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Questions, Answers, Information and Comments : Synopsis of Lotto Charlatan Ion Saliu

Fri, 23 Sep 2011 21:53:11 +0000

Author: Colin F
Subject: Synopsis of Lotto Charlatan Ion Saliu
Posted: September 23 2011 at 9:53pm

Ion Salui was a Romanian refugee in 1984, who was accepted by the USA arriving there in 1985 at the age of 35 and settling in Gettysburg, Pennsylvania which incidentally rhymes with Transylvania. Born in Gemeni, Romania on March 9, 1950 Salui claims to be a 1976 Political Economics graduate of the prestigious by Romanian standards, Academy of Economic Studies in Bucharest and therein is the first of many contradictions that the most mildly Socratic cannot ignore.

Given the ego of Ion Salui is on par with the worst case of the psychiatric illness Grandiose Delusions or Delusions of Grandeur one must ask why he has never to the date of this article appended his tertiary qualification to his name. Does he really have a degree involving the study of mathematics at a high level when his rambling writings indicate no more than a naive, schoolboy, poorish understanding laced with a high dose of numerology and occult poison and the most common intuitive but incorrect directions?

With a track record of repeated bald faced lying in various newsgroups and his own writings the circumstances of his flight from the Nicolai Ceauchescu communist regime, where he was a government employee, definitely needs to be clarified. A person who was hard of hearing claims that in songs of praise for the "beloved leader" the off key, enthusiastic warbling of Ion Salui never failed to make him wince and contort with pain.

With a degree in "Economics" one is excused for thinking that a job a bit above that of farmworker, mainly filled by uneducated border crossers from Mexico, would have been found but no. Salui worked as a lowly paid farmworker for the next 20 years and no effort was made to obtain a position more becoming his "qualification" with a much higher rate of pay.

Saliu had like many an interest in computers and with the 32 bit version of Microsoft Windows released in 1995 and the subsequent blooming of the web or internet he registered the URL IonSaliu and published a html page called The Fundamental Formula of Gambling (FFG) in 1997 which in its original form (I have a copy) he claimed to have written December 4, 1996.

One must firstly question the aptness of applying the likelihood of how long an event may not occur as being most appropiate to the title Fundamental Formula of Gambling rather than Percentage Return, especially for games such as Lotto with fair random selections. The reason is simple when it is understood that Salui and others assume the particular history of draws for a Lotto game can be used to predict what numbers are more likely to occur in the next draw. Any doubt that we are dealing with non other than an imposter to rational thought should now be well and truly dispelled.

This FFG article shows an abject ignorance of what is taught in High School or just one semester on introductory probability and basically does not go beyond the concepts introduced in the first chapter or so of any decent book on the subject. His article begs the question how could this be written by an Economics graduate and arouses a strong suspicion that if any degree is involved it is practically certain it is in numerology. Numerologists are fond of making big some mathematical axioms and then interlacing occultist nonsense to give it some credibility to the naive and gullible.

In particular it is highly unlikely that someone could study probability at tertiary level and still believe in the Gambler's Fallacy where prior independent events influence future independent events and indeed refuse to acknowledge that the whole basis for probability is built upon some events being classed as dependent and others as independent. Quite simply those that don't are wandering in the area of the occult and para-normal.

A close examination of the content of the article published 1997, The Fundamental Formula of Gambling, in its original form sets the tone for what followed from Ion Saliu.

We need go no further than the second paragraph to find the inevitable name dropping by Saliu of Blaise Pascal (1623 - 1662) and the attributing of a statement to him unquoted and unfounded, "... the past drawings do count in any game of chance and Pascal demonstrated that hundreds of years ago." What baloney! Count for what? Where and when was it written and in what context? Why not quote the source as is normal?

Prior to that statement Saliu states the obvious, as if he discovered it, that in a Pick 3 Lotto game, " ... all combinations have an equal probability of appearance." It is worth noting that he acknowledges this because later on, his ramblings throw up contradictions.

Paragraph two raises the question of how many events are required to be 99.9% certain of a particular event occurring which in any book or course on probability will be considered in the first or second chapter. A full treatment of how he arrived at what is simply a transformation from a fundamental probability equation is considered in two of my articles: -
Ion Saliu and his Fundamental Formula of Gambling
Fundamental Formula of Gambling Ion Saliu Plagiarism

It's worth mentioning the problem that was posed by The Chevalier de Mere (Antoine Gombaud) and discussed by Blaise Pascal and Pierre de Fermat back in the 17th Century as there is nothing new added by the numerologist Saliu. The question was which is the more likely, a 'six' in 4 throws of a dice or two 'sixes'in 24 throws of two dice?

The answer for 4 throws of one dice is 1 - (5/6)⁴=0.517746
The answer for 24 throws of 2 dice is 1 - (35/36)²⁴=0.491404

The third paragraph considers 9000 tosses of a fair coin and clearly shows he hasn't a clue about what is and what is not expected by simply doing a few runs. According to Saliu there should be only one run of either 9 Heads or 9 Tails. A simple experiment that any computer coding novice could do would show as I found using the Mersenne Twister algorithm there were 4 runs of 10 and 18 runs of 9 or more.

The overall problem which can't be got around is that if you wait for runs of 9 before participating then that represents 0.2% of the tosses and is clearly not practible. Either you are in a game like this or you're part of the audience. With a reasonable participation rate the continuation of the run or change to the flip side is pretty well 50%. Here is what Salui wrote, "There will be, however, 1 (one) defective series (sic). That series will consist of either 9 heads-only or 9 tails-only." So emphatically put but utter ignorance and rot!

The sixth paragraph gets to the nitty gritty of what numerologist Saliu is all about ie promoting his fantastical, primitive bit of reporting nonsense he calls his skip chart in Lotto Pick 3 which basically is the Gambler's Fallacy incarnate. You need look no further than my article on what follows an Unmatched, Double or Triple in Pick 3 to see that they follow the odds and nothing is gained: -
Pick3 Lotto Chances of Success after Multiple Consecutive Doubles or Unmatched
What Follows an Unmatched, Double or Triple in Pick 3

The outrageous claim is now made by Ion Saliu that by following his skip chart players can reduce the house margin from 50% to 2.3%. With the advent of online operators offering a house margin of only 10% for the same Pick 3 State draws, making Salui's claim starkly false, he withdrew the paragraph which I quote here: -

"You can diminish the house edge using the reporting feature (skip chart) of my application MDI Editor & Lotto. ... you can discard of 2 digits for example. In this case, you would have to play from a field of only 8 gigits, the odds being 512 to 1. The house edge is now only 2.3% or over 20 times better than in the case of 10 digits."

What utter deception, lies, rot and blatent nonsense. With the benefit of hindsight not even one example is provided by Saliu for where this has worked.

I always feel guilty about spending time writing on Ion Salui as he is basically just another Lotto nutcase but having started publishing web pages in 1997 and spamming the links anywhere and everywhere his name is there in web searches done on relevant topics to gambling and Lotto. Someone has to shoot down his nonsense and it seems it is up to me to make the effort.

Most of the maniacal, rambling writings of the fool Ion Saliu can be dismissed by any rational person who can persevere for a page or two. For any fair minded person one of his most bizarre claims among many false and grating claims is to be a Free Thinker. You don't necessarily have to be an atheist, agnostic or humanist to qualify as a Free Thinker but you must be honest, rational and capable of arguing in a Critical Thinking way. Have a look at any of the writings of Bertrand Russell to see how succinctly words of wisdom can be delivered.

Colin Fairbrother

History Methods : Repeat of Lotto Integers in up to 6 Previous Draws

Thu, 15 Sep 2011 07:18:47 +0000

Author: Colin F
Subject: Repeat of Lotto Integers in up to 6 Previous Draws
Posted: September 15 2011 at 7:18am

Lotto history buffs read a whole lot more into the significance of a Lotto draw history than it warrants including giving each history a special relationship with numbers that are subsequently picked. Basically it is just a bunch of random combinations for the prescribed Pool and Pick and whatever conclusions pertain to one history apply to another of like Pool and Pick. To ask from 3 draws what integers were in the previous 2 draws is no different to asking from 3 random selections as per the parameters of the Lotto game what integers in the last selection were in the previous 2 selections.

The following table analyzes 1636 draws of the UK 6/49 Lotto game and shows the integer repeats (or matches with the considered draw) for up to 6 draws prior to the considered draw. There is nothing useful in doing this to pick your numbers to play but it is handy to have the facts when dealing with predictionists that try to turn it around the other way and get numbers to play from those that have already occurred.

Integers Matched	Prev Draw	Prev %	Prev 2 Draws	Prev 2 %	Prev 3 Draws	Prev 3 %	Prev 4 Draws	Prev 4 %	Prev 5 Draws	Prev 5 %	Prev 6 Draws	Prev 6 %
0	687	42.00%	321	20.00%	134	8.00%	65	3.97%	41	2.51%	20	1.00%
1	679	41.00%	580	35.00%	377	23.04%	212	12.96%	107	6.54%	59	4.00%
2	243	15.00%	486	30.00%	487	30.00%	381	23.29%	259	15.83%	156	10.00%
3	26	2.00%	194	12.00%	396	24.00%	428	26.16%	381	23.29%	324	20.00%
4	1		45	3.00%	174	11.00%	320	19.56%	356	21.76%	331	20.00%
5			9	0.55%	45	3.00%	150	9.17%	267	16.32%	316	19.00%
6			1	0.06%	20	1.00%	56	3.42%	135	8.25%	220	14.00%
7					2		11	0.67%	56	3.42%	119	7.00%
8					1		12	0.73%	23	1.41%	58	4.00%
9							1		10	0.61%	22	1.00%
10									1		9
11											1
12											1

A quick check mathematically for the previous draw with 0 repeats can be done by dividing the possibilities excluding 6 integers ie 43c6 by that for all possibilities ie 49c6. The calculation is 6096454/13983816 = 0.435936 or 44% which is close to the empirical value of 42%.

Colin Fairbrother

Theory and Concepts : Probability of Success for Grouped Lotto Numbers

Sat, 03 Sep 2011 17:59:55 +0000

Author: Colin F
Subject: Probability of Success for Grouped Lotto Numbers
Posted: September 03 2011 at 5:59pm

Probability of Success for Grouped Lotto Numbers
by Colin Fairbrother

Classic Lotto has 49 balls or integers from which 6 are randomly picked for the first prize number. Favourite ways of categorizing these numbers by players with a numerology bent are: -

Odd and Even Integers
Odds/Evens Debunked
.
Summing the Integers
Sums in Lotto Debunked Part 1
Sums in Lotto Debunked Part 2
.
High, Middle and Low integers
Considered in this article.
.

All these categorizations have been considered in articles on the LottoPoster website.

The numerologists, whether they realize that is what they are or not, then go further and say some combinations are less likely to occur than others and so without any rational reason they filter them out.

In reality the integers as used in Jackpot Lotto have no magnitude and even if they did it is irrelevant in the random picking process. The rather glaring mistake that is made by the promoters of these methods is that it is better to play those that occurr more often such as Sums that add to 150. What is not mentioned is the occurrence is proportional to the extent they are represented in all the possibilities which is really applying the simplest notion of probability.

To illustrate this correlation I will consider some other categorizations and show that the occurrence of the winning numbers in some 1636 draws of the UK Lotto are proportional to the extent the category is represented in the total possibilities.

Consider first the usual scenario where it is stated you are better off playing numbers for a Pick 6 Lotto game where when considered in numerical order the first two lowest integers are from 1 to 16, the middle two are between 17 and 33 and the last two are the highest between 34 to 49. For a Pick 6, Pool 49 Lotto game we have 3,549,600 from the 13,983,816 possibilities that fall within these constraints or 25%. For 1636 draws from the UK Lotto game we have 410 that fit the constraints to give 25% which is little different to considering those with lexicographic ID of < 3,549,601 with 24%, > 10,434,216 with 25% and between IDs 5,217,108 and 8,766,708 with 24%.

We can make the UK 6/49 Lotto game with a first prize chance of winning of 1 in 13,983,816 a game with a chance of winning 1 in 7 by simply dividing the possibilites in either numerical (lexicographic order) or last number order by 7 as shown in the table below with results for the UK 1636 draws:

Category	ID Start	ID Finish	Lex Last	LNO Last	Lex Cat	LNO Cat
A	1	1997688	02 04 20 22 33 49	06 07 09 23 25 37	224	208
B	1997689	3995376	03 10 16 18 19 35	03 13 24 26 31 41	229	244
C	3995377	5993064	05 07 11 13 37 38	09 32 36 40 41 43	244	213
D	5993065	7990752	07 09 10 14 18 40	11 13 37 39 43 45	227	260
E	7990753	9988440	09 19 24 26 37 46	14 31 32 34 40 47	233	233
F	9988441	11986128	13 25 27 41 42 49	15 16 28 30 46 48	247	249
G	11986129	13983816	44 45 46 47 48 49	44 45 46 47 48 49	232	229

Another interesting categorization is by the balls or integers and for a 6/49 game 7 equal length sets can be used as in the following; the first in numerical order followed by another with an offset 7 but any order is just as applicable: -

Set 1
Group A: { 1, 2,   3, 4,   5,   6,   7}
Group B: { 8, 9, 10, 11, 12, 13, 14}
Group C: {15, 16, 17, 18, 19, 20, 21}
Group D: {22, 23, 24, 25, 26, 27, 28}
Group E: {29, 30, 31, 32, 33, 34, 35}
Group F: {36, 37, 38, 39, 40, 41, 42}
Group G: {43, 44, 45, 46, 47, 48, 49}

Set 2
Group A: { 1,   8, 15, 22, 29, 36, 43}
Group B: { 2,   9, 16, 23, 30, 37, 44}
Group C: { 3, 10, 17, 24, 31, 38, 45}
Group D: { 4, 11, 18, 25, 32, 39, 46}
Group E: { 5, 12, 19, 26, 33, 40, 47}
Group F: { 6, 13, 20, 27, 34, 41, 48}
Group G: { 7, 14, 21, 28, 35, 42, 49}

A formula may be applied where ! means factorial (Pl + Pk - 1)! / Pk! x (Pl - 1)! ie (7 + 5)! / 6! x 6! or 12! / 6! x 6! or 12 x 11 x 10 x 9 x 8 x 7 / 6 x 5 x 4 x 3 x2 x1 which can be simplified to 11 x 2 x 3 x 2 x 7 = 924 to get the number of combinations with repeats allowed of the categories.

For combinations without repetition of the categories we have the simple formula 7c6 ie 7! / 6! x (7 - 6)! or 7 categories ie

A B C D E F
A B C D E G
A B C D F G
A B C E F G
A B D E F G
A C D E F G
B C D E F G

There are 117,649 possibilities for each of these 7 unmatched categories giving a total of 823,543 which is just less than 6% of all the 13,983,816 possibilities. The table below shows the occurrence for both Group Set 1 and Group Set 2: -

Unmatched UK Lotto	Count Set 1	Count Set 2
ABCDEF	15	11
ABCDEG	12	15
ABCDFG	24	12
ABCEFG	11	12
ABDEFG	17	13
ACDEFG	15	13
BCDEFG	14	12

ABCDFG certainly stands out for Set 1 but is pretty well normal in Set 2. This is something not predictable but not unusual when dealing with random selections.

Considering all the 924 possibilities for groupings of 6 from the 7 groups ie A B C D E F G with repeats allowed, one can aggregate these into 11 groups based on Group Repeats with varying degrees of occurrence as in the table below: -

Group Occurrence for Number Drawn	Possibilities	Percentage of All Possibilities	Expected UK Lotto	Actual UK Lotto
Same Group x 2	5423859	38.78668	635	615
(Same Group x 2) x 2	4418526	31.59742	517	495
Same Group x 3	1678985	12.00662	196	201
Same Group x 2 with Same Group x 3	1066730	7.62831	125	158
Unmatched or All Different Groups	823543	5.88925	96	108
(Same Group x 2) x 3	329280	2.35472	39	32
Same Group x 4	184485	1.31927	22	20
Same x 4 with Same x 2	26460	0.18921	3	2
Same x 3 with Same x 3	25725	0.18396	3	5
Same x 5	6174	0.04415	0	0
All Same Group	49	0.00035	0	0

The table shows that proportionality applies however you categorize the integers.

The last category in the above table has only 49 possibilities and as expected no success for the 1636 UK Lotto draws. Comparing the probability for playing 49 numbers of 0.0000035 or 0.00035% with that for 1 number of 0.0000000715 we see there is a big difference but the latter is the only relevant probability, irrespective of any groupings made, as this is the one that is paid on. Just picture a 6/49 Lotto game as having 13,983,816 relevant groups and all should be clear as 13,983,816 x 0.0000000715=1 or certainty. Multiplying any grouping of distinct lines by 0.0000000715 gives the probability of success.

If money was no object and you were inclined to throw it away, then playing 25,725 lines per draw, where 3 of the integers were from one group and the other 3 from another over the 1,636 draws would have cost �42,086,100. Even though this group configuration did about 70% better than expected with 5 Jackpot wins a quick, rough calculation shows the return including sub prizes is only about the 50% mark.

Comparing theSet 1 and set 2 where the numbers are from the same group as in the table below we see that including 01 02 03 04 05 06 makes no difference to the probability of 0.00035% for the set winning 1st prize. Included for comparison is an optimized set where I deliberately made sure 8 lines with consecutive integers were included and the chances of this set winning first prize are identical to the other two.

The difference for the optimized set is that none of the paying subset CombThrees, CombFours and CombFives are repeated whereas for the other two sets they are excessive. So, with a possible 980 unique CombThrees for 49 lines the optimized set has this and covers 9,795,325 or 70% (as good as it gets) of the 13,983,816 possible combinations of 6 integers from 49. Set 1 and Set 2 have only 245 distinct CombThrees which are repeated 4 times with a consequent coverage of only 21%.

Set 1 Same Group	Set 2 Same Group	Set Optimized
01 02 03 04 05 06	01 08 15 22 29 36	01 02 03 04 05 06
01 02 03 04 05 07	01 08 15 22 29 43	07 08 09 10 11 12
01 02 03 04 06 07	01 08 15 22 36 43	13 14 15 16 17 18
01 02 03 05 06 07	01 08 15 29 36 43	19 20 21 22 23 24
01 02 04 05 06 07	01 08 22 29 36 43	25 26 27 28 29 30
01 03 04 05 06 07	01 15 22 29 36 43	31 32 33 34 35 36
02 03 04 05 06 07	08 15 22 29 36 43	37 38 39 40 41 42
08 09 10 11 12 13	02 09 16 23 30 37	43 44 45 46 47 48
08 09 10 11 12 14	02 09 16 23 30 44	01 14 20 33 41 46
08 09 10 11 13 14	02 09 16 23 37 44	01 23 25 35 38 44
08 09 10 12 13 14	02 09 16 30 37 44	01 13 36 42 48 49
08 09 11 12 13 14	02 09 23 30 37 44	01 16 19 26 39 45
08 10 11 12 13 14	02 16 23 30 37 44	01 10 17 27 34 40
09 10 11 12 13 14	09 16 23 30 37 44	02 07 13 21 32 45
15 16 17 18 19 20	03 10 17 24 31 38	02 15 20 26 38 47
15 16 17 18 19 21	03 10 17 24 31 45	02 22 31 37 44 49
15 16 17 18 20 21	03 10 17 24 38 45	02 11 25 36 40 43
15 16 17 19 20 21	03 10 17 31 38 45	02 08 17 24 30 33
15 16 18 19 20 21	03 10 24 31 38 45	03 15 23 30 34 46
15 17 18 19 20 21	03 17 24 31 38 45	03 14 21 28 38 43
16 17 18 19 20 21	10 17 24 31 38 45	03 11 18 24 42 44
22 23 24 25 26 27	04 11 18 25 32 39	03 08 29 35 40 47
22 23 24 25 26 28	04 11 18 25 32 46	03 09 16 20 25 48
22 23 24 25 27 28	04 11 18 25 39 46	04 11 17 21 31 48
22 23 24 26 27 28	04 11 18 32 39 46	04 08 23 27 36 39
22 23 25 26 27 28	04 11 25 32 39 46	04 10 15 22 25 32
22 24 25 26 27 28	04 18 25 32 39 46	04 07 26 35 42 46
23 24 25 26 27 28	11 18 25 32 39 46	04 09 24 28 45 49
29 30 31 32 33 34	05 12 19 26 33 40	05 13 24 26 31 43
29 30 31 32 33 35	05 12 19 26 33 47	05 11 15 28 35 39
29 30 31 32 34 35	05 12 19 26 40 47	05 10 16 23 29 42
29 30 31 33 34 35	05 12 19 33 40 47	05 09 18 21 37 47
29 30 32 33 34 35	05 12 26 33 40 47	05 12 22 36 38 45
29 31 32 33 34 35	05 19 26 33 40 47	06 12 17 19 28 46
30 31 32 33 34 35	12 19 26 33 40 47	06 09 22 27 42 43
36 37 38 39 40 41	06 13 20 27 34 41	06 07 24 29 36 37
36 37 38 39 40 42	06 13 20 27 34 48	06 08 15 31 41 45
36 37 38 39 41 42	06 13 20 27 41 48	06 10 21 33 39 49
36 37 38 40 41 42	06 13 20 34 41 48	06 13 20 30 40 44
36 37 39 40 41 42	06 13 27 34 41 48	07 18 23 33 40 48
36 38 39 40 41 42	06 20 27 34 41 48	07 14 19 25 34 49
37 38 39 40 41 42	13 20 27 34 41 48	08 14 26 32 37 48
43 44 45 46 47 48	07 14 21 28 35 42	09 17 29 32 41 44
43 44 45 46 47 49	07 14 21 28 35 49	10 18 19 30 35 41
43 44 45 46 48 49	07 14 21 28 42 49	11 13 19 27 33 37
43 44 45 47 48 49	07 14 21 35 42 49	12 18 20 29 34 43
43 44 46 47 48 49	07 14 28 35 42 49	12 14 30 31 39 47
43 45 46 47 48 49	07 21 28 35 42 49	16 22 28 34 41 47
44 45 46 47 48 49	14 21 28 35 42 49	16 27 32 38 46 49

Randomizing the optimized set gives the best chance for success for the lower prizes but as all the lines are different the chances of success for first prize are just the same as any other set of 49 lines where the lines are different.

So much for HOW TO WIN THE LOTTERY SCHEMES, however there is some brain stimulation in proving them wrong.

Colin Fairbrother

Keno and Lotto Compared : Lotto and Keno Odds, Prizes & Methods Compared

Sun, 21 Aug 2011 20:36:01 +0000

Author: Colin F
Subject: Lotto and Keno Odds, Prizes & Methods Compared
Posted: August 21 2011 at 8:36pm

Lotto and Keno Odds, Prizes and Methods Compared
by Colin Fairbrother

Keno is basically a game similar to Lotto where typically 20 integers are randomly picked from 80 per draw and you can decide which integers you would like to play. Unlike Lotto the size of the line you play for a particular game is not fixed. You can play lines that vary from 1 integer up to usually 15 but some operators allow 20.

What applies to Lotto in terms of Wheeling or being disadvantaged by playing less than the maximum number of integers your lines will allow is equally applicable to Keno. If you are playing lines of length 8 or Spot 8 then there is no better way of playing 10 lines other than the following template which of course you randomize.

01 02 03 04 05 06 07 08
09 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56
57 58 59 60 61 62 63 64
65 66 67 68 69 70 71 72
73 74 75 76 77 78 79 80

The above set has no duplicate integers and therefor no duplicate combinations of 2, 3, 4, 5, 6, 7 and 8. Each line has 28, 56, 70, 56 and 28 distinct combinations for respectively 2, 3, 4, 5 and 6 integers. There are 700 combinations of 4 integers to pitch against the possible 1,581,580 of which 4845 are in the draw of 20 integers. The coverage of the Comb Twos, Comb Threes, Comb Fours, Comb Fives and Comb Sixes for 10 lines cannot be improved on.

You could also randomize the following 16 lines of Spot 5:

01 02 03 04 05
06 07 08 09 10
11 12 13 14 15
16 17 18 19 20
21 22 23 24 25
26 27 28 29 30
31 32 33 34 35
36 37 38 39 40
41 42 43 44 45
46 47 48 49 50
51 52 53 54 55
56 57 58 59 60
61 62 63 64 65
66 67 68 69 70
71 72 73 74 75
76 77 78 79 80

- or 8 lines of Spot 10

01 02 03 04 05 06 07 08 09 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80

The easiest way to play these sets is by using cmnination bets or its equivalent as described in the How to Play Keno New South Wales Playing Guide

Basically, you use a distinct letter for each line - so, for the numbers on the entry form for the first line instead of marking a X you use A. For the second line you use B etc.

The odds in Keno can be easily worked out by applying the following formula:

Combinations of Match in Spot x Combinations of (Drawn - Match) in (Pool - Spot) / Combinations of Drawn in Pool

For a Match 4 in a Spot 8 line applying the formula: -

8c4 x (80-8)c(20-4) / 80c20

ie 70 x 72c16 / 80c20

ie 70 x 4116305022165110 / 3535316142212180000

to give a probability of 0.081504 or odds of 1 in 12

Spot 1
Playing 80 lines each with a distinct integer for the same draw in Keno gives a totally predictable and consistent result. You pay $80.00 for 80 lines and always get 20 correct so your return is (20x3)/80 x 100 = 75%. You can have a guaranteed prize of $3.00 by playing 61 lines each with a distinct integer and still get up to 20 correct for a respective return of as low as 5% to a high of 98%. (The notion that Lotto players were interested in getting a guaranteed prize, no matter how small, in every draw for an exorbitant number of plays was promoted by con-artists and even academics during the 90's and onwards until totally debunked by yours truly in articles on this site.)

Playing just 1 line you should average 1 win for every 4 draws but it is still possible to go as many as 52 draws without a win.

Realistically, you should not play a large number of lines for Spot 1 as there is no chance for a significant prize. By contrast playing the Spot 8 or Spot 10 sets above you have maximized your chances of a prize and also you have a remote chance of a $80,000 win for Spot 8 and a very remote chance of a million dollar prize or more for Spot 10, which is what Keno or Lotto is about.

Spot 5
Playing one 5 Spot line in Keno you have the following odds and Prizes for Australian NSW Keno at clubs and pubs: -
Match           Probability      Odds                Prize
     3            0.08395         1 in 11             $2.00
     4      0.012092       1 in 82           $14.00
     5            0.000645       1 in 1550      $640.00

Playing around 832 random lines or better still 52 draws with the 16 line set costing around $832 you can typically expect to get about $292.00 back or a return of 35% of that wagered. Playing Intralot your return is only around the 24% mark.

Spot 8
Playing one 8 Spot line in Keno you have the following odds and Prizes for Australian NSW Keno at clubs and pubs: -
Match           Probability         Odds                Prize
     4              0.081504        1 in 12              $2.00
     5              0.018303        1 in 54              $7.00
     6              0.002367        1 in 422            $60.00
     7          0.000160        1 in 6,232         $675.00
     8              0.000004        1 in 230,114      Up to $80K

Playing around 830 random lines or better still 83 draws with the 10 line set costing around $830 you can typically expect to get about $363.00 back or a return of 44% of that wagered. Playing Intralot your return is only around the 28% mark.

Spot 10
Playing one 10 Spot line in Keno you have the following odds and Prizes for Australian NSW Keno at clubs and pubs: -
Match           Probability       Odds                             Prize
     4              0.147319      1 in 6                             $1.00
     5              0.051428      1 in 19                            $2.00
     6              0.011479      1 in 87                            $6.00
     7          0.001611      1 in 620                        $50.00
     8              0.000135      1 in 7,384                    $580.00
     9              0.000006      1 in 163,381            $10,000.00
   10              0.0000001    1 in 8,911,711         $1m to $5m

Playing around 832 random lines or better still 104 draws with the 8 line set costing around $832 you can typically expect to get about $337.00 back or a return of 41% of that wagered. Playing Intralot your return is only around the 16% mark.

The important point is that if you play distorted sets with excessive repeats as in silly wheels based on much less than the pool of 80 you can expect to win less often.

Colin Fairbrother

Questions, Answers, Information and Comments : FUNDAMENTAL FORMULA GAMBLING ION SALIU PLAGIARISM

Tue, 10 May 2011 22:41:48 +0000

Author: Colin F
Subject: FUNDAMENTAL FORMULA GAMBLING ION SALIU PLAGIARISM
Posted: May 10 2011 at 10:41pm

FUNDAMENTAL FORMULA OF GAMBLING AND
PARADOX OR PROBLEM OF N TRIALS IS
PLAGIARISM BY ION SALIU

by Colin Fairbrother

As late as May 7, 2011 Ion Saliu wrote preposterously in a newsgroup, "It is totally documented that �degree of certainty� was coined by Ion Saliu and it was first published at saliu.com." IT IS TOTALLY DOCUMENTED THAT STATEMENT BY ION SALIU IS A LIE.

The question for the Fundamental Formula of Gambling centers around who in history first knew about enumerating the possibilities for 1 event, then for multiple events and to use the words of Jacob Bernoulli calculate the Degree of Certainty from his posthumous publication of Ars Conjectandi in 1705, "Probability is a degree of certainty and differs from certainty as a part from a whole.".

For an interesting article see The Significance of Jacob Bernoulli's Ars Conjectandi for the Philosophy of Probability Today by Glen Shafer http://www.glennshafer.com/assets/downloads/articles/article55.pdf

Humans understood Probability going back to our caveman days in working out that more men meant a greater chance of defeating ones enemies.

From the 17th Century a few mathematicians started to use a measuring stick which standardised to a number from 0 to 1 with each respectively designating impossible and certain and the gradations in between represented by a decimal number such as 0.5 meaning 50% or equally likely to go either way. This ratio was arrived at by dividing the favourable chances by all chances.

The general equation for multiple events is then dating from the 17th Century or before : - Probability of Success = Probability of Event ^ Number of Events or

PS = PE^NE

We can solve simply for Number of Events, NE, in basically two ways by using logs. Logarithms date back to the early 17th Century and amongst the mathematicians working on clarifying the idea was John Napier who encountered a constant that subsequently was named by Euler as simply e and ranks in importance alongside pi.

The first way is simply where PE is the base for the log: -

NE = log_PEPS

The second way is to log both sides of the equation and then use a log rule : -

log(PS) = log(PE^NE)
log(PS) = NE x log(PE)
NE = log(PS) / log(PE)

If we are more interested in the complement for the probabilities we deduct each probability from 1 as in : -

NE = log_1-PE(1 - PS)

NE = log(1-PS) / log(1 - PE)

Substituting a name such as Jacob Bernoulli's "Degree of Certainty" for PS and then describing the equation as the Formula of Bankruptcy and inviting others to call it The Fundamental Formula of Gambling as Ion Saliu did in 1997 shows neither creativity nor ingenuity. In a stupendous act of plagiarism Ion Saliu went on in later modifications of the original article to embellish it with this statement, "The Fundamental Formula of Gambling (FFG) is an historic discovery in theory of probability, theory of games, (sic) and gambling mathematics.". THE FUNDAMENTAL FORMULA OF GAMBLING IS BLATANT, FLAGRANT AND PREPOSTEROUS PLAGIARISM BY ION SALIU.

As previously mentioned the constant e which is approximately 2.71828 was encountered by John Napier in 1618 when working with logarithms. Dividing 1 by e we get 0.3678796 ... or approximately 0.37 or 37%. If we subtract a probability of 0.37 from 1 we get 0.63 or 63%. Recently I encountered 1 - 1/e when enumerating 14 million random selections for a Pool of 49 and Pick of 6 using the MersenneTwister algorithm as 63% were distinct as expected and I noted it at the time.

Included in 14 million from 13,983,816 possibilities: 8,845,381 or 63%
Not included in 14 million from 13,983,816 possibilities: 5,138,435 or 37%

Combinations appearing once only in 14,000,000: 5,143,806 or 37%
Distinct Combinations with appearance more than once in 14,000,000: 3,701,575 or 26%
Combinations including repeats with appearance > 1 in 14,000,000: 8,856,194 or 63%

Appearance
Count
Extension
1x 5143806 5143806
2x 2576162 5152324
3x 859154 2577462
4x 214693 858772
5x 43121 215605
6x 7256 43536
7x 1034 7238
8x 139 1112
9x
15 135
10x 1
10
Total: 14000000

See : -
Random Lotto Numbers using the Mersenne Twister
http://lottoposter.com/forum_posts.asp?TID=661

It is worth noting that the breakdown of 13,983,816 random selections as for Pool 49 and Pick 6 was hopelessly misunderstood by Ion Saliu and confirmed recently in a newsgroup rec.gambling.lottery April 29, 2011 where he stated, "If you RANDOMLY generate 13983816 combinations, the probability of appearance for one combo is only {1 � 1/e} or 63.2%. That also means that only 63.2% of the combos generated are UNIQUE; 36.8% of the outcome represents duplicates."

Needless to say at the outset and for each of the 14,000,000 events the chances of any one combination appearing is as per probability 1 in 13,983,816 but for a large number of possibilities there comes a point for a large number of events where the likelihood of the number randomly selected being already in previous selections is greater and for the 14 million combinations I generated this occurred around the 9,693,000th selection or 36% of the possibilities due to repeats.

Contrary to the understanding of Ion Saliu only 37% are "unique" or with a once only occurrence NOT 63% as he states. Of the 14 million combinations 26% occur more than once ie have duplicates and make up 63% of the combinations NOT 36.8% as Ion Saliu states ie the other way round. This from an idiot that claims he invented 1 - 1/e. Ion Saliu hopelessly suffers from the psychiatric illness referred to as Delusions of Grandeur or Grandiose Delusions.

The absurdity and naivety by Ion Saliu to state that in generating 13,983,816 random 6 integer combinations from a pool of 49 integers 63% or around 9,000,000 will be "unique" ie ONLY APPEAR ONCE and that 37% or around 5,000,000 will appear more than once is obvious for the total combinations would be in excess of 19,000,000 even for just one duplicate for each of the 5,000,000!

For a petty numerologist like Ion Saliu to claim 1 - 1/e as his own discovery by renaming it PARADOX OR PROBLEM OF N TRIALS IS ALSO BLATANT, FLAGRANT AND PREPOSTEROUS PLAGIARISM BY ION SALIU.

For further details with a table showing that the number of events may still be obtained using the equation above where the probability of the event is correct but where the probability of success is less than optimum eg 1 toss of coin has probability 0.5 but 1 event is obtained with a probability of success of 0.293. Perhaps I should call this the Paradox of Limited Success. see

THE MADNESS OF ION SALIU AND HIS SPURIOUS CLAIM TO
THE SO CALLED FUNDAMENTAL FORMULA OF GAMBLING
http://lottoposter.com/forum_posts.asp?TID=677

Colin Fairbrother

ps The following simple table is an example of the constant e. As N is increased by 10 for each line so 1/n is added and the result is raised to the power of N. It can be seen that at around 100 the result has very little increase although N is still being increased by the same amount.

n	1/n	(1+1/n)^n
1	1.0000	2.0000
10	0.1000	2.5937
20	0.0500	2.6533
30	0.0333	2.6743
40	0.0250	2.6851
50	0.0200	2.6916
60	0.0167	2.6960
70	0.0143	2.6991
80	0.0125	2.7015
90	0.0111	2.7033
100	0.0100	2.7048
110	0.0091	2.7060
120	0.0083	2.7070
130	0.0077	2.7079
140	0.0071	2.7086
150	0.0067	2.7093

Lotto Number Analysis Using Excel, Access and Visual Basic : ION SALIU AND HIS FUNDAMENTAL FORMULA OF GAMBLING

Thu, 05 May 2011 03:39:44 +0000

Author: Colin F
Subject: ION SALIU AND HIS FUNDAMENTAL FORMULA OF GAMBLING
Posted: May 05 2011 at 3:39am

THE MADNESS OF ION SALIU AND HIS SPURIOUS CLAIM
TO THE SO CALLED FUNDAMENTAL FORMULA OF GAMBLING
by Colin Fairbrother

In 1997 Ion Saliu published an html page (FFG) giving a table calculated from using a simple formula that relied on using the log rule that log_b(mⁿ) = n * log_b(m) and purported to show the number of events required in succession for various degrees of certainty up to 99.9% which he thought defined adequately the upper limit. He has variously lauded this simple equation as a great achievement despite the "calculated" data given being variously under-estimated, wrong, mis-applied or distorted. Because the equation is just a transformation from the standard probability equation for multiple events in any introductory book or paper on probability in reality it would barely warrant a pat on the head and a wry smile from a 3rd year high school teacher.

Probability is defined in its mathematical sense for a given scenario as the ratio of the events considered favourable to that of all possibilities and ranges from 0 (impossible) through 0.1, 0.2 etc to 0.5 (50/50 or equally likely to occur or not occur) and then on with 0.6, 0.7 etc to 1 which is certainty.

Consider a coin toss with the possibilities listed below for 3 throws: -
1 Throw H or T
2 Throws HT or TH or HH or TT
3 Throws HHH or HHT or HTH or HTT or THH or THT or TTH or TTT

With P as the probability, 1 as the number of occurrences of HHH which we will regard as favourable and 8 as the possible occurrences for 3 throws we have: -

P (Probability) = Events Favourable or 1 or 1 or 0.125.                  Possible Events      8    2³

We see that number of events, which is 3 in the example above, becomes the exponent n in the introductory and fundamental probability equation for multiple events that's been around for hundreds of years: -
Degree of Certainty or Probability of Success = (Probability of Event)ⁿ
or for the complement
Degree of Certainty or Probability of Non-Success = (1 - Probability of Event)ⁿ

As an expression "Degree of Certainty" is recorded in English as being used by Geoffrey Chaucer in the 14th century. You will probably find the term Probability of Success used more often than Degree of Certainty which was first used in a mathematical paper by Jacob Bernoulli in his seminal work "The Art of Conjecturing" or in Latin "Ars Conjectandi" published post humously in 1713. The English translation gives,"Probability is a degree of certainty and differs from certainty as a part from a whole."

The formula or equation as given by Ion Saliu is just a transformation from the standard format and you only need a rudimentary knowledge of arithmetic to realise this: -

N = log(1 - Degree of Certainty)    log(1 - Probability of Event)

If we have the probability of an event and the nominated probability for success we can solve to get an approximation of the number of events as a whole number.

The equation can be written: -
P_Success = (P_Event)^Events

To get the exponent Events we can log both sides and still preserve equality: -

log(P_Success) = log((P_Event^)Events)

Using one of the three basic log rules we know that the right side of the equation can be substituted with: -

log(P_Event^Events) = Events x log(P_Event)

Therefore: - log(P_Success) = Events x log(P_Event)

Events = log(P_Success)         log(P_Event)

If more interested in the complement for the two probability figures then we subtract from 1.

The simple equation now becomes: -

Events = log(1 - P_Success)         log(1 - P_Event)

To apply the equation consider the occurrence of 26 blacks consecutively on a roulette table at Monte Carlo casino August 18, 1913. This particular occurrence I have known about since a boy and have cited it often in my writings on the web dating from 2004 referring to it as the Monte Carlo Factor ie as a rule of thumb if the odds are 1 in 2 as for a coin face or pretty well a color in Roulette then multiply the 2 by 13 to give a possible and confirmed in real life run on a color of 26. For Pick 3 straights multiply 1000 by 13 to give a possible absence of 13,000 or more. The figures are useful in giving an indication of how long a run can go for and should dispel any reliance on something being "due".

Probability 26 consecutive blacks = 18/37 x 18/37 x 18/37 x ... 18/37 = (18/37)²⁶ = (0.486486486)²⁶ = 0.0000000073087.
The complement to this is 0.9999999926913.
The inverse of this figure gives 1 in 136,823,184.
It is a simple application of the multiplication principle found in the first chapter of any book on probability and possibly touched on in primary school.

Some would ask at this point if we are interested in how many events why not produce a list for the range we are interested in which can be simply done using the basic formula without transformation in any spreadsheet like Excel? Looking at the table below you see that for Number Events = 26 - the probability of success is 0.0000007 ie extremely unlikely - but it has happened. The exponent is a whole number so all the calculations have been done without using any logs.

Events = log(1 - 0.9999999926913) = -7.387216144  = 26         log(1 - 0.486486486486)    -0.289448123

Apart from this method one can also solve or transform for the exponent as in:DC = PEⁿby n = log_PEDC
where PE becomes the base for the log.
DC is Degree of Certainty or Probability of Success
PE is the Probability for the Event
and n is the number of Events

Apparently Ion Salui knew nothing about this alternative solving for the exponent as it is not mentioned in any of his maniacal writings up until the date this article was posted ie May 2011.

Ion Saliu wrote regarding Lotto Pick 3,"Self,how many drawings do I have to play so that there is a 99.9% degree of certainty my combination of 1/1,000 probability will come out?". For Pick 3 this gives 6904 draws and for both a series of same side coin tosses or same color roulette spins it is 10. The 1913 Monte Carlo experience of 26 blacks in succession, which anyone writing on gambling should have been aware of, shows there is only a 0.0000007% probabability of 26 spins with the same color run in roulette and using the same probability percentage 27 same side coin tosses are possible and using the complement probability of 99.9999993% 18,725 draws in Pick 3 are possible before a specific straight occurrs.

The chances are that you will never be part of a long run in roulette and anyone that placed any reliance on the upper limit figures given by Ion Salui would have wasted a lot of money just like the multi-millions lost in 1913 at Monte Carlo when the patrons were in a frenzy after 15 blacks in succession with less than a 1% chance as they thought of it continuing - but continue it did for another 11 spins.

Longshot figures are also hopelessly irrelevant as participation in a game requires something other than making a bet on something that takes years before occurring.

Generally, with Ion Saliu we are dealing with at the least muddled and distorted meanderings. When referring to the table below it helps to realise the following two self evident facts:

The probability of a particular straight being drawn in Pick 3 increases as the number of draws increases.

The probability of getting the same color in roulette or the same side in tossing a coin decreases as the tosses increase.

The table is easily done in Excel and applies the fundamental probability equation without using logs. In the case of Pick 3 with high exponent values we calculate the complement and subtract from 1 ie 1-(1-0.001)ⁿ.

The figures are to be taken with a grain of salt to show the approximate upper limits for absence and are not to be relied on as far as any betting scheme is concerned with limits. As an example consider a series of 12 coin tosses. From our starting toss the likelihood of 12 heads or 12 tails occurring is very unlikely ie HHHHHHHHHHHH or TTTTTTTTTTTT. For the 12th toss if 11 Heads or 11 Tails have occurred the probability of 12 Heads or 12 Tails is exactly the same. In other words knowing what has occurred previously gives you no advantage in anticipating what will occur next as the chances for what we regard as success are perfectly counter balanced by the complement or what we regard as failure for this binomial example.

Compare the accurate figures given with the red coloured wrong figures given by Ion Salui and what a difference. For three tosses he gives 90% when in fact it is only 87.5% ie 7 in 8 and for 9 tosses he gives 99.9 when it is 99.8 and the 0.1 in the calculation is meaningful. Whether he intentionally fudged the figures to deceive or to promote his crackpot Pick 3, con-artist scheme where he claims to reduce the House Edge from 50% to 2.3% or just through plain incompetence I will leave to others to conclude. In my considered opinion it is a combination of all three.

Probability of Success	Probability Success Exponent Calculation	Probability Single Event	1 - Probability of Success	Events	% Probability	% Probability Ion Saliu
Either Color Roulette 1 Spin	(18/37)¹ = 0.48648649	0.486486	0.513514	1	48.648649
Same Color Roulette 2 Spins	(18/37)² = 0.236666910	0.486486	0.763331	2	23.6666910
Same Color Roulette 3 Spins	(18/37)³ = 0.115136319	0.486486	0.884864	3	11.5136319
Same Color Roulette 4 Spins	(18/37)⁴ = 0.056012264	0.486486	0.943988	4	5.6012264
Same Color Roulette 5 Spins	(18/37)⁵ = 0.027249209	0.486486	0.972751	5	2.7249209
Same Color Roulette 6 Spins	(18/37)⁶ = 0.013256372	0.486486	0.986744	6	1.3256372
Same Color Roulette 7 Spins	(18/37)⁷ = 0.006449046	0.486486	0.993550	7	0.6449046
Same Color Roulette 8 Spins	(18/37)⁸ = 0.003137374	0.486486	0.996863	8	0.3137374
Same Color Roulette 9 Spins	(18/37)⁹ = 0.001526289	0.486486	0.998474	9	0.1526289
Same Color Roulette 10 Spins	(18/37)¹⁰ = 0.000742519	0.486486	0.999257	10	0.0742519
Same Color Roulette 15 Spins	(18/37)¹⁵ = 0.000020233	0.486486	0.993551	15	0.0020233
Same Color Roulette 26 Spins	(18/37)²⁶ = 0.000000007	0.486486	0.996863	26	0.0000007
Either Coin Face 1 Toss	(1/2)¹ = 0.500000000000	0.5	0.5	1	50.0	50
Same Coin Face 2 Tosses	(1/2)² = 0.250000000000	0.5	0.75	2	25.0	75
Same Coin Face 3 Tosses	(1/2)³ = 0.125000000000	0.5	0.875	3	12.5	90
Same Coin Face 4 Tosses	(1/2)⁴ = 0.062500000000	0.5	0.9375	4	6.25	95
Same Coin Face 5 Tosses	(1/2)⁵ = 0.031250000000	0.5	0.96875	5	3.125
Same Coin Face 6 Tosses	(1/2)⁶ = 0.015625000000	0.5	0.984375	6	1.5625	99
Same Coin Face 7 Tosses	(1/2)⁷ = 0.007812500000	0.5	0.9921875	7	0.78125
Same Coin Face 8 Tosses	(1/2)⁸ = 0.003906250000	0.5	0.99609375	8	0.390625
Same Coin Face 9 Tosses	(1/2)⁹ = 0.001953125000	0.5	0.998046875	9	0.1953125	99.9
Same Coin Face 10 Tosses	(1/2)¹⁰ = 0.000976562500	0.5	0.999023438	10	0.09765625
Same Coin Face 11 Tosses	(1/2)¹¹ = 0.000488281250	0.5	0.999511719	11	0.048828125
Same Coin Face 12 Tosses	(1/2)¹² = 0.000244140625	0.5	0.999755859	12	0.0244140625
Same Coin Face 27 Tosses	(1/2)²⁷ = 0.000000007450	0.5	0.999999992	27	0.0000007451
Specific Pick 3 Straight 1 Draw	(1/1000)¹ = 0.001000000	0.001	0.9990000000	1	0.10000
Specific Pick 3 Straight 106 Draws	(1/1000)¹⁰⁶ = 0.100623052	0.001	0.899376948	106	10.06230
Specific Pick 3 Straight 288 Draws	(1/1000)²⁸⁸ = 0.250346438	0.001	0.749653562	288	25.03464
Specific Pick 3 Straight 693 Draws	(1/1000)⁶⁹³ = 0.500099765	0.001	0.499900235	693	50.00997
Specific Pick 3 Straight 916 Draws	(1/1000)⁹¹⁶ = 0.600067024	0.001	0.399932976	916	60.00670
Specific Pick 3 Straight 1050 Draws	(1/1000)¹⁰⁵⁰ = 0.650246042	0.001	0.349753958	1050	65.02460
Specific Pick 3 Straight 1204 Draws	(1/1000)¹²⁰⁴ = 0.700188819	0.001	0.299811180	1204	70.01888
Specific Pick 3 Straight 1386 Draws	(1/1000)¹³⁸⁶ = 0.750099755	0.001	0.249900245	1386	75.00997
Specific Pick 3 Straight 1609 Draws	(1/1000)¹⁶⁰⁹ = 0.800073411	0.001	0.199926589	1609	80.00734
Specific Pick 3 Straight 1897 Draws	(1/1000)¹⁸⁹⁷ = 0.850124321	0.001	0.149875679	1897	85.01243
Specific Pick 3 Straight 2302 Draws	(1/1000)²³⁰² = 0.900056651	0.001	0.099943349	2302	90.00566
Specific Pick 3 Straight 2995 Draws	(1/1000)²⁹⁹⁵ = 0.950038296	0.001	0.049961703	2995	95.00382
Specific Pick 3 Straight 4603 Draws	(1/1000)⁴⁶⁰³ = 0.990001328	0.001	0.009998672	4603	99.00013
Specific Pick 3 Straight 6905 Draws	(1/1000)⁶⁹⁰⁵ = 0.999000699	0.001	0.000999301	6905	99.90007
Specific Pick 3 Straight 13000 Draws	(1/1000)¹³⁰⁰⁰= 0.999997754	0.001	0.000002245	13000	99.99997
Specific Pick 3 Straight 18725 Draws	(1/1000)¹⁸⁷²⁵=0.999999993	0.001	0.000000007	18725	99.999999
Any Win 6/49 Lotto 245 Draws	0.018637³⁷⁰ = 0.99905176	0.018637	0.000948235	245	99.905176%
Any Win 6/45 + 2 Bonus Lotto 388 Draws(Aus Saturday)	0.011802⁵⁹⁰ = 0.999092461	0.011802	0.000907538	388	99.909246%

Colin Fairbrother

Questions, Answers, Information and Comments : New game platform

Sun, 10 Apr 2011 11:53:28 +0000

Author: WeEf
Subject: New game platform
Posted: April 10 2011 at 11:53am

Hello laidback 22,

please try www.weefs-lottosysteme.de for wheels t<>m and change language to English and http://www.ccrwest.org/cover.html for wheels t=m.

Have a nice time

WeEf

Questions, Answers, Information and Comments : New game platform

Sun, 10 Apr 2011 08:47:51 +0000

Author: laidback22
Subject: New game platform
Posted: April 10 2011 at 8:47am

Hi All,
Anyone tried this site Blankety Blank.com?
They have 30 lottery games, and dozens of casino games.
Any recommendations on them?

Theory and Concepts : Chances of Success 1st Prize Lotto Pick 6, Pool 49

Sat, 05 Mar 2011 20:01:52 +0000

Author: Colin F
Subject: Chances of Success 1st Prize Lotto Pick 6, Pool 49
Posted: March 05 2011 at 8:01pm

The possibilities for 1st prize in a Lotto game such as UK Lotto where each line has six distinct integers from a Pool of 49 is 13,983,816. Each line has the same chance of being drawn as any other.

If you played one line your chances of a match for all six integers in one draw is 1/13,983,816 or 0.0000000715112 or 0.00000715112%.

The table below shows your chances of success for one draw with distinct combinations for 1 and multiples of 10 to 11,111,111 lines and the balance of 2,872,705 to make 13,983,816. Adding the probabilities gives 1 or certainty for 13,983,816 distinct combinations.

Lines	Probability
1	0.0000000715112
10	0.0000007151124
100	0.0000071511238
1000	0.0000715112384
10000	0.0007151123842
100000	0.0071511238420
1000000	0.0715112384202
2872705	0.2054306921659
10000000	0.7151123842018

Plays per Draw and Draws can be interchanged so in the UK Lotto playing 1813 plays per draw over 1584 draws from November 1994 gives 2,872,705 plays with a 20% chance of a 1st prize win.

An important concept is proportionality in terms of plays made and chances of success. Time and time again in this field of interest, Lotto number analysis, you will find the facts misconstrued by not taking into account proportionality especially by numerologists whether outed or not.

An example is consecutive ascending Numerical Order numbers of which there are 44 for a Pick 6, Pool 49 Lotto game as in the table below.

Comb6
01 02 03 04 05 06
02 03 04 05 06 07
03 04 05 06 07 08
04 05 06 07 08 09
05 06 07 08 09 10
06 07 08 09 10 11
07 08 09 10 11 12
08 09 10 11 12 13
09 10 11 12 13 14
10 11 12 13 14 15
11 12 13 14 15 16
12 13 14 15 16 17
13 14 15 16 17 18
14 15 16 17 18 19
15 16 17 18 19 20
16 17 18 19 20 21
17 18 19 20 21 22
18 19 20 21 22 23
19 20 21 22 23 24
20 21 22 23 24 25
21 22 23 24 25 26
22 23 24 25 26 27
23 24 25 26 27 28
24 25 26 27 28 29
25 26 27 28 29 30
26 27 28 29 30 31
27 28 29 30 31 32
28 29 30 31 32 33
29 30 31 32 33 34
30 31 32 33 34 35
31 32 33 34 35 36
32 33 34 35 36 37
33 34 35 36 37 38
34 35 36 37 38 39
35 36 37 38 39 40
36 37 38 39 40 41
37 38 39 40 41 42
38 39 40 41 42 43
39 40 41 42 43 44
40 41 42 43 44 45
41 42 43 44 45 46
42 43 44 45 46 47
43 44 45 46 47 48
44 45 46 47 48 49

If playing these 44 consecutives over 1584 draws the chances of a 1st prize match for 69696 plays is only 0.5%. However, for the 14 million random numbers generated using the Mersenne Twister algorithm playing the 44 lines we can expect about 44 successes. We actually get 39 of which 29 are distinct as in the table below with much to the consternation of numerologists 44 45 46 47 48 49 repeating twice. This is not unexpected as the 14 million generated random numbers only has 63% of the distinct combinations so 63% of 44 is 28. See Random Lotto Numbers using the Mersenne Twister

Comb6	Cnt
05 06 07 08 09 10	3
13 14 15 16 17 18	3
35 36 37 38 39 40	3
15 16 17 18 19 20	3
26 27 28 29 30 31	2
09 10 11 12 13 14	2
36 37 38 39 40 41	2
14 15 16 17 18 19	2
30 31 32 33 34 35	2
44 45 46 47 48 49	2
24 25 26 27 28 29	2
03 04 05 06 07 08	1
04 05 06 07 08 09	1
11 12 13 14 15 16	1
02 03 04 05 06 07	1
29 30 31 32 33 34	1
33 34 35 36 37 38	1
37 38 39 40 41 42	1
38 39 40 41 42 43	1
39 40 41 42 43 44	1
41 42 43 44 45 46	1
42 43 44 45 46 47	1
43 44 45 46 47 48	1
27 28 29 30 31 32	1

Colin Fairbrother

Theory and Concepts : Integer Occurrence UK Lotto for Order Drawn

Sat, 26 Feb 2011 07:51:49 +0000

Author: Colin F
Subject: Integer Occurrence UK Lotto for Order Drawn
Posted: February 26 2011 at 7:51am

Recently, I had a bizarre contributor in a Newsgroup who to be honest is not quite compos mentis state the following regarding 5 QuickPicks he purchased for the UK 6/49 Lotto, "Not with so many numbers above 8 TO 10, position 1 surely. 80% Of winning JACKPOT lines have a number between 1 AND 8 in P1"

For 1584 draws of the UK Lotto game you do have 67% starting with 1 to 8 when the line is in Numerical Order. To expect a small sample of 5 Random Selections to reflect this distribution is totally unrealistic. Indeed, if we divide the lexicograhic enumeration into thirds then we have 7 draws consecutively in the top third, namely draws 952, 953, 954, 955, 956 and 957. Harry thinks this shouldn't happen!

Basically to restrict the numbers played to a grouping that has the highest winnings is to ignore proportionality as is done with Sums, Odds/Evens and other numerology mumbo jumbo. If a grouping is preferred where the wins mostly occur your chances of success have not improved as evidenced by comparing the lines in the group to all possible combinations ratio and wins for that group over 1584 draws of the UK Lotto game. The ratios are pretty much the same as shown in the table below: -

From Lex Index	To Lex Index	First Integer	Lex Combinations	% All Lex	UK Lotto Wins	% All UK Wins
1	1712304	1	1712304	12.24	184	11.62
1712305	3246243	2	1533939	10.97	177	11.17
3246244	4616997	3	1370754	9.80	154	9.72
4616998	5838756	4	1221759	8.74	144	9.09
5838757	6924764	5	1086008	7.77	114	7.20
6924765	7887362	6	962598	6.88	113	7.13
7887363	8738030	7	850668	6.08	97	6.12
8738031	9487428	8	749398	5.36	80	5.05
9487429	10145436	9	658008	4.71	81	5.11
10145437	10721193	10	575757	4.12	65	4.10
10721194	11223135	11	501942	3.59	68	4.29
11223136	11659032	12	435897	3.12	49	3.09
11659033	12036024	13	376992	2.70	36	2.27
12036025	12360656	14	324632	2.32	35	2.21
12360657	12638912	15	278256	1.99	32	2.02
12638913	12876248	16	237336	1.70	26	1.64
12876249	13077625	17	201376	1.44	20	1.26
13077625	13247535	18	169911	1.22	26	1.64
13247536	13390041	19	142506	1.02	17	1.07
13390042	13508796	20	118755	0.85	9	0.57
13508797	13607076	21	98280	0.70	7	0.44
13607077	13687806	22	80730	0.58	10	0.63
13687807	13753586	23	65780	0.47	9	0.57
13753587	13806716	24	53130	0.38	10	0.63
13806717	13849220	25	42504	0.30	4	0.25
13849221	13882869	26	33649	0.24	7	0.44

Consider the following two samples of 5 lines for a 6/49 Lotto game. The first has lexicograhic indices below or equal to 6,298,682 or in the lower half of the 13,983,816 combinations. The second table has lexicograhic indices higher than or equal to 13,390,042 or the higher 1/24th of the 13,983,816 some 594,000. According to Harry you have a better chance with the first set. The reality is that they have an equal chance at all prize levels both with a Six coverage of 0.00004% and Three coverage of 9.29%

Lexicographic Index	Comb6
670034	01 06 11 16 21 26
2324197	02 07 12 17 22 27
3803853	03 08 13 18 23 28
5124008	04 09 14 19 24 29
6298682	05 10 15 20 25 30

Lexicographic Index	Comb6
13390042	20 21 22 23 24 25
13849221	26 27 28 29 30 31
13965253	32 33 34 35 36 37
13982893	38 39 40 41 42 43
13983816	44 45 46 47 48 49

I did point out if you are looking at the results in Numerical Order then for example 1 will always be in Position 1 and 49 always in Position 6. In other words you can't compare integer occurrences fairly when the presentation is in Numerical Order.

If the occurrence is compared for the order drawn this is a fair comparison and is shown in the table below for 1584 draws in the UK Lotto game. Integer 23 has the highest occurrence of 48 for the first main ball drawn and integers 20 and 10 have the lowest at 20 for respectively the first and second ball drawn.

Integer	Ball 1	Ball 2	Ball 3	Ball 4	Ball 5	Ball 6
1	35	39	24	27	23	36
2	30	37	37	31	37	27
3	36	30	38	26	27	36
4	30	35	30	30	30	35
5	29	22	31	37	33	31
6	24	38	35	35	37	32
7	22	32	34	21	33	40
8	33	32	26	36	26	32
9	31	35	37	30	36	36
10	36	20	38	37	30	33
11	38	33	39	44	29	32
12	35	37	22	34	30	36
13	25	30	34	28	27	25
14	38	33	30	25	29	25
15	24	36	28	30	28	30
16	38	28	28	25	29	27
17	29	26	38	37	29	31
18	27	43	41	21	32	27
19	30	34	33	36	40	21
20	20	21	26	38	21	34
21	34	28	25	38	24	22
22	33	31	23	33	35	33
23	48	31	30	33	39	33
24	31	32	35	32	37	30
25	33	39	38	32	36	33
26	30	29	32	29	36	33
27	34	27	37	33	43	31
28	40	32	34	32	34	23
29	26	41	30	29	27	33
30	35	31	26	29	39	43
31	34	29	32	39	41	38
32	33	37	39	31	29	36
33	35	34	29	36	36	44
34	36	31	35	24	40	27
35	40	33	35	34	30	30
36	24	29	36	30	33	31
37	29	37	31	30	24	27
38	29	37	38	38	39	39
39	26	31	35	33	44	34
40	37	29	40	35	30	38
41	35	32	27	24	21	26
42	32	31	33	27	33	39
43	44	40	31	34	35	31
44	34	43	22	39	34	41
45	35	23	33	40	22	43
46	33	29	28	33	31	33
47	31	32	32	40	41	31
48	33	33	34	38	30	26
49	30	32	35	31	35	30

-------------------------------------------------

Integer Occurrence For Order Drawn UK Lotto 1584 Draws
Integer	Position 1	Position 2	Position 3	Position 4	Position 5	Position 6	Max	Min	Avg	SD
1	35	39	24	27	23	36	39	23	30.67	6.83
2	30	37	37	31	37	27	37	27	33.17	4.40
3	36	30	38	26	27	36	38	26	32.17	5.15
4	30	35	30	30	30	35	35	30	31.67	2.58
5	29	22	31	37	33	31	37	22	30.50	4.97
6	24	38	35	35	37	32	38	24	33.50	5.09
7	22	32	34	21	33	40	40	21	30.33	7.39
8	33	32	26	36	26	32	36	26	30.83	4.02
9	31	35	37	30	36	36	37	30	34.17	2.93
10	36	20	38	37	30	33	38	20	32.33	6.71
11	38	33	39	44	29	32	44	29	35.83	5.49
12	35	37	22	34	30	36	37	22	32.33	5.61
13	25	30	34	28	27	25	34	25	28.17	3.43
14	38	33	30	25	29	25	38	25	30.00	4.98
15	24	36	28	30	28	30	36	24	29.33	3.93
16	38	28	28	25	29	27	38	25	29.17	4.54
17	29	26	38	37	29	31	38	26	31.67	4.80
18	27	43	41	21	32	27	43	21	31.83	8.64
19	30	34	33	36	40	21	40	21	32.33	6.47
20	20	21	26	38	21	34	38	20	26.67	7.63
21	34	28	25	38	24	22	38	22	28.50	6.25
22	33	31	23	33	35	33	35	23	31.33	4.27
23	48	31	30	33	39	33	48	30	35.67	6.80
24	31	32	35	32	37	30	37	30	32.83	2.64
25	33	39	38	32	36	33	39	32	35.17	2.93
26	30	29	32	29	36	33	36	29	31.50	2.74
27	34	27	37	33	43	31	43	27	34.17	5.46
28	40	32	34	32	34	23	40	23	32.50	5.50
29	26	41	30	29	27	33	41	26	31.00	5.48
30	35	31	26	29	39	43	43	26	33.83	6.40
31	34	29	32	39	41	38	41	29	35.50	4.59
32	33	37	39	31	29	36	39	29	34.17	3.82
33	35	34	29	36	36	44	44	29	35.67	4.84
34	36	31	35	24	40	27	40	24	32.17	5.98
35	40	33	35	34	30	30	40	30	33.67	3.72
36	24	29	36	30	33	31	36	24	30.50	4.04
37	29	37	31	30	24	27	37	24	29.67	4.37
38	29	37	38	38	39	39	39	29	36.67	3.83
39	26	31	35	33	44	34	44	26	33.83	5.91
40	37	29	40	35	30	38	40	29	34.83	4.45
41	35	32	27	24	21	26	35	21	27.50	5.17
42	32	31	33	27	33	39	39	27	32.50	3.89
43	44	40	31	34	35	31	44	31	35.83	5.19
44	34	43	22	39	34	41	43	22	35.50	7.56
45	35	23	33	40	22	43	43	22	32.67	8.64
46	33	29	28	33	31	33	33	28	31.17	2.23
47	31	32	32	40	41	31	41	31	34.50	4.68
48	33	33	34	38	30	26	38	26	32.33	4.03
49	30	32	35	31	35	30	35	30	32.17	2.32

Colin Fairbrother

Appearance	Count	Extension
1x	5143806	5143806
2x	2576162	5152324
3x	859154	2577462
4x	214693	858772
5x	43121	215605
6x	7256	43536
7x	1034	7238
8x	139	1112
9x	15	135
10x	1	10
	Total:	14000000

Integer	Ball 1	Ball 2	Ball 3	Ball 4	Ball 5	Ball 6
1	35	39	24	27	23	36
2	30	37	37	31	37	27
3	36	30	38	26	27	36
4	30	35	30	30	30	35
5	29	22	31	37	33	31
6	24	38	35	35	37	32
7	22	32	34	21	33	40
8	33	32	26	36	26	32
9	31	35	37	30	36	36
10	36	20	38	37	30	33
11	38	33	39	44	29	32
12	35	37	22	34	30	36
13	25	30	34	28	27	25
14	38	33	30	25	29	25
15	24	36	28	30	28	30
16	38	28	28	25	29	27
17	29	26	38	37	29	31
18	27	43	41	21	32	27
19	30	34	33	36	40	21
20	20	21	26	38	21	34
21	34	28	25	38	24	22
22	33	31	23	33	35	33
23	48	31	30	33	39	33
24	31	32	35	32	37	30
25	33	39	38	32	36	33
26	30	29	32	29	36	33
27	34	27	37	33	43	31
28	40	32	34	32	34	23
29	26	41	30	29	27	33
30	35	31	26	29	39	43
31	34	29	32	39	41	38
32	33	37	39	31	29	36
33	35	34	29	36	36	44
34	36	31	35	24	40	27
35	40	33	35	34	30	30
36	24	29	36	30	33	31
37	29	37	31	30	24	27
38	29	37	38	38	39	39
39	26	31	35	33	44	34
40	37	29	40	35	30	38
41	35	32	27	24	21	26
42	32	31	33	27	33	39
43	44	40	31	34	35	31
44	34	43	22	39	34	41
45	35	23	33	40	22	43
46	33	29	28	33	31	33
47	31	32	32	40	41	31
48	33	33	34	38	30	26
49	30	32	35	31	35	30

Integer	Ball 1	Ball 2	Ball 3	Ball 4	Ball 5	Ball 6
1	35	39	24	27	23	36
2	30	37	37	31	37	27
3	36	30	38	26	27	36
4	30	35	30	30	30	35
5	29	22	31	37	33	31
6	24	38	35	35	37	32
7	22	32	34	21	33	40
8	33	32	26	36	26	32
9	31	35	37	30	36	36
10	36	20	38	37	30	33
11	38	33	39	44	29	32
12	35	37	22	34	30	36
13	25	30	34	28	27	25
14	38	33	30	25	29	25
15	24	36	28	30	28	30
16	38	28	28	25	29	27
17	29	26	38	37	29	31
18	27	43	41	21	32	27
19	30	34	33	36	40	21
20	20	21	26	38	21	34
21	34	28	25	38	24	22
22	33	31	23	33	35	33
23	48	31	30	33	39	33
24	31	32	35	32	37	30
25	33	39	38	32	36	33
26	30	29	32	29	36	33
27	34	27	37	33	43	31
28	40	32	34	32	34	23
29	26	41	30	29	27	33
30	35	31	26	29	39	43
31	34	29	32	39	41	38
32	33	37	39	31	29	36
33	35	34	29	36	36	44
34	36	31	35	24	40	27
35	40	33	35	34	30	30
36	24	29	36	30	33	31
37	29	37	31	30	24	27
38	29	37	38	38	39	39
39	26	31	35	33	44	34
40	37	29	40	35	30	38
41	35	32	27	24	21	26
42	32	31	33	27	33	39
43	44	40	31	34	35	31
44	34	43	22	39	34	41
45	35	23	33	40	22	43
46	33	29	28	33	31	33
47	31	32	32	40	41	31
48	33	33	34	38	30	26
49	30	32	35	31	35	30

Integer	Ball 1	Ball 2	Ball 3	Ball 4	Ball 5	Ball 6
1	35	39	24	27	23	36
2	30	37	37	31	37	27
3	36	30	38	26	27	36
4	30	35	30	30	30	35
5	29	22	31	37	33	31
6	24	38	35	35	37	32
7	22	32	34	21	33	40
8	33	32	26	36	26	32
9	31	35	37	30	36	36
10	36	20	38	37	30	33
11	38	33	39	44	29	32
12	35	37	22	34	30	36
13	25	30	34	28	27	25
14	38	33	30	25	29	25
15	24	36	28	30	28	30
16	38	28	28	25	29	27
17	29	26	38	37	29	31
18	27	43	41	21	32	27
19	30	34	33	36	40	21
20	20	21	26	38	21	34
21	34	28	25	38	24	22
22	33	31	23	33	35	33
23	48	31	30	33	39	33
24	31	32	35	32	37	30
25	33	39	38	32	36	33
26	30	29	32	29	36	33
27	34	27	37	33	43	31
28	40	32	34	32	34	23
29	26	41	30	29	27	33
30	35	31	26	29	39	43
31	34	29	32	39	41	38
32	33	37	39	31	29	36
33	35	34	29	36	36	44
34	36	31	35	24	40	27
35	40	33	35	34	30	30
36	24	29	36	30	33	31
37	29	37	31	30	24	27
38	29	37	38	38	39	39
39	26	31	35	33	44	34
40	37	29	40	35	30	38
41	35	32	27	24	21	26
42	32	31	33	27	33	39
43	44	40	31	34	35	31
44	34	43	22	39	34	41
45	35	23	33	40	22	43
46	33	29	28	33	31	33
47	31	32	32	40	41	31
48	33	33	34	38	30	26
49	30	32	35	31	35	30