wheel algorithms?

Reply #42

SergeM — Sat, 23 Mar 2013 22:33:35 GMT

I am having a look at this wheel for keno. So for 5 euro costs I get with 4/9:

Payout P()

2 0,26

4 0,42

5 0,10

6 0,12

7 0,08

9 0,02

I have to play by two tickets, so I must play 6 euro.

The expectation for the payout is 4.16 with 4/9.

For 5/9: E(payout)=14.68

Payout P()

6 0,09

7 0,10

8 0,20

9 0,33

10 0,03

11 0,14

12 0,06

14 0,02

15 0,01

152 0,02

154 0,02

That is guaranteed break e... [ More ]

Reply #41

SkyLine69 — Fri, 22 Mar 2013 05:08:29 GMT

Can you explain ths to me please

Reply #40

SergeM — Fri, 01 Mar 2013 19:30:35 GMT

I am posting a wheel under All Or Nothing, it probably guarantees a hit percentage over twenty. This is one of my own wheels.

=4 and =8, pays for this 12/24 game.

Yesterday's results:

1 2 3 6 7 8 11 12 13 16 17 18 6, 6, 7, 5

1 2 4 6 7 9 11 12 14 16 17 19 5, 8, 9, 5

1 2 5 6 7 10 11 12 15 16 17 20 8, 7, 7, 6

1 3 4 6 8 9 11 13 14 16 18 19 5, 7, 7, 7

1 3 5 6 8 10 11 13 15 16 18 20 8, 6, 5, 8

1 4 5 6 9 10 11 14 15 16 19 20 7, 8, 7, 8

2 3 4 7 8 9 12 13 14 17... [ More ]

Reply #39

BobP — Fri, 01 Mar 2013 19:07:32 GMT

In general I agree. I am always amazed when people talk about testing wheels against a draw or history to see which would be the better wheel for future draws.

However, there are better wheels to use, those with multiple prize tier guarantees or better percentage of coverage for the prize desired. Some wheels just plain blow others away.

Like this one with an 88% (12,6,5,6)=22 where if you have all six winning numbers among the 12 and don't win the 5# prize you are guaranteed to win... [ More ]

Reply #38

SergeM — Fri, 01 Mar 2013 18:24:48 GMT

I wrote my own simple wheels by myself without copying anyone. Picking the right numbers is the key. Who can afford big wheels anyway

Reply #37

lakerben — Fri, 01 Mar 2013 17:23:05 GMT

It was not meant to funny, but some people would take it as such. It is very helpful in the fact that the big games can be won without wheels. Wheels are fine but an element of luck and timing are part of the winning equation. So, endless babbling about balanced wheels, and which wheel is best serves no purpose in the pursuit of winning.

Reply #36

BobP — Fri, 01 Mar 2013 10:07:27 GMT

Pool=v=the total balls we want to wheel

Pick=k=the ticket size (e.g. a 6 ball game has k=6)

Match=t=the prize division we want to guarantee a win

Hit=m=the condition that has to be met, in order to guarantee the t prize division win; m defines the least number of balls from our v set that must be correct.

Tickets=b=the total tickets required to play.

Assumes wheel is 100% less show percent= 66%(49,6,3.6)=46 may be 100% for lower tier prizes.

Match=t on some software can be set

Reply #35

lottoarchitect — Fri, 01 Mar 2013 09:51:09 GMT

How would we compute the theoretical minimum wheel for the t m requirement?

Check my forums at the knowledge base section. I have that equation for the general case posted there. It is the absolute minimum lowest bound however which assumes the wheel is a packed design which means a combination is covered by one and only one block in our wheel.

Reply #34

mathhead — Thu, 28 Feb 2013 23:28:42 GMT

JADELottery wrote: ``5 wheel combos / 126 total possible combos of 9 numbers taken 5 at a time = 5 / 126 .03968254 or 3.968254%.``

Aha! Thanks.

Reply #33

JADELottery — Thu, 28 Feb 2013 22:24:25 GMT

Thanks for adding your expert and practical knowledge to this discussion. Your step-by-step description of the behavior of your algorithm in the aforementioned discussion was very clear and helpful to me. (Thanks to Ramijami for pointing me to it.)

Could you explain the derivation of that percentage figure?

That particular wheel covers 25 of the possible 126 4-tuples, which is about 19.84%.

It also covers 46 of the possible 84 3-tuples, which is about 54.76%.

5 wheel comb... [ More ]

Reply #32

dr san — Thu, 28 Feb 2013 17:55:36 GMT

Hello, mathhead, one could also think of a new model of wheels, ie generate

Wheels with delta values ??at each position, so instead of choosing numbers

At each position delta values ??which can be coordinated vaores of deltas

Value of the horizontal (the same bet delta position by position) and also

Delta vertical line pair another hit = condition has saddled the delta of horizontal and vertical delta (the latter for the penultimate draw) the pivot is the last draw, this type of whee... [ More ]

Reply #31

mathhead — Thu, 28 Feb 2013 17:33:53 GMT

JADELottery wrote: ``The wheel you've generated should have the additional information as follows: [....] 3.968254% Coverage of 126 Combinations``.

Thanks for adding your expert and practical knowledge to this discussion. Your step-by-step description of the behavior of your algorithm in the aforementioned discussion was very clear and helpful to me. (Thanks to Ramijami for pointing me to it.)

Could you explain the derivation of that percentage figure?

That particular wheel covers 25 of... [ More ]

Reply #30

RL-RANDOMLOGIC — Thu, 28 Feb 2013 15:18:55 GMT

MH

Most likely all you will find are general examples used to explain the theory. I am sure most

would not be interested in sharing the actual code. A good wheel has commerical value so it

would not be in the best interest of the programmer to share it. Google lottery wheel theory

and go from there. Testing is fairly easy as you can compare against known wheels to see how

your code stacks up and to test coverage just build a pair, tray, quad, etc... generator and run

the resul... [ More ]

Reply #29

JADELottery — Thu, 28 Feb 2013 15:01:57 GMT

The wheel you've generated should have the additional information as follows:

Wheel

- Pick 5

- 9 Numbers

- 5 Combinations

- 3.968254% Coverage of 126 Combinations

Condition

- If 4 Drawn Numbers are in the Set of 9 Numbers,

- Then at least 1 Combination has 3 Winning Numbers.

____________________________________________

05 06 07 08 09

01 03 04 06 09

02 03 04 08 09

01 02 06 07 08

01 02 03 04 05

____________________________________________

Wh... [ More ]

Reply #28

lottoarchitect — Thu, 28 Feb 2013 13:11:21 GMT

The principle and the maths are straightforward to this. We have a wheel C(v,k,t,m)=b where

v=the total balls we want to wheel

k=the ticket size (e.g. a 6 ball game has k=6)

t=the prize division we want to guarantee a win

m=the condition that has to be met, in order to guarantee the t prize division win; m defines the least number of balls from our v set that must be correct.

b=the total tickets required to play.

We are interested to find the coverage achieved in a certai... [ More ]

Reply #27

mathhead — Thu, 28 Feb 2013 11:49:32 GMT

I wrote earlier: ``I don't exactly gronk the implications of the requirement 3 if 4 ... .``

And I wrote of the JADELottery example: ``That does not cover the 4-tuple 01 02 03 06, for example. And it does not cover the 3-tuple 01 02 09, for example.``

Never mind! I get it now.

If the drawing is 01 02 09 xx yy, xx or yy (or both) must be one of 03 through 08 in order to meet the match-4 condition.

So it is sufficient that 01 02 03, 01 02 04, 01 02 05, 01 02 06, 01 02 07 and 01 02 08 ar... [ More ]

Reply #26

mathhead — Thu, 28 Feb 2013 08:07:36 GMT

That's an ironic comment, considering the systems that you suggest in other discussions (e.g, click here).

Humor aside, I want to reiterate that I am not interested in using wheels. I am interested in understanding the algorithms for generating wheels. It is an academic exercise for my own edification.

So comments like yours are neither helpful nor wanted in this discussion. In fact, they are never constructive, IMHO.

Reply #25

lakerben — Thu, 28 Feb 2013 05:22:42 GMT

Put all your numbers on a piece of paper. Next, sprinkle some chicken feed on top of the paper. Turn the chicken loose and wait while the paper is being poked. Take the 5 or six biggest holes and use the numbers adjacent to them. Alas , you have your wheel. Don't laugh it worked for a farmer in Texas, he won big.

Reply #24

mathhead — Thu, 28 Feb 2013 04:54:50 GMT

I wrote: ``Unfortunately, the JADELottery explanation is not sufficient because the resulting 5-ticket wheel does not cover all 3-tuples or all 4-tuples. So it does not seem to guarantee a 3-win at all, as I (mis?)understand the wheel requirements.``

I meant to add the following footnote; just missed the 20-minute edit window.

JADELottery wrote that the 5-wheel solution is:

05 06 07 08 09

01 03 04 06 09

02 03 04 08 09

01 02 06 07 08

01 02 03 04 05

That does not cover the

Reply #23

mathhead — Thu, 28 Feb 2013 04:20:39 GMT

lottoarchitect wrote: By the way, 4if4of8 means nothing, you need 4 parameters to define a wheel.

Which is why I wrote: a 7-ticket wheel for 4-if-4-of-8 for a 6-draw lottery .

The 4-if-4-of-8 notation is derived from the terminology described in this forum under the title What's a Lottery Wheel at the Lottery Wheel link. So I thought it might be better understood than the algebraic notation (8,6,4,4)=7.

lottoarchitect wrote: Given a covering v,k,t,m=b, [.... for] your 4if8, given... [ More ]

Reply #22

dr san — Sat, 23 Feb 2013 02:30:25 GMT

1 pos 2 pos 3 pos 4 pos 5 pos 6 pos 7 pos lines X X X O O O O

1 pos 1 2 3 4 5 6 7 X X O X O O O

2 pos 8 9 10 11 12 13 14 X X O O X O O

3 pos 15 16 17 18 19 20 21 X X O O O X O

4 pos 22 23 24 25 26 27 28 X X O O O O X

5 pos 29 30 31 32 33 34 35 X O X X O O O

6 pos 36 37 38 39 40 41 42 X O X O X O O

7 pos 43 44 45 46 47 48 49 X O X O O X O

colun X O X O O O X

0 0 0 0 x x x X O O X X O O

line1 4 5 6 7 colun 1 1 8 9 X O O X O X O

X O O X O O X

Reply #21

dr san — Sat, 23 Feb 2013 00:19:18 GMT

Hello, lottoboner, the lines are ready for 7 digits

So, xxx of the row with the column 1 = 0000 mirror xxx0000

1 line long column two .....

Vice versa online with 0000 xxx column 1 = mirror 0000xxx

And so with each column crossing the segments with the lines,

After and see in matrix 7 x 7 numbers and change, is this

example 1, 2, 7 or this on xxx or this in the mirror 0000

Reply #20

LottoBoner — Fri, 22 Feb 2013 22:38:02 GMT

I want to play tic tac toe too!!!!

XOXOXOXOXOXOXO

OXOXOXOXOXOXOX

XOXOXOXOXOXOXO

Reply #19

dr san — Fri, 22 Feb 2013 21:41:26 GMT

Hello, sergem training has to be 7 digits and have to take care to give positions hit.

Example of segment xxx took the 3rd position in the column segment 0000 cannot repeat the positions, is not so easy to match by position, to give hit within the 7 x 7 array cannot be linear combinations, must be positional, won't be easy

on your list has a lot of repeated formations, tends to take advantage of the positional distrbuidoem coodenadas factor in matrix 7 x 7

Reply #18

dr san — Fri, 22 Feb 2013 19:56:15 GMT

Hello sergem has much repeated positional training

Has to do

row and column xxx 0000

Or xxxxlinha and 000coluna

The lines have become so

0000xxx = column and row

Xxxx000 = row and column

The training must be of 7 positional numbers without repetition in the array

Reply #17

dr san — Fri, 22 Feb 2013 19:43:49 GMT

Ok sergem, but is a combination of a line segment with column, because we're playing

With all the numbers of the 49/6, i.e. combining per array, with line segment with columns, what will depend on and how do we assemble the rows and columns, because it covers the numbers 49 49/6, can you explain your list

Reply #16

dr san — Fri, 22 Feb 2013 19:13:24 GMT

Hello then sergem crossing segments of rows and columns and mirror

We Have =

(0000) lines 35 times 35 columns (xxx) = 1225

(xxx) lines 35 times 35 columns (0000) = 1225

Total = 2,450 filtering can reduce lines at 80% of this

Reply #15

dr san — Fri, 22 Feb 2013 18:56:36 GMT

Ok, sergem, fanstastico, the rows and columns can monter in 4 pairs and three odd and vice versa too, so as the perfect matrix sergem this ai, everything depends on distributing in the rows and columns of the array, the array is 100% IE hitting within the thread, small temospr mios almost all sweepstakes, few cards

Thanks sergem

Reply #14

SergeM — Fri, 22 Feb 2013 18:47:45 GMT

X X X O O O O

X X O X O O O

X X O O X O O

X X O O O X O

X X O O O O X

X O X X O O O

X O X O X O O

X O X O O X O

X O X O O O X

X O O X X O O

X O O X O X O

X O O X O O X

X O O O X X O

X O O O X O X

X O O O O X X

O X X X O O O

O X X O X O O

O X X O O X O

O X X O O O X

O X O X X O O

O X O X O X O

O X O X O O X

O X O O X X O

O X O O X O X

O X O O O X X

O O X X X O O

O O X

Reply #13

dr san — Fri, 22 Feb 2013 12:53:28 GMT

Hello, let's try to innovate, wheels to catch small awards through an array with mirrors example of an array 49/6

Matrix 7 x 7 =

Then, the example below also do vertically,

0000xxx

0

0

X

X

X

0

Goal, and see small segentos in 7 rows and 7 columns with 3 and 4 segments with mirror,

Note has cross threads with 0000 xxx column line, catching so accumulated hits segments, and aainda see the positions, but in order to fit this need help from more advanced members of th... [ More ]

Reply #12

helpmewin — Fri, 22 Feb 2013 12:19:43 GMT

Reply #11

LottoBoner — Fri, 22 Feb 2013 09:23:20 GMT

An Abbreviated Lottery Wheel generates a combination that is much less in number

than that generated by full wheels to guarantee wins other than the jackpot. The

design of an abbreviated wheel itself is not a simple matter; there is no

formula for it and is mostly a result of iterations and trials and errors. In

fact, in mathematics, it is called Covering Design and belongs to a

branch of mathematics called Combinatorics.

Reply #10

SergeM — Wed, 20 Feb 2013 12:21:07 GMT

1 2 3 4 5

1 2 3 4 6

1 2 3 4 7

1 2 3 4 8

1 2 3 5 6

1 2 3 5 7

1 2 3 5 8

1 2 3 6 7

1 2 3 6 8

1 2 3 7 8

In Belgium you get forms for this, upper box for key numbers and lower box for wheel numbers in all combinations. Full wheels also are offered, just put more crosses in one box. For a 10 number wheel, you just cross ten numbers on the form, for 10 euros, I believe. All you have to do is picking the right numbers.

Reply #9

SergeM — Wed, 20 Feb 2013 12:17:12 GMT

Great program

Reply #8

Ramijami — Wed, 20 Feb 2013 10:16:31 GMT

This might be a useful place to start:

www.lotterypost.com/thread/228056/1968766

Reply #7

LottoBoner — Wed, 20 Feb 2013 09:58:57 GMT

Dont get crazy trying to develop wheels, unless you plan to sell them. But you will have LOTS of competition.

I would focus on learning on how to pick the correct numbers!!!!

Three power number wheels are generally the best in IMHO. But make sure you get them right

Reply #6

BobP — Wed, 20 Feb 2013 08:14:40 GMT

Balanced is taken to mean each number on the wheel appears the same number of times. It is not always possible for a wheel to be perfectly balanced and optimal / tightest at the same time.

If you mean (8,6,4,4)=7 CoverMaster made this in about one second.

1 2 3 4 5 6

1 2 3 5 6 7

1 2 3 5 6 8

1 2 4 6 7 8

1 3 4 5 7 8

2 3 4 6 7 8

2 4 5 6 7 8

100% (8,6,4,4)=7 not balanced

BobP

Reply #5

manual — Wed, 20 Feb 2013 04:03:50 GMT

I've created a system myself and have been struggling with how to best wheel the result. My main fault seems to be that I'm going for the gold, a straight. I could position the numbers I play and play them boxed but... hopefully that's not me just being greedy.

As for wheels themselves, I think that depends greatly on what system is being used, how the numbers are generated, etc. I would think (with my limited experience) that trying to create a blanket wheel that covered all circumstances wo... [ More ]

Reply #4

lottoarchitect — Wed, 20 Feb 2013 00:51:21 GMT

The only known to me available source for wheeling code is the old Cover32 program (not sure if it is still somewhere available). What source code do you refer to, because such things are really hard to find mostly because abbreviated wheel development is based on unique heuristics and nobody really wants to share his own work (I also have developed mine from scratch because I really couldn't find any source to work on - the same problem you face).

Also Iliya Bluskov's books do not contain an... [ More ]

Reply #3

SergeM — Wed, 20 Feb 2013 00:00:47 GMT

1 2 3 4

1 2 3 5

1 2 3 6

1 2 3 7

1 2 3 8

1 2 4 5

1 2 4 6

1 2 4 7

1 2 4 8

1 2 5 6

1 2 5 7

1 2 5 8

1 2 6 7

1 2 6 8

1 2 7 8

1 3 4 5

1 3 4 6

1 3 4 7

1 3 4 8

1 3 5 6

1 3 5 7

1 3 5 8

1 3 6 7

1 3 6 8

1 3 7 8

1 4 5 6

1 4 5 7

1 4 5 8

1 4 6 7

1 4 6 8

1 4 7 8

1 5 6 7

1 5 6 8

1 5 7 8

1 6 7 8

2 3 4 5

2 3 4 6

2 3 4 7

2 3 4

Reply #2

Ronnie316 — Tue, 19 Feb 2013 23:51:37 GMT

I believe the wheels on LP are for the use of premium members. I wish you the best on your project and hope you come up with some winning numbers that you can share with the rest of us. Welcome to LP.

Wheel: Pick 5 Abbreviated 4 if 4 of 8

Tickets: 20

Description: Minimum 4-number match, if 4 numbers drawn fall within your set of 8 numbers.

Input: 1, 2, 3, 4, 5, 6, 7, 8

1. 01-02-03-04-07

2. 01-02-03-04-08

3. 01-02-03-05-06

4. 01-02-04-05-07

5. 01-02-04-05-08

6. 01

Reply #1

SergeM — Tue, 19 Feb 2013 23:43:59 GMT

Could you post the C++ code

wheel algorithms?

mathhead — Tue, 19 Feb 2013 20:14:20 GMT

I am interested in learning about lottery wheel algorithms, specifically for abbreviated wheels.

And I am interested in techniques for proving that the resulting wheel is mathematically minimal (and balanced ?)

(What makes a wheel well-balanced ? Is it just some subjective concept of the variety or scope of numbers; for example, 1 2 3 4 5 might be poorly balanced , whereas 1 12 23 34 45 might be considered well-balanced ? Or is there a more-rigorous definition of balanced ?)

Please note... [ More ]