My Latest Conundrum

MY last post got me thinking about the difference between statistics and probability or expected outcomes vs. actual outcomes.

According to the law of big numbers, a large sample of random events will tend to move toward expected outcomes. Therefore, if you were to look at 38 million roulette decisions, you should see that each number appeared about 1 million times and that about 47% of the decisions would be red for example.

Now, IF this proposition is true then it is fair to say that the average gap between repeats would have to be about 38 spins. This means that if you were to take any particular number, like the number 3 for example and see how often it appears, the answer would be once every 38 spins.

IF it is true that numbers tend to appear every 38 spins in the long run, it would seem to me that we have an exploitable event.

Suppose you place one chip valued at $18 on the "high" numbers (outside bet on numbers 19-36), probability and statistics would show that you would probably win this bet almost half the time (because you have almost half the layout covered). Now suppose instead, you placed 18 individual bets on the inside placing one dollar chips on each of the numbers between 19 and 36. Statistics and probability would tell you that you should win almost half of these bets and in fact the results should be identical to the "other" way mentioned above.

Now lets look at a moving target. Suppose you were to place 18 individual one-dollar bets on the 18 numbers which are NOT the last 18 numbers to appear (not considering the zeros just for the sake of this example). Let me re-phrase that. Make a list of the last 18 numbers to appear and place 18 one-dollar bets on the "other" numbers. Would this provide you an advantage? Should you win this bet MORE OFTEN than half of the time?

Now looking back at our first proposition. IF IT IS TRUE that numbers tend to appear every 38 spins then it would seem that while many numbers appear less often than 18 spins many more numbers are appearing at intervals greater than 18 spins. (If the average gap between repeats is 38, then necessarily some number gaps would be greater than 38.)

NOW, IF the average gap is greater than 18, then wouldn't it make sense that by playing 18 numbers which are not the last 18, would give you an advantage? Wouldn't it seem that the next number to come up is more likely to NOT be of the last 18 than TO be of the last 18.

And if so, doesn't this fly in the face of the fact in my most recent thread that the last 38 decisions is likely to only be comprised of 24 numbers??

Something to think about . . .

PRELIMINARY TESTING

I took a look at some spins created by a random number generator. The sample is entirely too small to draw any conclusions, but the results are encouraging.

The First sample i looked at was 1000 spins. I recorded data for 982 spins (skipping the first 18). I looked at each spin and measured the distance since the last appearance of that number. If the number was 18 or less, I counted this as a loss of 20 units. If the number was greater than 18, I counted that as a win of 16 units. The explanation is as follows: if you bet 1 unit on each of the 20 numbers that do not represent the last 18 numbers to show, then you will win a net of 16 units if the next number is not one of the last 18 and you will lose 20 units if the number is among the last 18.

This produced +1960 units for the 982 spin sample. The gain is 2 units per spin (or about than 1/10th of the minimum bet).

If you play with $1 chips, you would need to bet $20 a spin. Each win will net you $16. You would have won $2 per spin or $120 per hour.

If you play with $5 chips, you would need to bet $100 a spin. You would have won $600 per hour.

Not bad at all.

What about drawdowns? I broke my preliminary batch of numbers into hour long sessions. Only 2 sessions ended up in the negative and they were -72 units. I would feel comfortable with a bankroll of 300 units or 400 units.

SECOND BATCH

The second batch of randomly generated numbers represented 282 spins. The total gain was 660 units (2.34 per spin) or slightly higher than the first batch average (2 units per spin). Perhaps the best way to look at this is a gain of about 1/10th unit per spin or 6 units per 60 spins or 6u/hour.

(I remind anyone who reads this that the preliminary test samples are very small at this point.)

THIRD BATCH

The 3rd batch was 982 spins which produced 1622 units or 1.65 units per spin.

Totals through 3 batches:

2,246 spins = 4,242 units or 1.89 units per spin (113.4 units per hour).

FOURTH BATCH

982 spins with a total gain of 2212 or 2.25 units per spin.

Totals through 4 batches:

3,228 spins = 6,454 units or 1.999 units per spin

Average = 120 units per hour (based on 60 spins per hour)

FIFTH BATCH

982 spins with a total gain of 2052 or 2.09 units per spin.

Totals through 5 batches:

4,210 spins = 8,506 units or 2.02 units per spin

Average = 121.2 units per hour

SIXTH BATCH (abnormally high results)

456 spins with a total gain of 1860 units or 4.078 units per spin.

Totals through 6 batches:

4,666 spins = 10,366 units or 2.22 units per spin

Average = 133.2 units per hour.

SEVENTH BATCH

979 spins with a total gain of 1947 units or 1.988 units per spin.

Totals through 7 batches:

5,645 spins = 12,313 units or 2.18 units per spin

(very impressive through 5,645 spins*)

*but see "THE ERROR" below

PRACTICAL CONSIDERATIONS

I have to admit that covering 20 numbers within a few seconds may be challenging. The task is not only to cover 20 numbers but to select those numbers as well. The key is to cover all except the last 18 to show. With a partner, one could be placing all the numbers as the other person reads the board and removes the most recent 18. If this works, I'm sure I can find a way to get the coverage I need.

Another idea might be to have a small laminated copy of the layout and to "x" out the last eighteen numbers with a dry-erase pen. Then use this to show you where to place your bets. Another thought would be that you do not need to place very bet, it would make sense that your chances of winning are the same if you placed a bet every other spin. So, if it took you a while to get your info together, you could just play a table minimum outside bet on one of the even chances and then place your 20 inside bets on the next spin.

The above numbers are actually quite staggering. Using $1 chips, you could expect to win 130 units per hour. Using $5 chips, you could expect to win $654 per hour. All with a bankroll of only 400 chips ($400 or $2,000).

The worst-case scenario (in the first 7 batches tested) is an hour with losses of 288 units ($288 or $1,440 using $5 chips).

The best hour (in the first 7 batches tested) is +396 units ($396 or $1,980).

ONE POTENTIAL FLAW

One potential flaw in my test numbers is that I am counting as wins any number that has not appeared in the last 18 spins. I am covering 20 numbers and leaving the last 18 uncovered. However, if the last 18 spins include any repeats, then 20 numbers would not be enough coverage. For example, 18 spins might only represent 14 numbers, if so, then I would have to cover 24 numbers to cover all numbers not included in the last 18 spins. This would mean that the only ideal time to bet is when the last 18 spins have no repeats.

THE ERROR (OF MY WAYS)

I've come to accept that the "one potential flaw" mentioned above is in fact the critical flaw of my testing. The very impressive numbers above are based on a scoring system where I assigned a +16 to each win (repeat gap larger than 18) and a -20 to each loss (repeat gap 18 or less). The problem is that this would only be accurate if the last 18 spins represented exactly 18 distinct numbers (which should rarely be the case). In order to truly test this tehory, I would have to look at the last 18 numbers to appear (not the last 18 spins). The question becomse, how many spins does it take to produce 18 numbers, my guess is something like 21 or 22. If I were to go back and re-score the test numbers using 21 or 22 spins, the result would be dramatically different (obviously worse). A different way to look at the test nukbers is that 18 spins probably only represents about 16 numbers on average (maybe even less). So, to cover all the other numbers, I would have to place 22 bets. This means each win would be only a +14 and each loss would be a -22. No doubt this would also drastically reduce the results above.

SO

So, does the law of big numbers help us to find an exploitable anomoly? Is the average gap between hits really 38 or is it more like around 24?

Back to the drawing board . . .

An Exploitable Anomaly?

I read somewhere that a typical collection of 38 roulette spins will only include 24 distinct numbers. If this is true, it seems that this fact could present an exploitable anomaly.

What is an anomaly?

Because there are 38 slots on a roulette wheel, math and probability theory would tell us that if you played one number straight up, you could expect to see the number hit once every 38 spins. There would be no reason for you to expect to encounter the number 17, for example, any more or less often than once every 38 spins.

If you were to set out to play one number for 38 spins, you would very often find yourself winning (once during the 38 spins). A single number on the inside of the roulette layout pays 35 to 1, this means that you will receive 36 chips back after placing one winning bet of one single chip. If you commit to play the number 17 for 38 spins in a row (stopping after a win), you will have a positive result if your number hits during the first 35 spins (with your expected gain diminishing with each spin). You would break even if your number hit on the 36th spin and you would suffer a small loss if your number came up on the 37th or 38th spin. (Of course, you would lose big if your number never hit during the 38 spins.)

IF the number did exactly as it is expected to do (appear every 38 spins), you would lose in the long run an amount equal to the house edge. The casinos rely on this.

But what about the "fact" that only 24 numbers will appear during the next 38 spins? Shouldn't this give us some potential edge?

Is it exploitable?

If you were to play 1 unit on each of the numbers 1 through 24 at the same time, a win would net you +12 units. You should win this bet 24 times for every 38 spins and if so, again you could expect to lose an amount equal to the house edge. You should win this bet 24 times out of 38 spins because math and probability theory tell us that your 24 numbers should each appear once during 38 spins.

BUT what if, instead of playing the same 24 numbers for each spin, you played the last 24 numbers?

It would make sense that IF all sets of 38 consecutive decisions contain an average of 24 spins, THEN the very next spin is likely to be one of the last 24 numbers. It SEEMS that it is more likely that the next number would be be one of the last 24 numbers than it is that the number would be of any other group of 24 numbers. IF SO, you should win this bet more often than the mathematical expectation and therefore you could eliminate the house edge and perhaps even come out ahead.

In order to fully exploit this fact, we should develop a progression. By using a progression, we are not simply betting that the next decision will be one of the last 24, instead we would be betting that we are not going to see 3 (for example) decisions in a row that are all three (each) not of the last 24 decisions. With a three-step progression, we would only lose when the next decision was not one of the last 24 decisions THREE times in a row.

Here's how a progression would work:

First bet (1u) = 24u, a win on this bet would give us 36 minus 24 = 12units

Next bet (3u) = 72u, a win on this bet would give us 108 minus 96 = 12units
Next bet (9u) = 216u, a win on this bet would give us 324 minus 312 = 12 units

60 decisions per hour
20 wins on first spin
15 wins on 2nd spin
5 wins on 3rd spin

40 wins x 12units = 480 units per hour
less one full series loss = 168 units per hour

The real question is: How often would you see a full-series loss? Is once an hour realistic or would you see more or less?

I wonder what a study of the Zumma roulette book would show?

Would it be difficult to program an Excel spreadsheet to identify if the next number is one of the last 24?

Is 24 the magic number? Or is there a better number to use?

Perhaps a better way of looking at the "units" required for this sort of play is to recognize that the smallest bet you play is 24 units. It is probably best to consider this 1 unit. Looking at this system from this angle, you will be winning .5 (one-half) unit with every spin (not counting losses).

1 unit = 24 chips

With the minimal chip size of 1 dollar, your unit would be $24. Usually, table minimums require a bet of at least $10 on the inside. Table maximums for inside numbers are often limits on the amount you can bet on a single number.

Here's a chart to show requirements and anticipated results:

Chip = $1

Unit = $24

Largest Bet = $216

Net/hr = $168 (with 1 full-series loss per hour)

Bankroll = $312 x 3 = $936 ($1,000)

******************************************

Ratio Between Wins and Full-Series Losses = 12/312 = 1 to 26

******************************************

Chip = $5

Unit = $120

Largest Bet = $1,080

Net/hr = $840

Bankroll = $1560 x 3 = $4680 ($5,000)

*******************************************

Double your bankroll in 6 hours.

But, does it work??

ANy thoughts?? Please comment.

The Star System

I have been reading "From Poorhouse to Penthouse via The Star System" by Dwaine C. Douglas (Island Publishing House - Tavernier, Florida)

I'm not sure of the true history behind this publication. I found it on a list of free gambling systems and I am quite taken by it (the same list I posted here under another thread). You can dowonload and print the 89 page manuscript here:

http://www.roulettesystemreviews.com/freesystems/StarSystem.pdf

The Star System is a conservative money management system created for Blackjack but quite adaptable to bacarrat, craps, and roulette.

I find it appealing because it fits nicely with the direction my research has been heading. Looking for something that seems to work with great reliability even if the winnings are small (i.e. a reliable grind so to speak).

My thought here is that one could employ a system such as this with a minimal bankroll and "snowball" the winnings by increasing the unit value based on the increase in bankroll.

I will continue to write in this thread as I get a better feel for the entire system. I am also looking for message board information from those players who have worked with this money management system.

11/17/08

I have finished the maunscript and have started re-reading (or studying) it. As I said above, the appeal to me is that this system pulls together many of the concepts that I have already embraced. The only thing about this system that I have never really worked with is the parlay or "rider" aspect that the author relies on.

I will need to practice this system a good deal with pen and paper in front of me before I could think of trying it in a casino at a blackjack table where they do not like you to be taking notes. I understand the progression and the recovery stages but I'm quite sure I'm not ready to to employ this method under fire.

I'm not going to explain the system here. Although it could be explained in a few paragraphs, I think the 89 page manuscript is the best way to appreciate the system.

I have also dug up some message board entries from folks who claim to have used this method successfully however, ther seems to be a general reluctance to increase bets into the 2nd recovery set as required. This reluctance has lead to some modified versions that I may elaborate on here at another time.

My plan (at the moment) is to create a scorecard or record-sheet to keep track of the STAR system (sets, sessions, progressions, recoveries etc.) and to practice on a software simulator. If the results are as the author claims, I will try to use the same system at an online casino for real money prior to heading for the real casino. I plan to continue this thread with ideas and to pbulish my progress (or lack thereof) here.

12/5/08

One concern I have about the STAR system as presented in the original manuscript is the sheer range of the size of the bets and bankroll required. I am a firm believer in the idea that a good plan must be well funded, but the STAR has you sitting at a table with $10,000 and placing a first bet in the amount of $10. Furthermore, you need to be willing to bet about $2,400 on a single decision in the worst-case scenario (2nd recovery set). (This estimate is based on a primary bas bet of $50 at a ten dollar table.)

I wonder how many players are willing to play this SYSTEM strictly as devised by Douglas?

12/9/08

My Star Notes on Requirements and Expectations

p.12

Bankroll = $600
Average Bet Size = $6
Total Profit = $4,200 in 108 hours
Profit per hour = $38.89
Unit size (?)

p.18

should lose 1 set per 28
(win 27, lose 1)

p.23

on a $10 table
your first pre-progression bet is $10
your primary base bet is $50
Your highest bet in the progression ladder is $400

p.30

playing blackjack, expect to win .25 per $1 base bet, per hand played
with a primary base bet of $10, you should avg. $2.50 per hand
Bankroll = base bet x 200

If anyone has any advice, please feel free to leave a comment.

All for now . . .

The "Cycle"

THE CYCLE

Part I

Lately I've been focusing my work on a concept I call the "Cycle."

I have posted elsewhere my idea of "going for half" and these two concepts work well together.

I have also written about mathematical expectancy and this is a good place to begin an explanation of the cycle.

All gambling propositions have a probability which can be described in the form of mathematical expectancy. A very simple example would be betting one number, 17 for example, straight up on an American roulette wheel. Since there are 38 numbers on an American roulette wheel, it is said that the probability of the number 17 hitting on the next spin is 1 in 38. The mathematical expectation is that we can "expect" a hit on the number 17 once in 38 spins. The "cycle" for this proposition therefore is 38 spins.

The simple example above is provided merely to illustrate the terminology. The concept becomes a little more complicated when we look at more complex bets, like betting 2 dozens and 2 columns for example, or using progressions.

We all know that the so-called even-money outside bets (like red/black for example) are close to 50/50 propositions. We also know that when you factor in the house edge, your chances of winning any particular "even-money" bet is a little less than 50%. In short, the "odds" are against you or in other words, you are more likely to lose this bet than to win this bet.

We also know that you can place bets that you are more likely to win but that the payoff is less than one to one. For example: Playing 2 columns gives you 24 of 38 chances to win, however the payoff is 1 to 2, you will be wagering two units in hopes of netting one.

My theory about "maximum coverage bets" (and I hope to come up with a better term than that) is that when you employ a progression, your chances of losing your series is drastically reduced.

NONE of this defeats the house edge I remind you. But, I accept that cold fact with all systems.

What I hope to develop here is a way of looking at cycles and maximum coverage bets to allow us to chose bets that will produce small but steady gains with rare losses (which will necessarily be large).

More later . . . .

The Cycle Within a Cycle

Using multiple levels of progression, leads to bigger cycles containing smaller cycles. For example: Suppose your bet was a three step martingale. You are betting on Red and you bet one unit on your first bet, then double after a loss, and again. Your progression is 1 2 4. Each winning series results in a gain of 1 unit. Each losing series results in a loss of 7 units. We know that you can expect to lose a series about once in 8 series. Assuming for this discussion that you are playing a true 50/50 game, a wheel with no house numbers, a wheel with exactly half of the numbers being red. Under these circumstances, you can expect to win 7 series and lose one. This is the first level of progression.

Now suppose you decide to add another level of martingale. After a losing series, your first bet will be 2 and your progression will be 2 4 8. After a win, you will return to your original series.

Now look at the cycle. Y0u have a cycle of 8 series where you can expect to win 7 series and lose one to break even for the cycle. This cycle can be expected to take 24 spins or decisions. By adding the 2nd level martingale, you are increasing your net by +1. IF you experience the mathematical expectancy of a typical cycle, you will end your 24 spins up one unit instead of break even.

OF COURSE, there is another mathematical expectancy of losing back to back series. This other expectancy has another point in a larger cycle where you can expect to be brought back to zero or even (or to a negative amount equal to the house edge) . In the original progression we saw that we can expect to lose one series out of eight. We then added a second level of progression gambling that we would not encounter our one in eight losses back-to-back. How often will that happen? [I have notes elsewhere and I'll return to fill in this gap] This would be the bigger cycle. Eventually, you can expect to be brought back to even (or zero) when the bigger cycle runs its course. By adding yet greater levels of progression you are increasing the size of the cycle and it is my theory that you are increasing the amount of time you can expect to be ahead of the game before being brought back to zero. AND MAYBE - if you have several tactics for stretching out the cycle of expectancy, then you can quit while ahead more often OR change strategies while ahead in the cycle.

More later . . .

The "No Lose" Expectancy

(Which, of course WILL Lose as expected)

As a general illustration of the discussion so far, I offer this example:

For this example, we are playing a wheel which produces 60 decisions an hour. We know that we can develop a system that has an expected loss of one time in 60 decisions. This one loss would be expected to eliminate all winnings from the cycle of 59 wins. If we play this game for only 30 minutes and IF we are ahead at 30 minutes, then we can quit under my notion of "going of half." The question then becomes, of all the 30 minutes sessions that we will play, how many will include the dreaded losing decision. Math would probably tell us half. Real play may show us something different. We know that IF we have one more winning 30 minute session than losing 30 minute session, then we'd be ahead in the big cycle. And if the sessions were kind enough to come evenly spread out, you'd always be only 30 minutes away from being ahead.

If we strip this theory down to it's simplest form, it becomes WAY less attractive. Yet there is something about the more complicated version that I find appealing.

Here is the stripped down version: Suppose we are playing a true 50/50 game and the game produced its mathematically expected results with regularity in the short run. So that if you flat-bet and you encountered a win/loss series like this: W L W L W L W L W L, you would always be just one or two decisions away from a profit. Following through with our example above, you could always quit while ahead and it would be easy to do so.

We find this to be unappealing because we know that Roulette and Baccarat and other near 50/50 games do not produce reliable results in the short run. We know that the 50/50 game is very volatile and that it takes THOUSANDS of spins or decisions for the results to approach the expected 50/50 mark.

My theory is that the smaller the cycle, the more volatile and unpredictable the game. BUT on the other hand, the larger the cycle, the more predictable the game becomes.

I found an Excellent article and example of a No Lose Expectancy System, I'll post a link here when i get my hands on it again.

More Later . . .

Collection of Systems

I came accross a decent list of Gambling Systems on the internet:

http://www.roulettesystemreviews.com/freeroulettesystems.html

Most of the ideas contained in this list are fresh twists on the same old systems contained in every book on gambling.

A few of the ideas there cought my eye and I am going to work with them and I'll report back here.

Please feel free to share any experiences you may have with these (or other) Systems.

Thanks and Good Luck!

10/26 - here's a link to some more systems from the VIP Lounge:

http://starthere.mysteria.cz/

and here:

http://www.freewebs.com/turbogenius/

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.