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Volume VII : Issue #7

Date July 2007

In This Edition:


A Word From Soft Touch

From the Editor

Distance Between Sevens

Off and On...

Today's Wisdom...

Newsletter Archive Links


 Soft Touch Say's


Hello everyone.


Thanks to all the readers who check-in with us to share their positive feed back.  I know that I can speak for Ed, Mike and the rest of our contributors, and state that we all appreciate the comments and suggestions regarding our site and content.


In this month’s issue you will find a fascinating piece by Mike in Hawaii. regarding his exploration of the distance between sevens. You can visit his “Monte Carlo” with his “little Engine that could” and follow the intrigue of how “noisy” the dice can be. Read his article to understand my meaning.


And, thanks Ed for writing your version of “Who’s On First” with regards to come betting.  I am sure our new readers who are beginning to learn the game should have “off and on” figured out after reading your explanation.


In the “What’s up with That?” category, Some student friends of mine report that the Golden Nugget is charging patrons $15 dollars for what used to be considered part of the comp experience when checking into a room.  I do not understand this.  $15 for a more courteous experience?  Anyone out there complaining?


A couple of other issues about the Nugget. Please keep track of your play hours at the table and check in with the shift manager to confirm the number of hours you actually played.  Players are reporting what seems to be a discrepancy with what The Golden Nugget rates you for the number of hours you put into play. So, do yourself a favor and check your hours if you intend to ask for "complimentary bonuses."


Remember, your comps for your current trip are under a “use ‘em or lose ‘em” policy. There is no longer a carry over of points for any subsequent visit.  This casino is not the first to do this and I am sure there are many more casinos to follow.


Until next month, I hope you are having as much of a hot time as I am, at the tables, that is.


Soft touch




PS If you have any suggestions for the new Dice Setter website or newsletter please send them to me at and I'll have a look and see how we can incorporate them into our future plans.


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From the Editor

Just a few of the emails we received regarding Mike In Hawaii's June article Fair Market Value.

Hello Editor, one of the best articles, Fair Market Value, I have ever read on pass/dont pass betting. Great Job, Mike H.     Tony

Thanks Ed I always enjoy the new letters and insight they bring. Keep up the good work.

Dave H.

Editor, Once again I don't wish to be labeled 'picky' but the article by Mike from Hawaii is confusing and has an easily spotted error. The first (and very confusing) is the immediate reference (twice) to the bet being on the Don't Pass and then the article immediately talks all about the Pass.  I could be reading it wrong. As a Darksider, in the main, I am usually thrilled if the Point is an outside number. Bill B.

Hi Ed, I have enjoyed Mike of Hawaii's articles in the past. This months article only adds to that appreciation. Mike has wonderful vision and imagination. The Fair Market Value article puts the very vague concept of casino “VIG” into a perspective that most of us non-mathematicians find easier to visualize. This article is very timely for me. Thanks for all you do there at Dice Setter Newsletter. It is refreshing to read about overlooked, and new concepts for the game of craps. After all, there are enough systems promoters out there touting the many ways to lose. Ken K.


And then this one... Hi, I use to visit this site a lot a few years ago but then took a break from all gambling for awhile.  This is my first time back on the site since and I just wanted to let you know it looks great.  I'm still going thru it seeing what's new and how much of the old info is still here.  Glad to see the site is still up and running.  Keep up the good work. O. J.

We appreciate having everyone's feedback and it helps us to publish the best gaming newsletter about craps on the Internet.

Ed Jones

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Distance Between Sevens

By Mike In Hawaii


There are two primary ways to do Craps math. One is the way God would do the Math (Capital M). To infinity and beyond! as a certain toy super hero likes to yell.


The other way is to "Monte Carlo" it. By that we mean make a "machine" on which you can turn the "crank". In this case a Craps shooting machine. It simulates throwing the dice a LOT of times! and allows you to record the results.


I wrote one in a language called C and can run it on a very powerful computer. Boy does it shoot Craps!  In about 1 second it can shoot the dice about 2/3rds of a million times and record all sorts of interesting statistics. (It is not really the computer that makes the difference, it is the simplicity of the code. No animations, no graphics, no dice layout, nothing but bare minimum gears and wheels.)


As for the data, Seven appears (111288 / 667722) times or 16.6668% of the time. Very reassuring since God Math would say exactly 1/6th of the time or 16.6667% of the time you should find a Seven. Keep in mind that throwing Seven is the most common thing that can happen in Craps.


Originally I had it using just 10,000 rolls of the dice. Sounds like a lot, but it is impressive how skewed the data on some of the less common outcomes such as hardway 4's turned out. In fact even the number of Sevens could be off by quite a bit in only 10,000 rolls. So I upped the ante until I found a number that would give me some statistics I could believe in. That started to happen when I got to about 500,000 rolls. (More on this later.)


Where did I get my random numbers? Well of course. Assembled in batches at random times over a number of sessions over the period of a week.


So how many hands in 667,722 rolls? 197,905. That would be the average length of a Dice hand, if you define "hand" as the series of events that starts with a come out roll, ends with immediate craps 2,3,12, or an immediate win with 7 or 11, or sets a number and continues rolling until you either make that number or Seven Out.


In other words the series of events from when you first pick up the dice until there is something that results in a decision. The program says that number is about 3.37 rolls of the dice on average.


Some might object to my use of "hand" for this. Saying a "hand" is from when you first get the dice until you have to pass the dice. I have not taught my little engine to capture that exact data yet.


So what does the little engine have to say about the distance between Sevens? Before you peek answer this question:


What is the most common, most likely, distance between Sevens in Craps?


ZERO!  Yes indeed. The most common distance between Sevens in Craps is no distance at all! The most common distance is consecutive Sevens.


That one had me chasing my tail for a bit. I could not get my "Sevens" to add up. Finally the light came on. I was recording all distances between Sevens from 1 to 127 and a whole bunch were missing!  Duh....  When I fixed the program to carefully record consecutive (gap of zero) Sevens, shazam, like Bo Peep, I found all my missing sheep.


In fact, there were 18,539 consecutive Sevens out of a total of 111288.   That is 16.66% of the time. WOW! Bingo! What is the chance of rolling a Seven on any given throw? One in Six. or 16.667%. Choirs of Angels Sing. (As they say when Math works). Hard core proof that given enough throws, dice in fact seem to have no memory.


So what about the other Monte Carlo distances:

Gap        #               Percent            Cumulative

0          18539            16.66%            16.66%

1          15632            14.05%            30.71%

2          12684            11.40%            42.10%

3          10706            9.62%              51.72%

So four rolls of the dice cover just over half of the possible cases. Starting from a Seven and then hitting Seven again on the very next, second, third or fourth roll.


What is scary for certain strategies is the rest of this chart. It fades away, but because there is fully a 5/6th chance the next number will NOT be a Seven, it does not fade away that fast.


Here is the Rest of the data out to a gap of 25 between Sevens. This really starts to enter the Twilight Zone:

Gap      #            Percent             Cumulative

4          9023          8.11%              59.83%

5          7380          6.63%              66.46%

6          6209          5.58%              72.04%

7          5286          4.75%              76.79%

8          4320          3.88%              80.67%

9          3574          3.21%              83.88%

10        2985          2.68%              86.57%

11        2426          2.18%              88.75%

12        1973          1.77%              90.52%

13        1765          1.59%              92.11%

14        1517          1.36%              93.47%

15        1274          1.14%              94.61%

16        1001          0.90%              95.51%

17        788            0.71%              96.22%

18        729            0.66%              96.88%

19        614            0.55%              97.43%

20        471            0.42%              97.85%

21        413            0.37%              98.22%

22        336            0.30%              98.52%

23        293            0.26%              98.79%

24        223            0.20%              98.99%

25        195            0.18%              99.16%

There is one case of a gap of 72 rolls! The first zero appears at a gap of 54 rolls. Two cases of 55 rolls, one case of 57 rolls, two cases of 59 rolls, and one case of 65 rolls between Sevens. Every gap of 50 or less has at least several occurrences. From 29 to 40 every gap has 10 to 92 occurrences. From 28 down there are at least 115 occurrences.


By Math (Capital M)


We have stated that we are going to start with a Seven so the chances of the first number being a Seven are 100%.


The chances the next number will be a Seven are the same as the chances you will get a Seven any time you roll the dice (random roller of course). 1/6th or 16.67%


So what about the other numbers? Well the chances of NOT getting a Seven are 5/6th. So the chances of skipping one number are:


1 * 5/6 * 1/6 or .1389 or 13.89%  =  the chances of  a distance of one gap between two Sevens.


For larger gaps you just multiply by more 5/6th's

1 * 1/6                                     16.67%         0 gap

1 * 5/6 * 1/6                            13.89%         1 gap

1 * 5/6 * 5/6 * 1/6                   11.57%         2 gaps

1 * 5/6 * 5/6 * 5/6 * 1/6            9.65%         3 gaps

Total so far:                            51.77%

Notice several things here. First these numbers do not exactly match those from the Monte Carlo example above even though we used nearly 668,000 rolls. They are close, life is good, they do agree, the Monte Carlo at about 2/3rds of a million rolls is working OK. But it is not perfect! Expressed as percentages we are still getting errors in the first decimal place even with these "very common" occurrences.

Gap      Percent             Cumulative

0            16.67%              16.67%

1            13.89%              30.56%

2            11.57%              42.13%

3              9.65%              51.77%

4              8.04%              59.81%

5              6.70%              66.51%

6              5.58%              72.09%

7              4.65%              76.74%

8              3.88%              80.62%

9              3.23%              83.85%

10            2.69%              86.54%

11            2.24%              88.78%

12            1.87%              90.65%

13            1.56%              92.21%

14            1.30%              93.51%

15            1.08%              94.59%

16            0.90%              95.49%

17            0.75%              96.24%

18            0.63%              96.87%

19            0.52%              97.39%

20            0.43%              97.83%

21            0.36%              98.19%

22            0.30%              98.49%

23            0.25%              98.74%

24            0.21%              98.95%

25            0.17%              99.13%

What is the house advantage when you bet the pass line and take double odds? Expressed as a percentage it is down in the first decimal place. And the Monte Carlo data represents about how many dice rolls a dedicated shooter throwing once a minute, 24 hours a day, seven days a week for over 15 months might make. Now that is a session. And still there is "noise" in the Monte Carlo data even with this most common of events. And we are only looking at absolute errors. A better idea of the "noise" would be to look at the relative error size, which in this case is six times larger.


How Noisy is 10,000 Rolls?


Noise in this case is error. As pointed out before there are two ways to try to analyze a betting system or the probability of something happening. You can try to calculate it using Math. Or you can build a model of it that carries out the steps of the game over and over again like a little mechanical version of the game, turn the crank and keep track of what happens over time.


With Craps there are 36 possible outcomes just on the roll of the dice. That is a LOT.


As questions get more complicated and you look at events that are relatively rare, the number of turns of the crank required on such a simulation or Monte Carlo starts to either become extremely large, or the data wobbles around so much it becomes almost nonsense due to the overly small sample.


More bad news! In order to double your confidence in your result, you do not have to double the number of rolls, you have to increase them by 4 times. The noise goes down with the square root of the number of observations. So if you want to increase your confidence by a factor of 10, one decimal place, you need to increase the number of rolls by 100.  Yes, you have to go get 100 times more random numbers.


One might think that 10,000 rolls is a reasonable number. So let's have a look at what happens when we Monte Carlo Craps with a bit over 10,000 random rolls, 66 times, using a different set of 10,000 random numbers each time.


In terms of hands, that is defining a "hand" as pick up the dice, throw them, either win immediately with Seven or 11, or crap immediately, or set a number and then continue until you Seven Out or make your point.  Start throwing dice, reach, one of the above conclusions.  On average the slightly over 10,000 random rolls generate approximately 3,000 such hands. So that again sounds like a LOT.


Let's just look at two things that can happen frequently, and make up fully one third of all come out roll results on average. You either (A) win with 7 or 11, or you (B) lose with craps 2, 3, or 12.  The odds on the first result is a nice clean 2/9ths. The odds on the second result is a nice clean 1/9th. As percentages those are: 22.22% and 11.11% for a total of 33.334% of what happens to all come out rolls. (The other 2/3rds of the time you set a point and have to try to make it).


Let's begin with a very carefully selected example from the 66 trials. It is enough to make Angels weep. There are 2,971 "hands" in this run which generate 659 wins with either 7 or 11 on the come out roll. And generate 332 loses with 2, 3 or 12.   That is an absolute error of only -0.04% on the immediate win column (22.18% vs. 22.22%) and only 0.06% on the loss column (11.17% vs. 11.11%).  Even viewed as relative error it is just -0.19% on the win column and 0.57% on the loss column.


Now what is the big deal? What is wrong with that!! Well very little. But this was a most carefully selected example from the 66. The majority of these runs have rather nasty errors. The absolute errors on the win side go from -1.79% (too low) to 1.57% (too high). Something that is supposed to be happening 22 percent of the time off by over a full percent much of the time.  In relative terms it is a shocking -8.06% to 7.09% off base.


The loss side which is supposed to be happening 11% of the time has similar absolute errors, ranging from -1.56% (too low) to 1.29% (too high). In relative terms that is a horrifying -14.05% to 11.59%.  Yes that is over 11% relative error on one side and 14% relative error on the other side. With 10,000 rolls!


So what does that mean for a real Craps session of (be generous) 250 rolls?  Well chances you will see percentages like the Math (Capital M) predict for even the most common occurrences are not good. Any real Craps session is most likely to be significantly off on its probability distributions. (With just 250 rolls, confidence, or chance for drifting off the Math derived probabilities, would actually be about six times worse).


Think for a minute about a session in which people are losing to craps on the come out roll 11% more often than they should be, or winning with 7 or 11 fully 8% less often than they should be, or conversely losing to craps 14 % less often than they should or hitting 7 or 11 fully 7% more often than they should. Nothing to do with dice control, or how they throw the dice, just the variability in the math (lower case real world math) itself with a sample size of just 10,000 rolls.


Even at 10,000 rolls of the dice, the numbers are not settling. Even at 2/3rds of a million rolls the less common events are still drifting off the absolute values calculated by Math, such things as the number of 12's, the number of hardways, and even the number of times someone will set a four and then make their point.


Whenever you extract a real life subset of dice rolls at a Craps table, you will very likely get something significantly different than the razor edged, 10,000th of an inch, ultra balanced, spun and serial numbered precision of infinite Math probabilities.


Next time someone says "I tested my system once on WinCraps with 1000 rolls and it works!" Please raise at least ONE eyebrow...


Copyright © 2006 Mike in Hawaii

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Off and On...


From the email bag...


Hey Ed, dealing craps, one of the bets not talked about much is the off and on bet or the continuous Come Bet. I don't run in to it too often, but once in a while I'll have a player keep making come bets and I simply pay the odds and he or she is up again on the same number. Perhaps you could discuss this in the newsletter... how it is paid and why it functions as it does. Just thought I'd bring it up. It is confusing to some player and dealers as well, because you don't return all the come bet money.


Regards, Nick


What Nick is referring to has to do with come bettors that keep placing come bets. Let's say the point is 5 and the come bettor has a $10 come bet with double odds established on the  6, 8 and 9. The come bettor makes another come bet. The next number to roll is a 6. The dealer pays the come bettor $34 dollars and says, "off and on". What's up with this? Well, to keep the game moving along, it is obvious to the dealer that this player is making a come bet with every roll of the dice. So, instead of making extra, unnecessary, movements with the chips, the craps dealer simplifies the action.


How is this done? The winning come bet of 6 is paid $24 for the odds and $10 flat for  the come bet right?. However, since the player is obviously making a come bet, with odds, for every roll, the dealer is taking a short cut for all concerned. He leaves the chips already on the come bet of 6 in place. Why? Well, the player had a come bet in the come field and a come bet established on the box number 6 when the dice rolled 6. Thus, the come bettor won on the come bet of 6 and at the same time, the bet in the come field became a new come bet, back on the 6. Thus, the player won the come bet on the 6 (and was paid off). At the same time the player is back on the 6 (with the new come bet with double odds). The come bet 6 was paid and off the layout technically. Since the player had a come bet in the come field it followed the same number to the 6 to be back on as a new established come bet.  See, Off and On?


This is what it looks like when off and on are used by a dealer. The come bet with double odds is sitting on the number 6, waiting for the next roll. When 6 is rolled, the come bet player is paid $24 for the odds portion and $10 for the flat come for a total of $34. The only movement with chips the dealer has to make is with the $34. The player's only movement is picking up the $34. No other bets need be made, no other chips are moved and the layout with the come bets looks the same. The player is all set for the next roll with his come bets in place with double odds back on the 6 and has a come bet of $10 in the come field waiting the decision of the next roll.


Now, why is that so confusing for come bettors to understand off and on? You come bettors better be laughing, because it took me two hours to write three paragraphs.




Today's Wisdom:

The Silent Consolidation...

      The initial point in consolidating your silent power is to discipline yourself to stop leaning. When you are the most desperate to lean in on people, that's when you should exercise control. The game is called: "Stand Straight in Life." Not many have heard of it.


      First, don't lean toward things you don't have. Affirm, visualize, and take action instead.


      Second, try not to lean into the future by talking or thinking about it constantly. Instead, take time each day to make the "now" special, honoring what you do have and what you have achieved. Avoid what I call plan-itis. Endlessly making plans and talking about them -- "one day, someday..." trashes your power and gets you nowhere - no results and no action.


      Third, start to design your life so that you don't require things from others. Try to need only those things you can get yourself. And don't suck on people emotionally or intellectually.


Stuart Wild - "Silent Power"


Dice Setter Newsletter Thanks You!


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