**Head For The Gap!****and****Distance Between Sevens**

Reprinted with Permission From Playing 4 Keeps Newsletter October 2006

By Michael Vernon

In the final year of producing Stuart Wilde’s *Warriors in the Mist* eight-day seminar, a small group of Irish attended one of the programs. They were a fun loving group and they loved their grog. After the last campaign, Stuart, my wife Lin, a few others in the production company and myself, flew over to the U.K. for a few weeks vacation. We spent five days in Ireland with our Irish friends. They had this funny little saying when driving drunk, “Head for the gap”. I found out by experience that it meant to keep the car on the road by aiming it between the hedgerows and rock walls…. Otherwise it is to keep a distance between certain other objects that would result in a crash, if the car were not maintained in the gap. I just found out that this Irish phenomenon is common to the game of craps.

In the past month, I have had numerous email dialogs with Mike In Hawaii. We have been discussing the math of the game and how the house edge on bets insures the casino’s win. We also got into looking at the random game of dice, and how “monster hands” come about. One thing led to another and the question of how to explain a “monster hand” with math became Mike’s quest. Can math explain the random monster hand?

The article that follows in this newsletter, written by Mike In Hawaii, may well be the most important study for dice in our time. I’d even say that it has broader application for all gambling in general. Yeah, that is a pretty big check to cash! Understanding Mike’s computer model, his study of probability, has caused me more excitement, thought provoking inspiration and a much deeper understanding of what I have been teaching about the game of dice. I feel that his math model allows for an explanation of those places that I say a player is able to touch into with their perception. That is, when pushing out with one’s feelings and being able to glean information from another dimension before it manifests in this reality. “Reading the energy!” Now I add a new description calling it “touching into the Gap”. I will let Mike’s article explain how it all comes about as you can read it for yourself following this bit.

What I want to interject here is that I now feel confident that the energy concepts, the metaphysical concepts for gaming can be better understood with Mike’s study. It is quantum physics at work and once you read Mike’s article, my guess is that you will understand in simpler terms what I often have referred to as, “the dice acting out of probability”.

Mike’s study produced information revealing how the math of the game does adhere to probability over hundreds of thousands of rolls. What surprised us was that even though probability is held up, as one would expect, there are numerous “gaps” in random generated numbers where the dice rolls do not adhere to probability. It is during these gaps that the monster rolls occur and are explained. Mike calls it *“Distance Between Sevens”*.

What his study revealed is that the numbers rolled, do in fact adhere to mathematical probability. What he discovered by running over 600,000 random rolls, was there are numerous gaps between sevens occurring in the trial. That is to say, instead of a seven showing up every three to six rolls, there are times when there may be a distance between sevens up to over 60 rolls between their occurrences. Although a lot of the gaps are less, even those gap hands would still be consider “out of probability” and profitable hands in terms of an opportunity to make money in a craps game.

In subsets of 10,000 rolls, many statistics were regularly, and significantly, out of line including the number of naturals rolled, number of craps, and number of times place bets would hit or miss. The less common an event was, the more likely it was to not match its predicted performance. But even the most common events such as winning on the come-out roll, frequently just wandered off, as if unaware of their true probabilities.

I am making a connection here to those aspects of what I have been writing about, perception and reading the energy. I believe that when a player is aligned to the energy, and perceives the “positive vibes” of a winning game, that they are in fact experiencing a quantum physical phenomenon. Mike In Hawaii likes to tease me, calling it “juju”. I believe that the energy or intention sent out by a person can touch into the energy of a game and in doing so, is also able to perceive the experience of the gap.

That is saying, with perception and awareness of other dimensions, a player is able to recognize the occurrence of the inordinate distance between sevens. So, when the player engages this kind of energy, they can position themselves in a game that is about to act outside of probability. When they are switched on and perceive correctly, they find themselves playing in a profiting game. The other side of the experience is when “pushing out” with perception and not picking up a feeling for a positive game, the player is touching into a game adhering to probability. No Gap! It is what I refer to as “no game” and one would witness random rolls or a choppy game.

What I say next is bound to create controversy within the dice influencing community. Mike suggested that it would be like stuffing three ally cats into a burlap sack and tossing them over a clothesline. Here goes…. There is a guarded secret about dice control captured in slow motion movies. I am aware of three separate recordings, independent of one another, of slow motion filming of dice setter’s dice in action. Mike has witnessed one of the films and agrees with what I am aware of for the way that dice react upon landing. The other two films were explained to me by trusted authority, two experts of the game, each performing independent slow motion filming, that when the dice land after being tossed by skilled dice influencers, that the dice “bounce all over hell” time and again.

Even with desired results, the results occurred randomly and did not adhere to the axis theory commonly held. I say again, no way do the dice tumble on axis, as is the accepted theory of today’s dice setters. The sharp edges of a die are too unlikely to land flat consistently, without catching the felt on edge or by a sharp corner and abruptly changing trajectory. Thus, the dice are not able to maintain the desired axis, as is professed by those believing the theory of dice influencing. That theory says that the dice can land perfectly flat, maintain the true forward motion, rebound off the back wall of pyramid rubber and return to the layout and stop on the set axis. Near perfect cubes with razor edges, how is that practical?

I’ll answer my own question. Not very practical! At the same time, I continue to use my skill with setting and tossing. Why? I believe in consistency when throwing the dice. Dice setting is one way to do that. Over the career of my dice play, I figure that doing the same thing over and over as best as I can, it will result once in a while with the dice doing what theory predicts. I do not know if it is 1% or more. But let’s say even if it is just 1%, that is an advantage. Could it be more? Sure! Certainly depends on the shooter’s level of skill.

At the same time, I am prepared to propose that when any player rolls a hand using dice influencing or rolling random, that they are doing nothing more than hitting the “gaps” that are mathematically prevalent as demonstrated in Mike’s study of over 600,000 random rolls. For me, it explains “why” dice setting works great some times and other times it is not different from random.

Okay, I wanted to keep my explanation of the math, metaphysics and quantum physics low keyed and simple. So, for now, I will leave it to you to decide for yourself. Review the findings in Mike’s study. Consider this, if it is possible to touch into another dimension and perceive the energy prior to it manifesting in this reality, can you perceive the energy of the distance between sevens? Can you head for the Gap?

Copyright © 2006

Michael “The Professor” Vernon

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 random.org 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…

©Aug 2006 Mike in Hawaii

Playing 4 Keeps®