Paperless Modified Labouchere in 3D

I've been working on a way to keep track of my bet progressions by chip stacking instead of maintaining a paper-trail. This might not be very helpful in roulette and baccarat where scorekeeping is routine. But, my goal is to apply this to Blackjack where scorekeeping is not allowed (and where creative chip stacking seems to make the pit staff nervous).

I am going to present my method in several parts (only because I do not want each particular post to be too long and I may need to write at several different times). Again, this post is really about a manageable way to monitor the progress of your labouchere line(s) without using paper.

The First Component - The Modified Labouchere

Because I am setting out to keep track of a labouchere line without pen and paper, I chose to begin with a very simple modified labouchere which comes from Marten Jensen's book "Secrets of Winning Roulette."

This MM system has you winning 1 unit on any first bet after the successful cancallation of any line. Although I find it a very appealling and very conservative method, it will not appeal to those who'd rather not bet 6 or 8 units in order to get back to zero after having lost only 1 unit.Jenson sets forth his modified labouchere on page 155. No doubt my attempts to explain his system here will be less effective than studying his text on your own (which I obviously recomend). Nevertheless, the key to the "modified" labouchere is that the line begins with no numbers. You place a bet of 1 unit and if you win, you place that bet again and again. If you lose, your next bet would be the first number in your line and a win there would cancel the line and end the series. So, after your first loss of a 1-unit bet, your would then place a bet of 1 unit to recover. A second loss would be the 1st loss in your line and you would place your next bet at 2 units (then 3, 4, 5, etc.). As with any labouchere, a win cancels the last 2 numbers in your line. Unlike other laboucheres, when you cancel Jensen's "modified labouchere" you have no gain (nor loss) for the series. Your net wins are only from the "first" bet wins after a series, which is NOT a number in your line. Perhaps I can elaborate on this if there are any questions. I assure you it all makes good sense in the Book.

The Second Component is the Segregation of your chips.

I propose segregating your chips into three piles:
1) Your "chip locker"
2) your "win vault"
3) your "labouchere line"

YOUR CHIP LOCKER:

Suppose you buy into a $10 table for $300. You are given 30 red chips and you stack them somehow neatly and together, this area is basically your session bankroll which I call my "Chip Locker". (Not to be silly, but you might want to stack them in 6 stacks of 5 for example and keep those 6 stacks clustered together so that you can easily assess the balance in your chip locker).

You've sat down. You've bought in. You've stacked your chips and you can easily see that you have 30 chips in your "chip locker" which means you are even with the house.

YOUR WIN VAULT:

Now its time to you place your first bet. Move one chip from your locker onto the layout, and you win. Your win/loss record would look like this: W. Take both chips and place one in your chip locker and the other next to your chip locker by itself in an area we'll call your "win vault." As long as you have 30 units in your chip locker (as you do now) and NO chips in your labouchere line (as you do now), the win vault represents your net gain for the session (presently up one chip).

Now place your next bet of one chip on the layout and continue this way until you lose.Lets suppose you lose your very next bet. Your win/loss record looks like this: W,L. You placed your second bet on the layout and you lost. Now you have 29 chips in your locker and 1 chip in your vault for a net gain or loss of zero.

YOUR LABOUCHERE LINE:

Because you lost your most recent bet, you now take a chip from your chip locker and place this chip in your third segregated area, your labouchere line. This chip is the first number in your labouchere line and tells you how much to wager on the next (third) bet. Think of this as being a new labouchere line with one digit "1" represented by one chip. Now place one chip (from your locker) on the layout. For this your third bet, one of two things will happen: you will win or you will lose (pushes have no consequence).

IF YOU WIN (this third bet) (your win/loss record would look like this: W,L,W) - take your two chips from the layout and place them in your chip locker, you have cleared your line, so you place your single labouchere chip back in your locker and notice that you now have 30 chips in your locker and one chip in your win vault. You are once again up by one chip. And you will place a new bet of one chip on the layout but no chips in the labouchere line area because you have NO line at this time.

OR

IF YOU LOSE (this third bet) (your win/loss record looks like this: W,L,L) - take another chip from your locker and place it next to (adjacent and to the right of) your single labouchere line chip. This tells you that your next bet needs to be 2 chips (by adding the only two numbers in the line 1 + 1). So place 2 chips stacked on the layout. Your fourth bet (after W,L,L), is 2 chips. At the risk of sounding redundant, lets look first at if you win this 4th bet.

IF YOU WIN (this fourth bet following W,L,L) - You take 4 chips from the felt and place them in your Chip Locker. You cancel your labouchere line by removing the 2 chips from your segregated labouchere line area and place those two chips back in you chip locker and you are again up by one chip. Notice that you have won 2 bets and lost 2 beats and are up by one unit.

OR

IF YOU LOSE (this fourth bet following W,L,L) - You take two chips from your locker (two chips because that is the number of chips you lost on the 4th bet) and place them stacked next to the two single chips in your laboucher line (now your line on paper would read 1,1,2). Your next bet is 3 chips because the last two numbers in your line add up to 3.

I am going to stop here for now. I hope that there is enough informaiton here to get you going. I hope that you see that any time you clear your labouchere line, you should have 30 units in your locker and pure profit in your vault.Please post any questions.

For the next part of this post, I will be adding my 3D element and looking at a long W/L run to show you some of the benefits of the modified labouchere and this practical method of tracking your progress.I hope you will see this method is easily learned and when diligently applied, you can at all times know exactly how far you are up or down and what you need to do to cancel your current line.

PART II

OK - I've been working on this chip stacking thing and the modified labouchere in 3D and I'm not sure how to post my information graphically, but of course I'll try.

I reiterate what I said at the onset: THIS IS NOT A SYSTEM TO HELP YOU WIN<>

The idea is simply to build a grphical representation of your position so that you can comfortably chose the size of your next bet AND decide when to stop playing based on wins or losses. I have been owrking on this because I use notepads to keep my labouchere lines going when I play at home and I've been wanting to become proficient with something I could take into the casino wihtout the need for notes.

Key:
(1) <<<< = one chip
(2) <<<< = two chips stacked
(3) <<<< = thre chips stacked, and so on
-----<<< = the dashes are used to make the verticle lines intersect and have no other meaning


The Modified 3D Labouchere Chip Stacking Method for Blackjack:


As with the orignal modified labouchere, we will bet one unit until we lose. After a loss, we begin a labouchere line with one single digit (one unit). This is represented on the layout by removing a single chip form your Chip Locker and placing it in the Labouchere Line area of the felt. Thus:

(1)

Your next bet is 1 unit. A win clears the line. A loss tells us to add a digit to the line equal to the loss. Thus:

(1)(1)

Now with the 3D concept, you can lose three more bets without escalating your bet. Any win while betting 1 unit clears one chip from the 3D line. Notice that YOU ARE not clearing 2 digits as with a traditional labouchere line. With 4 straight losses (5 counting the intitial loss prior to beginning the line), your 3D line should look like this:

---(1)
(1)(1)(1)
---(1)

Now you begin betting 2 units because you have 2 intersecting lines, each line with 1 unit at each end.A win of 2 units here would clear 2 chips. A loss would require us to add a stack of 2 chips to the diagram:

---(1)
(1)(1)(1)(2)
---(1)

At this point (as with any point along the way), you can chose between betting 2 units and add the loss to the left of the horizontal line OR bet 2 units and add the loss to the top or bottom of your vertical line.

------(2)
------(1)
(2)(1)(1)(1)(2)
------(1)
------(2)

IF you built your line symetrically as above, you'd start betting 4 units on your next bet. However, the above illustration would be how your ships would look if you lost 10 decisions in a row (highly unlikely in perfect basic strategy Blackjack). More than likely, your 3D lines will be more often less symetrical.So what is the point of all of this??In order to appreciate this scorekeeping method, you really have to play with it. The chip stacking element allows you to focus on the cards and your basic strategy decisions. You can assess your overall picture of how much you are up or down by looking at your three chip areas. You can decide how much to bet on the next bet by looking at your 3D lines. The 3D element often gives you flexibility to chose from a smaller bet or a larger bet. As you win, you can shift the remaining chips around so that the smallest denomination is in the center and there is a graduation of chip stacks radiating out in 4 directions. You may find yourself with something like this:

---(3)
(4)(2)(3)
---(3)
---(5)

Here you could bet 3 or 4 or 5 or 7 or 8 in an effort to clear the lines when you are winning and/or balance them when you are losing.Keep in mind that pit staff are often bothered by chip stacking. They are prone to think that you are counting cards. When they see that you are not wildly escalating your bets at the end of a shoe, they should have no problem letting you do whatever you want.


Please feel free to email with any questions!

"Unlikely" vs. "Highly Unlikely"

The Difference Between an “Unlikely Event” and a “Very Unlikely Event”

I have mentioned elsewhere that “math” negates all systems. Or perhaps better put, the reality of systems (that they will not overcome the house edge) becomes apparent when one applies strict rules of mathematics.

But, now I’m looking at things a little differently:

To understand my new theory, let’s look at a very old one. Suppose we employ a very simple martingale system as follows (looking at a true 50/50 decision): We’ll bet one unit on the first decision and if we lose we will double the bet (2 units) on the second decision and then double again after a second loss. This three-step martingale gives us three shots at making a one unit profit. If we lose all three stages, we are out 7 units. This “beginner” approach tends to make us feel comfortable because we “know” that in a 50/50 game, we should be winning more often than one in three hands. Math tells us, on the other hand, that we will break even (no house edge in this hypothetical) because we “should” encounter the full-series loss of seven once for every 7 single-unit wins. As players we know that “in the short run” the 50/50 probability of a win is not reliable and that it would be well within the realm of possibilities to encounter a “bad run” of full-series losses in any particular session.

Math helps us see that although we have a 50% chance of winning the very next decision we also have a 50% chance of losing. When looking at the proposition of winning one of our next three decisions, we see that the likelihood is one in 8. This means that if we play 100 series of 3 hands, we should win 7/8ths of those series and lose one eighth. We will win 7 units for each successful series of three and lose 7 units for every full-series loss (or failure of our system). If we encounter a session where we get the “expected” results, we can expect to break even.

The lure of this system is (in part) based on the mathematical fact that we begin each series of three decisions with a 87.5% chance of winning that particular series. We all would admit that an 87.5% chance of winning anything “sounds” good. We know however that, our 87.5% chance of winning 1 unit is counter-balanced with a 12.5% of losing 7 units. NOTHING we can do will overcome this fact.

So, why bother?

Well, let’s look at this fact from a different angle. Suppose a typical session at a roulette wheel is 300 spins. How many times would we expect to be brought back to zero using the three-step martingale mentioned above? Three hundred spins will produce one-hundred series of three. We “should” win 87.5 of those series and lose 12.5. If we play for 5 hours (at 60 spins per hour), we’d be losing or “brought back to even” 2.5 times per hour. If we only played 30 minutes, we could expect to be brought back to even 1.25 times and if we played for 15 minutes, theoretically, we would not encounter enough decisions (or series of decisions) to have one losing session.

[House Edge: Before you start writing me and saying that I left out the house edge, let me explain that I am trying to keep the math simple for the purpose of this discussion. Think of the game in my example as “no-edge” Roulette. At an American Roulette wheel (using the example above) you would expect to win 7 series and lose 1 series but instead of ending up at a break even point, you would end up down 5.26% of a unit, because of the house edge. If you are interested in the “real” odds on an American roulette wheel, then you need to begin with the fact that a bet of one unit on black has a 47.4% (less than the 50% above) likelihood of winning and if you set out to win at least one decision of the next three consecutive decisions, your likelihood of winning at least one in the next three would be 85.44% (which is of course below the 87.5% in the example below).]

My thought is that we can reduce the “likely” to the “highly unlikely” by increasing coverage of the layout. For example: Suppose we cover 2/3rds of the layout instead of 50% in the earlier example. We know that we can not overcome the odds. We know that we will be brought back to even eventually. However, lets look at the short run. Employing a three-step martingale, we are now betting that we will win at least one of the next three decisions and we have 66% of the layout covered. Instead of losing one in eight series of three, we now can expect to lose only one in 27 series of three.

(Of course we would expect to lose 26 units and once again be brought back to zero. The math would go like this: our first bet would be 2 units, one on each of 2 dozens for example, after a loss, our bet would have to be increased to 6 units (3 on each of 2 dozens) and after two losses, we’d increase our bet to 19 (or 9 on each of 2 dozens). This three-step martingale progression would produce a win of 1 unit for each successful series and lose 26 for each three-step loss.)

Lets go back to our 5 hour session of 300 decisions. Again we are looking at this session as 100 series of three decisions. How many of those series can we expect to lose? The answer is 3.6. How many can we expect to lose in an hour? The answer is: .72.

Now, math tells us that if we play this game for one hour, it is unlikely that we will encounter a loss. We should see 60 decisions and win 20 units. And one might say that we are “due” a loss around the corner.

Stopping While Ahead and Minimizing Volatility

Suppose you played a game where you always won 50% of your decisions in the short run (like in 100 decisions), suppose also that this game rarely produced streaks of more than 4 or 5 losses in a row. It is likely that you could sit at any session and play this sort of game flat-betting and stop when up by one unit. Some sessions would only be one decision long and other might take 100 decisions but under these circumstances you could almost certainly eventually hit a point where you were up by one single solitary unit. One might say that when you quit, you were due a loss on the very next decision. Being only up by one unit, you were due to be brought back to even. Never the less, with minimal volatility, you could always play until up by one unit. Eventually you’d get ahead.

Now shift back to the game where you are expected to lose 27 units in one decision and win one unit for each of 26 decisions. Using my theory of stopping while ahead and minimizing the volatility, you should have many opportunities to stop when ahead by less than 26 units. Of course, if you started out losing, you’d have a long row to hoe. But math tells us that each bet you place has a 2 in 3 chance of winning and the likelihood of losing three such bets in a row is less than 4%. The chances of getting into a point where you are ahead by half of a successful series (win stop of 13 units) are very good indeed.

Final Thoughts

As with all systems, any play based on the ideas contained here needs to play well capitalized, and as always, successful players need to be disciplined and patient.

[PS – No doubt, these ideas have been around in one form or another for many, many years. I do not claim to be presenting any sort of original breakthrough. These ideas merely represent my current thoughts on a better way for me to look at the sobering application of math to gambling systems.]

Labouchere - Merely a Scorecard!

(I Originally Posted This to the Meassage Board at Gambler's Glen)

I am fascinated with the recent discussion here about a bet selection method that wins more than 50% of the time. While I’ll be quick to agree that we could all make a lot of money with such a sure-fire method, I would be happy with “much less”.

I would be delighted to be able to guess (with certainty) the correct outcome of any one of the next four decisions. I would be happy with 25%. Surely, you would all agree that if we could be guaranteed to get one single decision correct out of the next four, we would all be rich in no time.

The reality of Baccarat is that the Casino is “giving” us about half of the decisions. These are gifts. They are enticing enough to get us to keep giving them the rest of the decisions. If you don’t believe this, simply look at any series of shoes (real or computer generated) and see how you would have done flat betting “player” all the way through.The game gives us almost half. The problem (of course) is that we never know exactly when we are going to get our half.

I have long given up on the feeling of despair after losing 65% of the decisions in a session (or in a shoe). The only despair I feel is when I have more money on the table when I lose and less on the table when I win.

I love the Labouchere. You can too!

The key to embracing the Labouchere is understanding what it is and what it is not. The Labouchere is NOT a system for winning. The Labouchere IS a method of keeping score. It is merely a method of knowing where you currently stand against the house.The Labouchere works for Baccarat players who don’t mind increasing their bets in an attempt to recover recent losses.We all know that while employing the martingale (which I rarely do beyond 3 steps), the question is “How much do I need to bet right now to make up for those last few losses and come out ahead?” And the answer is “Double you last bet!”When using the Labouchere, the question is more often something like this: “How much do I need to bet over the next six or seven decisions so that that IF I were to win two or three of those decisions, I can recover most of my losses or perhaps come out ahead?” And the simple answer is: “Look at your line and add up the first and last numbers.”

Now, keep in mind what I said earlier, with Baccarat, the house is giving us about half of the decisions. SO, most of the time I feel good about guessing correctly two or three of the next 6 or 7 decisions. (I am NOT saying that most of the time I am successful in guessing correctly 2 or 3 of the next 6 or seven decisions ONLY that I usually feel good about my chances of doing so!) I know that if I can guess “good enough” to get close to the “gift” that the casino offers me (about 50% win rate on decisions) then I WILL eventually come out ahead. Now, by “eventually” I do not mean one day down the road. I mean today, this shoe or the next.

It was recently expressed in a thread on this message board the uncomfortable feeling of carrying a long Labouchere line over into the next shoe. I believe that all discomfort can be removed with good discipline and some pre-established stopping points.

Consider this hypothectical: Suppose your initial line is 1,1,1,1,1. You need to work with this line and discover your confort zone. You need to decide at what point you will abandon this line and start over with a fresh line. It makes no difference if you are at the beginning of a shoe or at near the end. Everyone need s a point to say “no more”. BUT here’s the key: When you abandon a line, you are not “writing off a loss.” You are merely reducing (or limiting) the level of aggressiveness that you are willing to employ to recover those losses. Your comfort zone might be that you do not want to place a single wager more than 20 units. If so, you will find yourself getting to the point in your line where the sum of the first and last numbers equals 20 or more and that is when you start over. NOW, if on your fresh line (1,1,1,1,1 again), you are able to reach your coup, go back and reduce some of the numbers in your abandoned line by five. Suppose you abandoned your line because your numbers were 3,4,6,11,17 (you dug yourself a nice little hole) and your next bet is above your comfort level. You begin a fresh line (your next hand may be immediately thereafter, or after a dinner break, or in the next shoe or the next trip to the table, it does not matter) and if you are successful, you now have 5 units to remove from your abandoned line. I might reduce the two largest numbers, 11 and 17 to 10 and 13. At this point there isn’t much sense in going back to the abandoned line because you could quickly get back into the “uncomfortable” zone. Start another fresh line and when (if) you reach your coup again reduce the abandoned line. Eventually (be patient) you will return to your abandoned line and cancel it out. Only then will you be back in the black.

Remember this: The Labouchere is nothing more than a score card telling you where you presently stand against the house with the added feature of making suggestions as to how much you should bet over the next few decisions if your goal is to recover your losses soon. Once you are comfortable using the Labouchere, it should not bother you to carry a line forward into another shoe or even to have multiple abandoned lines. We all know that there will be good times and bad times and your scorecard tells you how bad the bad times are and what you need to do to overcome them.For me, it is a wonderful feeling to end a shoe having only guessed correctly on 45% of the decisions but to be up 15 units because you cancelled your Labouchere three times!! And all you have to do achieve this is to play a shoe that is somewhat evenly distributed. My experience tells me that the “somewhat evenly distributed shoe” is always right around the corner.

3D Labouchere

(I Orginally Posted this idea at Gamblers Glen)

My latest novel idea is a 3D labouchere. The appeal here is only for those who buy in to my notion that the Labouchere is best seen as a score card. Here's the basic 3D Labouchere:

1 1 1

1 1 1

1 1 1

First, get yourself a nice piece of graph paper with a printed grid of squares covering the sheet. Draw the above diagram in the middle of your paper (like tic-tac-toe), your goal is 9 units. Your first bet is 2. Here's the beautfiul part: If you lose, you can add the "2" to the left or right or top or bottom of any line. This means that you could lose the "2" bet 12 times in a row before your diagram forces you to bet "4" (beacause at that point you would have added a "2" to both ends of every line.

Remember, this is a only score card, at any time during your session, you can add up the numbers on the paper and subtract 9 and that's how far down you are. If some of your lines add up to 6 and others add up to 3, you can pick which bet you "feel" best about at that time, and you can add your losses wherever you want. I deally I would try to keep some sort of balance.

If I played this way for very long and did not reach my gaol of 9, I would probably look for a point where the total on the page was less than 9 and simply stop with whatever gain I had.I have not tried this method of scorekeeping in a real casino nor have I worked with my software or zumma shoes.

My interest in this approach is only to find a way to keep multiple lines going on one page in a coherent (and less confusing) manner.

Good Stuff - Bad Stuff

Since beginning this blog, I have discovered an interesting message board http://www.gamblersglen.com/ . I highly recommend it for anyone interested in systems play. I have gone back and read many of the archive entries and I find the people who post there to be serious about wanting to learn ways to win money. Some of the comments reveal smart individuals who are open minded while others do not. I have also discovered through this message board some useful links to other sites where systems are being discussed, explained, supported, debunked, sold, etc..

I thought I'd try to bring together some of this information here. I hope to include in this thread ideas that I find interesting as well as absurd. My plan is to add information within this post, so please check back.

Saturday, August 30th, 2008 - I recommend these sites for the phenomenon that they are. Regardless of their value in helping you as a gambler, I think you will find the information interesting.
Gambler's Glen Message Board: http://www.gamblersglen.com/cgi-bin/teemz/teemz.cgi?board=_master - Here you'll find a lively discussion amongst people who (like me) want to be better gamblers and who (I think) believe that there are methods to improve your game.
Donny Millionaire: http://www.donnymillionaire.com/ - A slick systems seller. Most of the folks on Gambler's Glen are convinced that this guy is a scammer. Some of the members who support him are accused by the others to be merely shills. (I'll have to admit that some of his supporters do appear to be merely shills and not gamblers who have benefitted from systems that they purchased from Donny.) I'd also like to point out that some of the people who call Donny a scammer seem to be saying that anyone who sells a system is a scammer because systems don't work. My thoughts are that anyone who makes claims about their system that are not true is running a scam.
Mr. Oops: http://www.xerxx.se/oops/index.html - This well presented site for roulette players with an emphasis on statistics and probabilities. There is some great information here. Those who will to take the time to go through it all will come away with an appreciation for his efforts.

The Wizard of Odds: http://wizardofodds.com/ - This guy has ALL the answers! Especially if the questions is one that can be answered mathematically. A HUGE amount of free information for anyone who is looking at gambling from a mathematical angle.

John Solitude: http://www.john-solitude.be/download.html - This site has a useful guide called "Roulette Fact or Fiction." The free 125 page guide answers common questions about systems sellers and scammers. The introduction to probabilities and statistice and their application to gaming is easy to follow (you can skim the math parts) and the conclusion is that there are NO guranteed systems and you shold avoid all seller's who are not straight forward about the level of risk associated with the system. You can download the guide by clicking the link above. John Solitude also accepts donations to keep the site going.

"Statistical Propensity" and "Diminishing Probability"

Are we simply guessing that a specific random event will occur? If so, are we nothing more than victims (or benefactors) of the fickle finger of lady luck?

I believe that some betting opportunities are "better" than others. In Roulette, betting that a series of 7 black decisions in a row will end within the next 5 decisions seems to be a "good" bet. It seems to me that it is a "better" wager than to bet that a series of 2 black decisions in a row will end within the next 5 decisions. Betting that 7 won't continue to 12 "seems like" a "better" wagering opportunity than betting that 2 won;t go to 7 BUT the mathematicians will tell us otherwise, the odds are exactly the same.

So why does it feel better? I think it feels better because we find ourselves encountering runs of 7 much more often than runs of 12. (But we also find ourselves encountering runs of 2 much much more often than runs of 7). Perhaps it is because of what Barstow calls the Law of Diminishing Probability and/or what R. D. Ellison calls the Law of Statistical Propensity. Although spins of the wheel and dice decisions are random events not related to previous decisions, it appears that over time the decisions tend to conform to or at least gravitate toward their mathematically expectations.

Ellison says:

"Taking all 38 numbers into consideration, the least number of times any number showed up was 16, and the most number of times was 50. This is a wider range, which accounts for the greater possibility of unconventional trends in a larger sampling, but not one of the 38 numbers tried to escape from the corral. Meaning, each one was compelled to show up a minimum number of times, but not too many times."

From: "American Roulette Is Now Mathematically Beatable" - by R.D. Ellison
See: http://www.thegamblersedge.com/propensity.htm

I believe that perhaps we can discover ideal betting opportunities. These would be bets that we would win more often than we'd lose AND (here is the tricky part) when we lose it is less than our winnings for that session or period of time. For example: suppose we should win this bet 7 out of ten times and with each win we'd gain one unit and with each loss we'd lose 2 units. For every 10 decisions, we should average a net of 3 units.

Eillison is promoting his 3Q/A Roulette system (which I have not tried) and arguing Statistical Propensity in support of it. I'm not sure (because I have not done the math) but if Ellsion is saying that the mathematical expectation is such that his wagering plan wins more often than it loses and wins more money than it loses, then it passes my test (and I imagine everyone else's) for a "good" bet.

BACCARAT - Barstow, Zumma and Excel

In Frank Barstow's excellent treatise on gambling systems, "Beat the Casino" (1979 Carlyle) the author makes some pretty strong claims about expected success using his pet systems. He claims on page 216, for example, that his "Barstow System" "can" average 12 units per hour profit. His conclusions are the result of a combination of reasoning, simulated trials and "real" Casino play.

It strikes me that with today's technology and information we can "test" Barstows claims in a way that he could not have easily accomplished.

Erick St. Germain's "72 Days at the Baccarat Table" (1995 Zumma) lists the outcomes of each decision in 600 "real casino" Baccarat shoes (about 40,000 decisions). Using a simple Excel spreadsheet, I have been able to test some of the the Zumma shoes against several systems in Barstow's book. Although I do not expect to discover the keys to the kingdom, I firmly believe that this time-consuming task will help illustrate the strengths and weaknesses of certain systems and be helpful in identifying trends within the shoes.

I'm curious if any of YOU have tried a similar approach and might be willing to share the results or are you aware of where this information may be obtained. Also, would you be interested in testing some of these 600 shoes yourself?

I plan on making some of my research available on this blog to give you all a better idea of what I'm talking about.

In the meantime "happy number crunching."