24% 58.84% 39.46% 1.69% 64 -595
PB S40E C -1.17% -1.21% 65.55% 33.16% 1.30% 59 -27
PB S40V A -1.24% -1.25% 58.72% 39.75% 1.53% 66 -617
PB S40V C -1.19% -1.22% 65.73% 33.08% 1.19% 59 -27
RA S40E A -1.26% -1.25% 58.60% 39.81% 1.59% 67 -462
RA S40E C -1.23% -1.23% 65.16% 33.51% 1.33% 58 -27
RA S40V A -1.26% -1.27% 58.47% 39.95% 1.57% 67 -484
RA S40V C -1.25% -1.25% 65.40% 33.39% 1.21% 58 -27

Data Set: 102,600 baccarat shoes used, including Zumma 600, Zumma 1000, Wizard of Odds 1000, and Virtuoid 100,000 (ref. My Baccarat Shoe Factory).

Player’s Advantage is the net units won after commissions divided by the total units bet.

A, C refer to Money Management Procedures (ref. Money Matters).

Flat betting and U1D2M2 betting progression (ref. Money Matters).

P = Player
B = Banker
R = a derivative of PB
A = a derivative of PB

S40E = System 40 (Ellis’ rules)

S40V = System 40 (Virtuoid’s version)

% Shoes Won, Lost, Broke Even, and Best and Worst Scores are from shoes using U1D2M2.

__________________________________________________________

Graphs of Net Units Won (after commissions) per Shoe:

P/B and R/A Results:

System 40 E and V Strategies (flat bet and U1D2M2):


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.

Squeaky Parts

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on October 13, 2010 by virtuoid

Thus far, I have completed 5 series of baccarat simulations.

They include the following elementary baccarat methods:

1.  Single Side Betting, Repeat, Opposite, Repeat-Opposite Toy Method

2.  TB4L, OTB4L, OTT Toy Method

3.  Repeat-Down Series: RD12 (RD1), RD3

4.  F Series:  F2, F3

5.  Random Coin Flip Betting

The results of the first two series were discussed in the previous posts Series 1 Discussion and Series 2 Discussion.

In Series 3 and Series 4, I examined Ellis’ methods RD (Repeat-Down) and F (Follow).  Because they are proprietary to Ellis, I will offer no detailed explanation or discussion of these methods here.  Ellis’ students will recognize them.  Suffice it to report that played on their own throughout the 102,600 shoe data set, they performed no better than single side betting Player or Banker.

In Series 5, I programmed the computer to simply randomly “guess” Player or Banker (and R or A), which is equivalent to flipping a coin to decide which side to bet,  and again, the results were comparable to simple, single side betting.

Indeed, thus far all methods yielded Player’s Advantages (P.A.s) not significantly better than single side betting of Player or Banker.

Whether flat betting or using the U1D2M2 progression, the P.A.s remained essentially the same.  Using U1D2M2 lost more in terms of actual number of units and suffered a greater rate of loss, but the resulting P.A.s did not significantly differ than when simply flat betting.

Money management also did not significantly improve the P.A.s, whether using a simple stop loss or a more comprehensive money management procedure.

The results suggest that betting progressions such as U1D2M2 and comprehensive money management procedures are unable to turn a losing method into a winning one.

It can be argued that each of the methods I have tested so far performs better under certain shoe conditions than others.  So, each might be used as a building block of more complex systems to maximize strengths and minimize weaknesses.  The goal is to formulate a more effective and efficient baccarat strategy or approach, where the sum is greater than its parts, squeaky though they are.

Thus having examined the parts carefully, we now begin to consider the larger systems and approaches, such as Ellis’ System 40, Mark’s Maverick/MU, and Scott’s random sets and birthday paradox approach.

So, the fun has just begun!

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.

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