New Geneforge Story

[SamSniped]

I have read sharx's thread and got a very good idea...start my own story!I will add anyone in the story,and if you want Dikiyoba you can be a IFTF(intelligent freindly talking fryora)

 

Book one-The Academy

Chapter one-The Tragedy

The sound of metal striking metal clanged through the air. At Greenwood Academy,Orion Des'Xoas and many other recruits were training to be a Guardian,one of the three sects of Shapers. While all the other trainees used steel broadswords,he used his father Koran Des'Xoas's Shaped Blade(which was named Bloodsword for it's color).

Koran Des 'Xoas was said to be the greatest Guardian that ever lived.Instead of three years of training he passed in one and a half because of his expert skills with the sword.he fought the rebels off the island chain that Greenwood adcademy was on,but sadly died to a rouge Unbound while destroying Northforge Citadel.His son was given the blade he used and was instantly taken to Greenwood academy,to live his father's legacy.

One year later,he was an expert swordsman and was almost ready to become a guardian.

That same day,a tragedy happened at Greenwood Academy.

The Rebellion was still alive,and when they found out that Orion Des'Xoas was at that school,they attacked.

Again.

The first sign of attack was a Drayk-which somehow made it in through the gate.Orion saw the dragonlike beast start to unleash a torrent of flames from between his jaws. He jumps out of the path of flames that strike the guy behind him in the center of his chest. The poor guy screams in agony as Orion lands behind the drayk, he grips the hilt of his father's balde and plunges it into the Drayk's neck which kills it almost instantly.

Orion saw a strange symbol on the creation's scaly hide-the symbol that all novice shapers put on their creations when shaped-Three interlocking blades.Only one shaper in Greenwood could make a drayk-Master Erason,the protector of this school.

Instead of going to fight off the creations,Orion went to try and kill the source of the problem.

Greenwood Academy's protector.

TBC...

©2009 Empire Of Sand Inc.

TBC in chapter two.

[SamSniped]

I guess so.I'll do it.

Chapter Two-The Hunt

Orion did a Blitzkrieg pass through the rouge filled corridors on his way to the protector.From measly Worms to high powered Cyrodrayks,nothing could stop him.Bloodsword picked up more and more blood,strengthening it.The sword was enchanted in Pophyra by Orion's father's close friend Lord Iraelithe*.It was enchanted to adsorb blood,sharpening the sword's blade.But,it dulled at midnight.The blade's only downside.

Right in front of the door to Master Erason's chamber were two creations floating above the ground-Wingbolts.Not good, Orion thought.He and the Wingbolts were shocked by the next move.Orion charged the Wingbolts,and in two mighty blows from his shaped blade,they were dead. Orion cast a heal spell on himself,shaped a Cyora,and adsorbed the essence of a dead Wingbolt.

When he approached the master's door, he drew Bloodsword,and bashed the door down.He found Master Erason shaping more rogues,which were smitten by Bloodsword.Erason noticed Orion,and said in a slight English accent,"You're paying for that door,you know."

Orion took a heavy swing at the Lifecrafter,but ended up having it bounce off the floor.For a shaper,Erason was fast.He dodged the blow masterfully,drew a somewhat dulled dagger,and tried stabbing Orion.The dulled dagger bounced off the heavy plate armor,and Orion spun around lightning-fast,shaped sword striking Erason's sword arm.

{If you cannot stomach gruesome details,DO NOT READ SPOILER.}

Click to reveal..

He cried out in agonizing pain,as the sword teared through human skin,flesh,and muscle,almost cutting through the bone itself.Blood spilled everywhere,and even the major healing spells Erason casted weren't enough to stop the flow of blood.

Heavily injured,Erason had only one option-teleporting to the rebels to be healed.Just as Orion went in for the kill,Erason teleported away.Where Erason stood last was a note,written hastily and blood-spattered-

YOU SHALL PAY!

TBC...

*spelling changed purposefully

Shark-credits for the idea of teleporting magic.It should have been invented by now shouldn't it have?

P.S.-It seemed longer when typed here...

[Drakon Sssharxx]

Mate if you going to write a story the chapters are a tad short. Mabey use these two short paragraphs as a plan for the acctual chapters, I find it easier to plan the chapter by writing a basic layout of what will happen and then when I come to write the chapter I add in details like a description of the main charicter and such.

 

Also revise your use of brackets in chapter two, you tend not to get many books that contain brackets, try writing something allong the line of...

Click to reveal..

Orion saw the dragonlike beast start to unleash a torrent of flames from between his jaws. He jumps out of the path of flames that strike the guy behind him in the center of his chest. The poor guy screams in agony as Orion lands behind the drayk, he grips the hilt of his father's balde and plunges it into the Drayk's neck which kills it almost instantly.

 

The story itself though is believeable except a novice would be unlikely to defeat the protector of the academy at such an early stage of the story. Good work.

 

Sharx.

[Velzan]

Greenwood needs better defenses.

[Drakon Sssharxx]

It gets attacked way too often lol.

 

P.S. WOO shock trooper!

[Lord Iraelithe]

I'll defend it, WITH MY ARMY OF MAD BOTS AND FLAMERS! XD Well, as loong as Alorael doesn't snipe them first.

[SamSniped]

Originally Posted By: Drakon Sssharxx

Mate if you going to write a story the chapters are a tad short. Mabey use these two short paragraphs as a plan for the acctual chapters, I find it easier to plan the chapter by writing a basic layout of what will happen and then when I come to write the chapter I add in details like a description of the main charicter and such.

Also revise your use of brackets in chapter two, you tend not to get many books that contain brackets, try writing something allong the line of...

Click to reveal..

Orion saw the dragonlike beast start to unleash a torrent of flames from between his jaws. He jumps out of the path of flames that strike the guy behind him in the center of his chest. The poor guy screams in agony as Orion lands behind the drayk, he grips the hilt of his father's balde and plunges it into the Drayk's neck which kills it almost instantly.

The story itself though is believeable except a novice would be unlikely to defeat the protector of the academy at such an early stage of the story. Good work.

Sharx.

Who said he kills the protector?lololol.

Thank you for the hint.Time to upgrade my writing.I notice that part isn't copyrighted by anyone,so...

Originally Posted By: Velzan

Greenwood needs better defenses.

Yes,yes it does.

Lord Iraelithe-How does Pophyra after it's rebuilt sound?
© 2009,Empire of Sand Inc.
P.S.Open for suggestions/info.

[Alorael at Large]

Does this "Empire of Sand Inc." actually exist in a legal sense?

 

—Alorael, who would like to additionally point out that you don't need to append a copyright notice to everything you write online. First of all, the contents are yours for writing it. Secondly, well, who are you protecting it from, and how are you intending to defend a copyright based on someone else's copyrighted material?

[SamSniped]

Originally Posted By: Stormy Weather

Does this "Empire of Sand Inc." actually exist in a legal sense?

—Alorael, who would like to additionally point out that you don't need to append a copyright notice to everything you write online. First of all, the contents are yours for writing it. Secondly, well, who are you protecting it from, and how are you intending to defend a copyright based on someone else's copyrighted material?

No it doesn't exist i was just bored yesterday...lol.
You ruin the fun.

[Ouroboros]

You don't have to lol at everything

[Drakon Sssharxx]

Besides didn't I just rebuild and defend Poryphra in my own story? So technically that would fall under my copyright hehe. Don't worry you can use the idea just makeing a point to research before you stick a copyright notice upon something.

[Lilith]

Originally Posted By: Drakon Sssharxx

Besides didn't I just rebuild and defend Poryphra in my own story? So technically that would fall under my copyright hehe. Don't worry you can use the idea just makeing a point to research before you stick a copyright notice upon something.

you cannot copyright plot ideas, if you could then those dudes who wrote Holy Blood, Holy Grail would be swimming in money right now

conga line of window treatments

[SamSniped]

Sigh...more complaints about small matters than COMPLIMENTS (hint,hint).

[Lilith]

aren't compliments supposed to be for things that are good

[SamSniped]

I take that as a large insult.

[Insurgance]

Look at it more like, say... constructive criticism.

[SamSniped]

only one post so far was helpful surge.Read the post from sharx earlier up.

Chapter Three-A New Adventure

All of a sudden,four guardians-in-training rushed through the open door.Orion's best friend Dakro Barlen The Sixth asked,"What the hell happened here..."

Orion answered,"You don't want to know."

"Well,I found a dying rebel lifecrafter and told him,'where is the leader of the rebellion?' and he answered-"

Orion cut him short,"-Master Erason."

"Actually,he did.How did you know?"

"Drayks with the shaper mark on them."

"I'm going to tell the Servant Mind."

An armor clad Guardian walked up and said,"The Servant Mind wishes to see you."

Orion sighed and walked on.When they reached the Servant Mind,they received a strange instruction."Master Dakro the Fifth saw the whole fight and reported it to me,Orion.Good sword fighting.Now,travel to Dillame and get further instructions from Alwan."

Orion and Dakro stood there amazed.They were going to see one of the shaper generals.

"We will prepare a boat for you,"the servant Mind continued,"and you will leave tomorrow.Good luck,Guardians."

TBC...

[SamSniped]

Chapter Four-Dillame

The next morning,Orion and Dakro got on the boat and left for Dillame.The ride was uneventful,but long.Five hours after getting on the boat,they saw the outline of many buildings,including Rivergate Keep,the largest building for miles.When they reached land,a Guardian was waiting for them.

"Follow me,Alwan wishes to see you."

After a somewhat short walk,they made it to Rivergate Keep.The Guardian said,"take a left,a right,then go straight.You'll make it there."

They followed the directions,and made it to Alwan. "So,is it true?You are Orion Des'Xoas,son of my greatest warrior,and Dakro Barlan the Sixth,the one to follow the legacy of your family?"

They both replied yes.

"Well then,why are you here?"

They explained the story,Orion about the Drayks and Master Erason's betrayal,and Dakro about the assault he helped fend off.

"Damn,Erason was the best person I could put there.Instructions,you ask?Go to Pophyra and visit Lord Iraelithe for me.I would like you to get a report and further instructions from him.By the way,here are some passes to get you past Shaper strong-points.Good luck,men."

As they left Alwan said,"Oh yeah,look for house number 218,you are allowed to stay there."

They left Rivergate Keep,and Dakro went to buy a better sword.Orion left to find the house.

******

Orion found the house,all right.It was the best house In Dillame.But,Orion knew two people that stayed in here before-Orion and Dakro's fathers.They had been together when they assaulted Northforge Citadel,and Dakro the Fifth killed the Unbound that killed Orion's father.

When Orion opened the door,he was shocked at who was there.

[Shaper Cirikci]

I'm going to guess that it is either 1. Master Erason or 2.Orion's dad

[Lord Iraelithe]

Or....ME! Lol,I just wanna see were I come in >

[SamSniped]

Lord Iraelithe,you are in the story in at maximum 10 chapters.

and Shaper Cricki,wrong,and wrong.

[SamSniped]

Ready to find out?

Chapter Five-Shaper Cirikci

Sitting in the house was the LAST person Orion would have expected there-Shaper Cirikci,the third greatest shaper ever (next to Shaper Andras and The rebel Shaper Litala).Cirikci heard the door open and was shocked,too.He recognized the Guardian who walked in the door as Orion Des'Xoas,his friend's son.

Orion and Cirikci knew each other well,Cirikci was the one who brought Orion to the Academy."Ummm...hi Cirikci,"Orion said,still shocked.

"How's it going Orion?"He replied calmly.

"Pretty good.I have to leave for Pophyra tomorrow.Alwan's orders."

"Hmmm...gotta head up that way to see a couple friends of mine...I'll come with you."

Orion shrugged and went to rest for a while.In the meantime,Dakro got a nice shaped sword,recently made.When he got to the house and saw Cirikci,Dakro groaned. He knew Cirikci,and they hated each other."Don't tell me you're going to Pophyra too,"Cirikci said in a pretty ticked off way.

"Unfortunately," was Dakro's response before going outside to train with his new sword.

TBC...

[Lord Iraelithe]

Uhuh.....ok...

[Shaper Cirikci]

if that supposed to be me you spelt it wrong and two you better not make me a rebel. i follow the shapers ways so strongly that i sometimes have to cause myself physical aliment if i want to play a rebel playthrough.

[Spddin Ignis]

I think this could make a great story, but the plot is moving a little to fast for my tastes.

[SamSniped]

Originally Posted By: Shaper Cirikci

if that supposed to be me you spelt it wrong and two you better not make me a rebel. i follow the shapers ways so strongly that i sometimes have to cause myself physical aliment if i want to play a rebel playthrough.

Don't worry,only thing you do for the rebels is put them out of their own misery...MWHAHAHAHAHAAAAA!
I'll change your name and fix it right away,Cirikci

Originally Posted By: Shaper Spddin

I think this could make a great story, but the plot is moving a little to fast for my tastes.

I hate parts without action,sorry.It sorta slows down during battles and rebel controlled areas...and there's more description.

[SamSniped]

this double post was by all means intentional.the story and answering questions doesn't go well...

Chapter Six-Through fields and Rocky Point...

Next morning,everyone in the three person group had a specific job-Dakro stocked up on healing and essence pods for the group,Orion sharpened the two swords and Cirikci's Shielding Knife,while Cirikci shaped up two lightning-breathing Kyshakks and three Cyrodrayks,all with the order to attack rogues and rebels on sight.When everything was ready,they set out to Pophyra.

Easier said than done.

Their plans to get there-Go through Dillame fields,Rocky Point,cut through West Barrier Zone,Thornton Ruins, and East Barrier Zone to get to Eastern Pass,then through Arizaph Fens to Burwood Province and finally Pophyra.

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

They set out of Dillame to the nearby fields.Something was wrong.Bodies of Shapers and Guardians lay about the blood stained fields.All of a sudden,a breath almost as cold as liquid nitrogen shot out into the trees,followed by a rogue squealing in pain.They all drew their swords.

Then,they were surrounded.

Bolts of electricity came from the Kyshakks, exploding into rogues killing them almost instantly. Orion sized the forces up:

Rogues-11 Clawbugs,5 Fyoras,one Wingbolt,and one strangely glowing Cyrodrayk.

Shapers-2 Guardians,1 Shaper,2 Cyrodrayks,and 3 Kyshakks.

Odds-almost 3 to 1.

Orion charged the Wingbolt,slashing it apart while dodging poisonous Clawbug stingers.Dakro killed anything in his way with a couple sword swipes.Cirikci sent spheres of acid at the Radiating Cyrodrayk,while his creations fought to the death.The Wingbolt sent essence orbs at the Kyshakks,killing one of them before dying.

One by one,the rogues died.The Radiating Cyrodrayk went last,leaving Cirikci wounded and with only an injured Cyrodrayk.Orion cast healing spells on Cirikci while he adsorbed the Cyrodrayk.Cirikci used a couple essence pods on himself and they ventured on.

On their way to Rocky Point,they heard a groaning sound.Everyone drew their swords as they saw something come out of the bushes-a Shaper soldier!He was heavily injured and managed to gasp out,"Rocky Point...attacked..."Before fainting.

TBC...

[Spddin Ignis]

If your going by the shaper laws in the game cryodrayks are still illegal. If this is the future or the past, then by all means ignore me.

[SamSniped]

Originally Posted By: Shaper Spddin

If your going by the shaper laws in the game Cyrodrayks are still illegal. If this is the future or the past, then by all means ignore me.

Did the Shapers realized that when you created Drayks,Cyrodrayks,Drakons,and Ur-Drakons in the endgame area?
Didn't think so.
Anyways,lets assume they made them legal.

[Spddin Ignis]

Who said i made drayksm cryodrayks, drakons, and ur-drakons in the endgame area...oh wait...i didnt.

 

Anyways i was just giving advice/asking a question...i said if they made it legal, then ignore the comment...no need to be a jerk about it.

[Acky]

Spddin was talking about the canonical fact that the Shapers don't allow those kinds of creations to be made and kill them on site. For engine purposes, yes, the Shapers don't do anything if you have illegal creation with you. That would just be annoying.

[Shaper Cirikci]

1). I am technically a full shaper because they only teach those high powered creatures to full shapers so i'll make it legal for me to have them and 2). since i am technically a full shaper Dakro has to do what i say so i can tell him he's not allowed to show that he hates me

[Insurgance]

Theirs only one thing i want to say about the story...

 

If you could create some spaces at the appropriate spaces it would make it easier(at least for me to read)

 

Or line breaks would be nice at least...

[Spddin Ignis]

Just because you are a full shaper doesnt mean you make the law, Cirikci. Thats what the council is for.

[Shaper Cirikci]

true but in the game many shapers bent the rules without any repercussions.

[Spddin Ignis]

yeah, but usually council peoples. I guess when your in a wat the shapers cant arrest everyone they need to fight it. But im the kinda shaper who doesnt go down to the rebels level.

[Shaper Cirikci]

i go to the rebels level when entire islands start switch to the rebels control in a matter of days thought i never go so far as to use canisters

[SamSniped]

hey guys can u keep this thread alive for a while?Couple of my friends are coming down from Arizona for a week...see you in a week or so!

[Spddin Ignis]

Wait...does he want us to make random comments for a week?...Pshhh.

[Dikiyoba]

This thread will still be around for you to post updates in a week from now. No one make random posts in it.

 

Dikiyoba.

[Lilith]

A Million Random Digits with 100,000 Normal Deviates

by The RAND Corporation

 

Errata (PDF)

Foreword to the Online Edition

 

This book was a product of RAND's computing power (and patience). The tables of random numbers in the book have become a standard reference in engineering and econometrics textbooks and have been widely used in gaming and simulations that employ Monte Carlo trials. Still the largest known source of random digits and normal deviates, the work is routinely used by statisticians, physicists, polltakers, market analysts, lottery administrators, and quality control engineers.

 

A humorous sidelight: The New York Public Library originally indexed this book under the heading "Psychology."

 

Acknowledgments

 

The following persons participated in the production, testing, and preparation for publication of the tables of random digits and random normal deviates: Paul Armer, E. C. Bower, Mrs. Bernice Brown, G. W. Brown, Walter Frantz, J. J. Goodpasture, W. F. Gunning, Cecil Hastings, Olaf Helmer, M. L. Juncosa, J. D. Madden, A. M. Mood, R. T. Nash, J. D. Williams. These tables were prepared in connection with analyses done for the United States Air Force.

 

Introduction

Early in the course of research at The RAND Corporation a demand arose for random numbers; these were needed to solve problems of various kinds by experimental probability procedures, which have come to be called Monte Carlo methods. Many of the applications required a large supply of random digits or normal deviates of high quality, and the tables presented here were produced to meet those requirements. The numbers have been used extensively by research workers at RAND, and by many others, in the solution of a wide range of problems during the past seven years.

 

One distinguishing feature of the digit table is its size. On numerous RAND problems the largest existing table of Kendall and Smith (Ref. 1) would have had to be used many times over, with the consequent dangers of introducing unwanted correlations. The feasibility of working with as large a table as the present one resulted from developments in computing machinery which made possible the solving of very complicated distribution problems in a reasonable time by Monte Carlo methods. The tables were constructed primarily for use with punched card machines. With the high-speed electronic computers recently developed, the storage of such tables is usually not practical and, in fact, much larger tables than the present one are often required; these machines have caused research workers to turn to pseudo-random numbers which are computed by simple arithmetic processes directly by the machine as needed. These developments are summarized in Refs. 2, 3, and 4, where other references may be found. Refs. 5, 6, 7, and 8 discuss the uses and applications of Monte Carlo methods and give references to other applications.

 

Production of the Random Digits

 

The random digits in this book were produced by rerandomization of a basic table generated by an electronic roulette wheel. Briefly, a random frequency pulse source, providing on the average about 100,000 pulses per second, was gated about once per second by a constant frequency pulse. Pulse standardization circuits passed the pulses through a 5-place binary counter. In principle the machine was a 32-place roulette wheel which made, on the average, about 3000 revolutions per trial and produced one number per second. A binary-to-decimal converter was used which converted 20 of the 32 numbers (the other twelve were discarded) and retained only the final digit of two-digit numbers; this final digit was fed into an IBM punch to produce finally a punched card table of random digits.

 

Production from the original machine showed statistically significant biases, and the engineers had to make several modifications and refinements of the circuits before production of apparently satisfactory numbers was achieved. The basic table of a million digits was then produced during May and June of 1947. This table was subjected to fairly exhaustive tests and it was found that it still contained small but statistically significant biases. For example, the following table[2] shows the results of three tests (described later) on two blocks of 125,000 digits:

 

Block 1 Block 2

Probability Probability

Frequency (9 d.f.*) 6.0 .74 21.0 .02

Odd-even (1 d.f) 3.0 .09 7.0 <.0l

Serial (81 d.f.) 78.7 .55 105.6 .03

 

*The letters "d.f." (degrees of freedom) identify a parameter associated with the test. A discussion of the test may be found in any textbook on statistics.

 

Block 1 was produced immediately after a careful tune-up of the machine; Block 2 was produced after one month of continuous operation without adjustment. Apparently the machine had been running down despite the fact that periodic electronic checks indicated it had remained in good order.

 

The table was regarded as reasonably satisfactory because the deviations from expectations in the various tests were all very small--the largest being less than 2 per cent--and no further effort was made to generate better numbers with the machine. However, the table was transformed by adding pairs of digits modulo 10 in order to improve the distribution of the digits. There were 20,000 punched cards with 50 digits per card; each digit on a given card was added modulo 10 to the corresponding digit of the preceding card to yield a rerandomized digit. It is this transformed table which is published here and which is the subject of the tests described below.

 

The transformation was expected to, and did, improve the distribution in view of a limit theorem to the effect that sums of random variables modulo 1 have the uniform distribution over the unit interval as their limiting distribution. (See Ref. 9 for a version of this theorem for discrete variates.)

 

These tables were reproduced by photo-offset from pages printed by the IBM model 856 Cardatype. Because of the very nature of the tables, it did not seem necessary to proofread every page of the final manuscript in order to catch random errors of the Cardatype. All pages were scanned for systematic errors, every twentieth page was proofread (starting with page 10 for both the digits and deviates), and every fortieth page (starting with page 5 for both the digits and deviates) was summed and the totals checked against sums obtained from the cards.[3]

 

Tests on the Random Digits

 

Frequency Tests. The table was divided into 1000 blocks of 1000 digits each and the frequency of each digit was recorded for each block. Then for each block a goodness-of-fit was computed with 9 d.f. These 1000 values of provided an empirical fit to the distribution (with 9 d.f.); to test the fit, a goodness-of-fit was computer using 50 class intervals, each of which was expected to contain 2 per cent of the values. (The number of intervals was chosen in accordance with the result of Wald and Mann (Ref. 10).) The value of the test was 54.6 which, for 49 d.f., corresponded to about the 0.45 probability level.

 

To examine further the frequencies, the digits were tallied in 20 blocks of 50,000 digits each. The results are shown in Table 1 together with the goodness-of-fit for each block. On the total frequencies the (13.316) for 9 d.f. has been partitioned into three components as follows:

 

d.f. Probability

Odd versus even digits 1.37 1

0.25

Within groups of odd digits 7.90 4

0.10

Within groups of even digits 4.04 4

0.40

 

Table 1

 

Frequencies of One Million Digits

Block No. 0 1 2 3 4 5 6 7 8 9

1 4923 5013 4916 4951 5109 4993 5055 5080 4986 4974 7.556

2 4870 4956 5080 5097 5066 5034 4902 4974 5012 5009 10.132

3 5065 5014 5034 5057 4902 5061 4942 4946 4960 5019 6.078

4 5009 5053 4966 4891 5031 4895 5037 5062 5170 4886 15.004

5 5033 4982 5180 5074 4892 4992 5011 5005 4959 4872 13.846

6 4976 4993 4932 5039 4965 5034 4943 4932 5116 5070 7.076

7 5011 5152 4990 5047 4974 5107 4869 4925 5023 4902 14.116

8 5003 5092 5163 4936 5020 5069 4914 4943 4914 4946 13.051

9 4860 4899 5138 4959 5089 5047 5030 5039 5002 4937 13.410

10 4998 4957 4964 5124 4909 4995 5053 4946 4995 5059 7.212

11 4948 5048 5041 5077 5051 5004 5024 4886 4917 5004 7.142

12 4958 4993 5064 4987 5041 4984 4991 4987 5113 4882 6.992

13 4968 4961 5029 5038 5022 5023 5010 4988 4936 5025 2.162

14 5110 4923 5025 4975 5095 5051 5035 4962 4942 4882 10.172

15 5094 4962 4945 4891 5014 5002 5038 5023 5179 4852 16.261

16 4957 5035 5051 5021 5036 4927 5022 4988 4910 5053 4.856

17 5088 4989 5042 4948 4999 5028 5037 4893 5004 4972 5.347

18 4970 5034 4996 5008 5049 5016 4954 4989 4970 5014 1.625

19 4998 4981 4984 5107 4874 4980 5057 5020 4978 5021 6.584

20 4963 5013 5101 5084 4956 4972 5018 4971 5021 4901 6.584

 

Total 99802 100050 100641 100311 100094 100214 99942 99559 100107 99280 13.316

 

Of the 200 frequencies recorded in Table 1, 59 (29.5 per cent) deviate from 5000 by more than (= 305 = 67.08), and 8 (4 per cent) deviate from 5000 by more than 2. Of the twenty values in Table 1, eight exceed the 50 per cent value (8.34), two fall below the 10 per cent value (4.17), and two exceed the 90 per cent value (14.7).

 

Poker Tests. Sets of 5 digits in blocks of 5000 digits were taken to be poker hands and were classified as:

 

Class Symbol Expected Frequency Per Block

Busts abcde 302.4

Pairs aabcd 504

Two pairs aabbc 108

Threes aaabc 72

Full house aaabb 9

Fours aaaab 4.5

Fives aaaaa 0.1

 

 

There were 200 sets of 1000 poker hands in the table, and for each set a goodness-of-fit was computed with 5 d.f. (the fours and fives were combined). The manner in which these 200 values fit the distribution is shown in Table 2.

 

Table 2

 

Distribution of Chi-square Values

 

Probability Values of Expected Frequency Observed Frequency

P > .90 0 - 1.60 20 22

.90 >P > .80 1.61 - 2.35 20 19

.80 > P > .70 2.36 - 3.00 20 22

.70 > P > .60 3.01 - 3.70 20 19

.60 > P > .50 3.71 - 4.35 20 20

.50 > P > .40 4.36 - 5.20 20 29

.40 > P > .30 5.21 - 6.10 20 22

.30 > P > .20 6.11 - 7.30 20 15

.20 > P > .10 7.31 - 9.20 20 15

P < .10 9.21 or more 20 17

 

___

 

___

 

200

 

200

 

The goodness-of-fit test gives:

 

= 7.7 for 9 d.f., P = 0.55.

 

The combined frequencies of poker hands in the whole table are shown in Table 3. The largest difference between expected and observed frequencies (for threes) is about 2.25 times its standard deviation, which is roughly at about the 9 or 10 per cent probability level (looking merely at the largest of five independent normal observations).

 

Table 3

 

Poker Test on The Million Digits (200,000 Poker Hands)

 

Classes Expected

Frequency Observed

Frequency

Busts (abcde) 60,480 60,479

Pairs (aabcd) 100,800 100,570

Two pairs (aabbc) 21,600 21,572

Threes (aaabc) 14,400 14,659

Full house (aaabb) 1,800 1,788

Fours (aaaab) 900 914

Fives (aaaaa) 20 18

____________ ____________

200,000 200,000

 

The goodness-of-fit test gives:

 

= 5.5 for 5 d.f., P = 0.35.

 

Also, the frequencies of poker hands were computed for each of ten blocks of 100,000 digits and the mean and standard deviation was computed from the ten values for each kind of hand. The results are shown in Table 4.

 

Table 4

 

Mean and Standard Deviation of Frequencies in Seven Classes of Poker Hands

 

Classes Theoretical Mean Actual Mean Theoretical Std. Dev. Actual Std. Dev.

Busts 6048 6047.9 64.9 60.3

Pairs 10080 10057.0 70.7 78.4

Two pairs 2160 2157.2 43.9 45.8

Threes 1440 1465.9 36.9 26.6

Full house 180 178.8 13.4 8.9

Fours 90 91.4 9.5 11.5

Fives 2 1.8 1.4 1.9

 

Serial and Run Tests. Some further tests were made on the first block of 50,000 digits to look particularly for any evidence of serial association among the digits. The serial test classified every successive pair of digits by each digit of the pair in a ten-by-ten table. The frequencies of the different pairs are given in Table 5, where the first digit of the pair is shown in the left column of the table and the second digit is shown at the top. Thus there were 5l0 cases in which a zero followed a one. The frequency for the row (or column) totals is 7.56, which is about the 0.60 probability level for 9 d.f.

 

Table 5

 

Frequencies of Ordered Pairs of Digits

 

First Digit Second Digit 0 1 2 3 4 5 6 7 8 9 Total

0 508 456 509 507 502 489 471 504 488 489 4923

1 510 514 474 514 504 481 496 486 507 527 5013

2 451 523 493 484 502 466 514 506 493 484 4916

3 500 472 476 466 513 478 540 513 530 463 4951

4 513 561 481 485 526 513 485 510 524 511 5109

5 475 490 527 507 493 481 489 512 465 554 4993

6 494 486 491 483 525 504 530 539 513 490 5055

7 508 512 454 498 550 533 516 504 485 520 5080

8 463 503 475 514 520 544 514 491 520 442 4986

9 501 496 536 493 474 504 500 515 461 494 4974

Total 4923 5013 4916 4951 5109 4993 5055 5080 4986 4974 50000

 

Several essentially equivalent values were computed from Table 5. First, assuming all pairs equally likely (expected value of 500 for each cell), a of 107.8 was computed, which for 90 d.f. (because row totals equal column totals) is about the 0.10 probability level. Second, given the row frequencies and assuming digits equally likely to follow (expected value of 492.3 for cells of the first row, for example), a of 98.9 was computed which is about the 0.25 level for 90 d.f. Third, the expected cell sizes were computed as 1 /10 the column totals to give a value of 100.4, which is about the 0.20 level. Fourth, fitting all means to both row and column totals gave a of 91.9 with 81 d.f, which is at about the 0.19 probability level.

 

Finally, in the same block of 50,000 digits all runs were counted with the obviously satisfactory results shown in Table 6.

 

Table 6

 

Run Test

 

Length of Run

Expected Frequency

 

Observed Frequency

r = 1 40500 40410

r = 2 4050 4055

r = 3 405 421

r = 4 40.5 48

r = 5 4.5 5

 

Normal Deviates

 

Half of the random digit table was used to produce 100,000 standard normal deviates by solving for x in the equation

 

(1)

 

where D is a five-digit number from the table and

 

is the cumulative standard normal distribution. The Bureau of Standards tables of F(x) were used (Ref. 11).

 

The deviates were determined by the five-digit numbers on the left-hand half of every page of the digit table. The deviates in the first column correspond page by page with the five-figure digits in the first column of the first 200 pages of the digit table; the deviates in the second column correspond page by page with the first column of the second 200 pages of the digit table. Similarly, the third and fourth columns of deviates were derived from the second column of five-figure digits, etc.

 

A test of the fit of the entire table of deviates to the normal distribution was performed using 400 class intervals (Ref. 10) with roughly 250 expected in each. The value was found to be 346.4, which for 399 d.f. indicates a very close fit; the probability of a larger value of is about 0.97. The detailed data for this test are given in Table 7.

 

Table 7

 

Goodness-of-fit Test for Normal Deviates

 

 

A more refined test of the fit in the tails was made on the deviates exceeding 2.326 in absolute value. Eighty intervals (Ref. 10) were used, each with an expectation of approximately 25. The value was 76.26, with 80 d.f.; the probability of a larger value is about 0.61. The details of this test are given in Table 8.

 

Table 8

 

Goodness-of-fit of Normal Deviates in 1 Per Cent Tails

 

 

The only tests made on the squares of the deviates consisted in computing sums of k squares and comparing the distribution of the sums with the distribution with k d.f., employing again the standard goodness-of-fit test. This was done for k = 25, 50, 100, 300, with the following results:

 

k Number of Sums Number of Intervals (i) with i - 1 Degrees of Freedom Probability of a Larger

25 4000 100 92.92 0.66

50 2000 100 92.45 0.67

100 1000 50 57.75 0.19

300 333 34 38.70 0.23

 

The fourth column gives the goodness-of-fit value for the fit to the distribution with k degrees of freedom. Intervals of approximately equal probability were used in all cases.

 

Use of the Tables

 

The lines of the digit table are numbered from 00000 to 19999. In any use of the table, one should first find a random starting position. A common procedure for doing this is to open the book to an unselected page of the digit table and blindly choose a five-digit number; this number with the first digit reduced modulo 2 determines the starting line; the two digits to the right of the initially selected five- digit number are reduced modulo 50 to determine the starting column in the starting line. To guard against the tendency of books to open repeatedly at the same page and the natural tendency of a person to choose a number toward the center of the page: every five-digit number used to determine a starting position should be marked and not used a second time for this purpose.

 

The digit table is also used to find a random starting position in the deviate table: Select a five-digit number as before; the first four digits give the starting line (the lines being numbered from 0000 to 9999) and the fifth digit gives the starting position in the line.

 

Ordinarily, the table is read in the same direction as a book is read; however, the size of the table may be effectively increased by varying the direction in which it is read. Thus, one may read columns instead of lines, may read the table backward, may read lines forward but pages from bottom to top, etc. Of course, care must be taken in using these devices to avoid introducing correlations when the table is used more than once on the same problem.

 

To obtain a random permutation of the integers 1, 2, . . . , n, select a random starting position; use the five-digit number containing the starting position and the following n - 1 five-digit numbers; put the integers in the same order as these n five-digit numbers. In case of ties among the five-digit numbers, use additional columns to the right to make six or more digit numbers. The same procedure is used to obtain a random permutation of n objects, some of which are indistinguishable, by merely numbering the objects arbitrarily from 1 to n.

 

To obtain random observations from any distribution G(x), use Eq. (1), substitute G(x) for F(x), and employ as many digits in D as required for the desired accuracy of the observations. Of course the negative exponent of 10 in Eq. (1) must be equal to the number of digits in D. If G(x) has a discontinuity at x0, define it to be continuous on the right and take the solution of Eq. (1) to be x0 when the left side of Eq. (1) falls between G(x0-) and G(x0). For example, if

 

G(x) = 1 - e-x,

 

and one is content with three-figure accuracy, then the three-digit number 082 determines an observation from a population distributed by G(x) as follows:

 

.0825 = 1 - e-x,

 

x = .086.

 

A technique suggested by von Neumann, called the "rejection method," enables one to substitute for the solution of Eq. (1) a stochastic process involving a much simpler computation; this technique will be discussed in a forthcoming book by Kahn (Ref. 8).

 

To obtain pairs of normal deviates with given correlation , use pairs (x, y) of independent deviates from the table and transform them to

 

Thus for = -.6, for example, if (.732, -1.205) are two deviates from the table, then

 

(.732, -1.403)

 

is a pair of deviates from a normal population with the desired correlation.[4]

 

In general, to obtain a random observation from a bivariate population with distribution G(x,y), one uses a marginal distribution on one variate, say, G1(x), and the conditional distribution, say, G2(y/x), on the other. Two random numbers determine the observation: one determines x by employing G1(x) in Eq. (1), and the other determines y by employing G2(y/x) in Eq. (1). Thus, if a probability density is uniform (and equal to two) over the triangle bounded by x = 0, y = 0, x + y = 1 and is zero elsewhere, then

 

and two four-digit random numbers, 5402 and 1770, determine the observation (.3220, .1200). The direct generalization of this procedure will determine observations from multivariate populations.

 

 

The tables of random digits and normal deviates comprise very large files, so only a sample page of each is included here.

 

Access to the complete tables in compressed format is provided on the document's main page.

 

References

 

1. Kendall, M. G., and B. B. Smith, Random Sampling Numbers, Cambridge University Press, 1939.

 

2. Juncosa, M. L., Random Number Generation on the BRL High-Speed Computing Machines, Ballistic Research Laboratories Report No. 855, Aberdeen Proving Ground, Maryland, 1953.

 

3. Meyer, H. A., L. S. Gephart, and N. L. Rasmussen, On the Generation and Testing of Random Digits, WADC Technical Report 54-55, Wright-Patterson Air Force Base, Ohio, 1954.

 

4. Moshman, Jack, "Generation of Pseudo-random Numbers on a Decimal Calculator," J. Assoc. Computing Machinery, Vol. 1, 1954, p. 88.

 

5. The Monte Carlo Method (Proceedings of a Symposium held in 1949), National Bureau of Standards Report AMS 12, Government Printing Office, Washington 25, D.C., 1951.

 

6. Curtiss, J. H., "Sampling Methods Applied to Differential and Difference Equations," Seminar on Scientific Computation, International Business Machines Corp., New York, 1949.

 

7. Kahn, H., and A. W. Marshall, "Methods of Reducing Sample Size in Monte Carlo Computations," J. Operations Res. Soc. of Amer., Vol. 1, 1953, pp. 263-278.

 

8. Kahn, H., Applications of Monte Carlo, The RAND Corporation (to be published).

 

9. Horton, H. B., and R. T. Smith, "A Direct Method for Producing Random Digits in Any Number System," Ann. Math. Statistics, Vol. 20, 1949, pp. 82-90.

 

10. Mann, H. B., and A. Wald, "On the Choice of the Number of Class Intervals in the Application of the Chi-Square Test," Ann. Math. Statistics, Vol. 13, 1942, pp. 306-317.

 

11. Tables of Probability Functions, 2d ed., U.S. Government Printing Office, Washington, D.C., 1948.

 

[1] References are listed on page xxiv.

 

[2] For readers who are not statisticians: The (chi-square) test is a standard statistical criterion used to measure discrepancy from expectation. The probability value associated with the criterion ranges between zero and one. A small probability value, e.g., less than .05, indicates the possibility of a discrepancy or bias. For very large samples, such as is the case here, with 125,000 digits, the test is extremely sensitive and will result in a small probability value even though the bias may be quite trivial from a practical standpoint.

 

[3] Some issues concerning discrepancies in the numbers presented here are discussed in an addendum prepared in April 1997.

 

[4] RAND has a table of deviations for Gaussian-Markov chains with a discrete time parameter. There is one chain of 10,000 observations for each of the correlations: .600, .800, .900, .950, .970, .980, .990, .995.

Copyright © 1955 by The RAND Corporation

 

All rights reserved. Permission is given to duplicate this on-line document for personal use only, as long as it is unaltered and complete. Copies may not be duplicated for commercial purposes.

 

RAND is a nonprofit institution that helps improve public policy through research and analysis. RAND's publications do not necessarily reflect the opinions or policies of its research sponsors.

[Spddin Ignis]

that was a very interesting article actually...

[Alorael at Large]

No, it was a very random thing to post.

 

—Alorael, who does not condone metaspam no matter how much he relishes the chance to use the word.

[Shaper Cirikci]

1). did any read that whole thing?

2). that is the longest post i ever saw

3). where did you get that?

[Lilith]

Originally Posted By: Shaper Cirikci

1). did any read that whole thing?
2). that is the longest post i ever saw
3). where did you get that?

http://lmgtfy.com/?q=one+million+random+digits&l=1

[Alorael at Large]

Originally Posted By: Shaper Cirikci

1). did any read that whole thing?
2). that is the longest post i ever saw
3). where did you get that?

1. Yes. Okay, I'll admit to some skimming, but mostly I read.
2. It's not the longest post to end up on Spiderweb. It's not even the longest one that didn't break the thread.
3. Thuryl is a knowledgeable fellow, isn't he?

—Alorael, who also suspects that the man is a master of googling it for himself.

[Lilith]

If I actually wanted to be a jerk, I'd have just posted the digits.

[Micawber]

I rather liked the bit about how the 100,000 normal deviates were accidentally filed under 'psychology'. Reminds me of how the curiously organized London bookstore, Foyles, had filed a book named "Signal Catastrophe" under railways. That book is about the C19 Afghan war.

[SamSniped]

Just PLEASE don't get the topic locked...

[SamSniped]

Originally Posted By: RC2112

Just PLEASE don't get the topic locked...

Yay people listened to me!