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PerfectLotto™
 LottoPoster Forums : LOTTO THEORY, CONCEPTS AND METHODS OF PLAY : PerfectLotto™
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Colin F
Lotto Systems Tester Creator & Analyst
Lotto Systems Tester Creator & Analyst
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To dream the impossible dream ...

Joined: September 30 2004
Location: Australia
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Posts: 678
Quote Colin F Replybullet Topic: PerfectLotto™ Introduction
    Posted: July 24 2007 at 11:53pm
 
PerfectLottoTM
by Colin Fairbrother
 
Back in 2001 in my early days of Lotto number analysis I asked myself, "Self, what do Lotto History Buffs really want?"
 
Self, after a bit of muttering and the necessary process of allowing my subconscious to mull over this in my sleep came up with what he calls PerfectLottoTM (people who do creative programming are want to leap out of bed at 3.00 am in the morning and rush to record an idea or solution before they lose it - the absolute fanatics can't go back to bed and have to crank up the computer to try it out straight away!).
 
So, here's how it works. For 49 draws a random selection is made from an initial pool of 49 integers but once an integer has appeared 6 times it is eliminated from the pool for the next draw. Obviously, if you have the preceding 48 draws then the 49th draw is 100% predictable but what about the 48th draw when you know the preceding 47 draws? Well, as you probably worked out there is a maximum of 12 integers from which the next draw can be formed each with an occurence of 5, which means there are up to 924 possible sixes.
 
So, even though you know the history and it is relevant for PerfectLottotm you are still looking at odds in picking the next six after 47 draws close to that of picking a straight in Pick (Cash) 3! Further, the odds do not possibly drop until the 7th draw and in this example remain the same of 1 in 13,983,816 right up to the 25th draw when the identifier 6 is eliminated and it drops to 1 in 12,271,512. So much for the swindlers, charlatans and con artists that say the can work it out from the previous 3 draws. Ah, the sweetness of logic, 'tis a blessing and source of much pleasure to the literate and a spoiler to the scammers.
 
There is however the highly unlikely but possible scenario that after the 47th draw only 6 integers remain that have not appeared 6 times ie an occurence of 4 -  in which case the last 2 draws would be identical and certain. In a real world application a stop on the draws would occur when the payouts exceeded the odds - to be profitable to the operator there always has to be a house margin and a good measure of uncertainty.
 
Here is an example with the 12 integers that have not appeared 6 times. The odds for 1 line played are 1 in 924 for a six, 1 in 132 for a five, 1 in 33 for a four, 1 in a 11 for a three, 1 in 6 for a two and 6 in 12 or 1 in 2 or 50/50 for one integer. Let's initially make the payouts 900 to 1 for a six, 128 to 1 for a 5, 32 to 1 for a 4 and 10 to 1 for a three. (Ah, a house margin of 2.6% - we wish!).
 
Contrast the odds and payouts of PerfectLottoTM as outlined above with those in a normal 6/49 Lotto game. For a Three win with odds of 1 in 57 the payout is around 4 to 1. In other words for an average $57.00 spent you get $4.00 back or 7%. A Four win pays about 80 to 1 so for an average $1032 spent you get $80.00 back or 7.75%. Generally then for your Three and Four wins for an average $1,089 spent you get $84.00 back or 14.75%. If you are lucky enough to get a Five win which is 1 in 54,200 then your payout is only 3,000 to 1 ie 5.53% return. So, for 54 years you spend a little over a $1,000 per year and with luck on your side you get less than a ¼ or $11,004 back ie 20.3%. Now you know why Lottery Operators obfusticate the returns by only quoting odds on multi-plays!
 
With payments of only 4 to 1 for a Three Win in a real 6/49 Lotto game you would need to eliminate 34 integers to produce a 4 line Cover from the remaining 15 integers and that is just to break even. In other words for the example given see if you can predict profitably the 47th draw knowing the previous 46 draws - with up to 18 integers a Cover of 7 lines costing say, $7.00 is only going to pay $4.00 - still not enough to be profitable. But, as you well know all the integers are used each draw and that makes it impossible. I never cease to be amazed by the ignorance of those that espouse real bouncing balls where they see the full number of balls and then they turn around and ignore that fact when doing their history calculations.
 
Can you predict or make a profit on the 48th draw being limited to one line? How would you organize it?
Hints: Any operator offering the payouts above would go broke. Click Me! Click Me!
 
ID
Sel1
Sel2
Sel3
Sel4
Sel5
Sel6
1
7
11
20
29
38
48
2
2
22
25
26
35
36
3
1
7
11
18
23
38
4
8
16
22
29
32
43
5
4
13
15
16
29
39
6
20
21
31
35
38
49
7
12
15
21
25
41
42
8
4
5
8
9
19
22
9
3
6
10
14
17
24
10
7
14
17
26
32
48
11
6
12
21
26
27
33
12
8
11
13
17
24
48
13
28
30
34
37
40
44
14
5
18
41
45
46
49
15
4
6
16
33
35
44
16
1
10
25
26
30
40
17
2
3
9
19
23
27
18
9
12
36
40
45
47
19
6
17
19
22
33
40
20
5
9
18
24
32
37
21
28
31
34
39
42
43
22
5
10
34
35
44
47
23
6
7
19
35
46
48
24
6
9
17
22
37
47
25
1
2
3
13
14
15
26
5
7
13
23
24
45
27
12
13
26
35
41
44
28
3
5
32
33
43
46
29
20
27
28
30
31
36
30
13
17
21
28
47
48
31
12
19
22
23
27
44
32
7
27
28
29
32
39
33
1
2
4
8
10
11
34
16
20
42
45
47
49
35
10
12
14
26
41
43
36
4
9
18
37
41
47
37
15
25
30
31
34
36
38
8
23
25
33
34
48
39
16
18
28
32
40
49
40
18
25
27
37
40
49
41
1
2
3
11
14
15
42
1
8
31
36
41
42
43
10
11
19
21
44
49
44
20
24
29
30
38
39
45
4
14
16
24
38
39
46
31
38
42
43
45
46
47
2
3
21
29
45
46

 

Identifier
Cnt
46
5
43
5
42
5
39
5
37
5
36
5
34
5
33
5
30
5
23
5
20
5
15
5

 
 
 ..............................................
 
 
For a Pool of 12 integers the Three prize paying 10 to 1 would be profitable to the player with a Cover of 2 lines. If participation is limited to one line then a simple sharing process with another player is necessary. Needless to say no Lottery Operator is going to offer such payouts for the odds given.
 
At a Pool of 18 integers it would still be unprofitable to the operator as a Cover of 7 lines would guarantee a Three win - spend $7.00 and get $10.00 back.
 
At a Pool of 24 Integers with odds of 1 in 134,596 for a Six prize and 1 in 8 for a Three, playing random numbers you would in the long term be in front with the Three Prize wins - a Cover of 20 lines only guarantees 50% but good old Mr Random makes sure the balance is delivered. Once again no Lottery Operator would offer such payouts for the odds given.
 
So, for payouts of 10 to 1 for a Three Prize win the Lottery Operator would need a Pool of 30 or more integers. With the constraint of eliminating an integer after it has occurred 6 times your odds for 1st prize with a Pool of 30 integers are 1 in 2,035,800. For the example given above the Pool of integers is not reduced to less than 30 until the 43rd draw! For a Three prize you are looking at odds of around 1 in 15 - about 75% back or less than slot machines.
 
Integers with Occurrence less than 6 after the 42nd Draw.

 
Identifier
Cnt
11
5
23
5
1
5
16
5
49
5
15
5
33
5
34
5
19
5
37
5
10
5
41
5
8
5
4
5
44
5
3
5
2
5
14
5
30
4
20
4
21
4
29
4
31
4
36
4
43
4
45
4
24
4
38
3
39
3
42
3
46
3
 
So, we have 18 integers that have appeared 5 times! Hot! Hot! Hot! you reckon? Well, once again for a Pool of 18 integers you can do a Cover of 7 lines which will make sure you get a Three prize if the Three is in the 18,564 Sixes that can be formed from the 18 integers with occurrence 5. Good for the player - no good for a Lottery Operator that dared to offer this type of Lotto game - so it wouldn't be offered. 
 
Do you think a Lottery Operator would offer you the opportunity to predict the 42nd Draw to get at least a Three win? If so show from the already known results how you would work it out.Hug
 
35 Integers with Occurrence less than 6 after 41 Draws
 
Identifier
Cnt
27
5
4
5
8
5
10
5
16
5
18
5
19
5
23
5
25
5
33
5
34
5
41
5
44
5
40
5
2
4
3
4
45
4
11
4
14
4
15
4
43
4
29
4
20
4
36
4
21
4
24
4
1
4
49
4
30
4
31
4
37
4
39
3
46
3
38
3
42
3
 
The PerfectLottoTM model created here illustrates that even if for very peculiar reasons someone thought that they could eliminate certain integer identifiers on the basis of occurrence or absence for a normal Lotto draw despite the Pool of integers not reducing for those draws they gain nothing much for some 30 draws? But in the world of Lotto wierdos there are those who believe the tarnish or wear on the balls is critical to their success. (The rationale for the assumption that it always works against them has always eluded me.)
 
From this it should be obvious that the payouts are determined by the odds - that is how Lottery Operators work it out taking into account Covers or Guaranteed Wheels etc- that is how you determine whether it is attractive to play. A safe corollary from this is: -
The Prize Payout for a Cover or Guaranteed Wheel is
only profitable to the Player
when the
odds are unattractive to the Lottery Operator.
 
A question I ask myself is, "Is there any skill involved here?" The answer is YES for PerfectLottoTM because history is relevant and the objective is to choose some numbers that give you the best chance of winning a prize! For ordinary Lotto - history is irrelevant - the full pool of integers is available each draw - which means it's all in the luck of the draw. Profitability to a Lottery Operator lies in the randomness of the draw, payouts commensurate with the odds and enough participation to make sure the odds work.
 
Regards
Colin
Lotto Draws have no relationship to one another; the integers serve just as identifiers. Any prediction calculation on one history of draws for a same type game is just as irrelevant as another.
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