Hi Colin,

I hope your well and congratulations on a great site.

Would it be possible for you to post the 289 lines used for your record on this forum, or send them to my email address.

I would love to backtest this set against previous Australian Lottery draws.

It's a pity this site is not more active as you have alot to offer on this site.

Best Regards

Millsy

Hi Millsy

Thanks for the comments.

This is a record which mainly is of interest to those who program in the area of Coverage. **The analysis data provided where the set of numbers is tested against all possibilities is what people who are expert in this area are looking for.** You don't see much response because most with the expertise have been in the past, if not now, involved in the creation of deliberately distorted Covers which may have a valid use outside the Lotto field, where the size of something to do something is more important than how wasteful it is. In a way I'm poking fun at them because they have been so stupid conceptually, even if clever in achieving their lower bounds in applying those distorted Covers to the Lotto field, where percentage return in the short term is the most important consideration. (First prize maximization is easily achieved by simply keeping all your lines different.) Generally, I think most of them have moved on after noting they didn't get that one right but there are still plenty of recalcitrants around who just hope I'll fade away. People that have been involved in something since the '80s are loathe to admit that they got it all wrong and that they wasted a huge chunk of their life.

Let's not forget the simple probability premise that it is all based on. If you have 10 identical balls in a box, 8 of which are red and 2 blue then after jumbling **all** the balls and picking one sight unseen, then 80% of the time you will get a red. That you got 10 reds consecutively does not make a blue more likely to come up in your next pick a very hard fact for Lotto history buffs to swallow.

I have had my own VBA program since 2000 where I can run the full set or part of it over how many draws I want and get back performance data whether it be history or from my own RNG. It has a whole bunch of tricks including playing the same numbers or randomizing from a template. I authorize no one else to test my sets against history as it is too easy to pick the worst performing sets albeit it more difficult with my Unique 3's™ as an integral part of their design is their consistency and they perform very well as the analysis data indicates they should. In other words it is possible to produce sets with 1st or 2nd or 3rd prizes from the histories. Notice the "or" because with my sets no repeat Threes means there are no repeat Fours, Fives and Sixes. Sets with repeats can be manipulated to give multiple high prizes. Basically what I'm saying is the tests I do are honest but I can't vouch for those done elsewhere.

I'm not advocating that someone should spend $179.00 per draw playing the full 289 line set although I am aware of people that vainly and unfortunately spend $1,000 to $4,000 per month on Lotto. They mainly do system plays, the 2nd worst way of playing Lotto and because so and so got first prize playing say a System 12 they won't have a bar of anyone doubting its merits. My sets in the main are directed to people like myself who spend $11.00 per week or those that fork out 2 or 3 times that. However, I am open to approaches from bona fide syndicate organizers wanting to play the full set.

If you know how to test then you should have no problem in constructing a set of 50 to use as a template for randomizing (the first 7 lines can be done by just keeping all the digits different) - failing that then I'm always glad to receive your $5.00 for a 12 month subscription to LottoToWin.

If you have programming skills you can have a go at posting a record.

Regards

Colin Fairbrother

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Hi Colin,

I hope your well and congratulations on a great site.

Would it be possible for you to post the 289 lines used for your record on this forum, or send them to my email address.

I would love to backtest this set against previous Australian Lottery draws.

It's a pity this site is not more active as you have alot to offer on this site.

Best Regards

Millsy

]]>
Pick 6 from Pool 45 Lotto games are played in Australia and Singapore where the former pays with two bonus integers and the latter with one. You can obtain a set of numbers to play using this structured template from a random order of the 45 integers from LottoToWin for only a $5.00 annual subscription.

The odds for getting a Three win with a Bonus integer can be calculated from 1 in 45c6 / 6c3 x (39c3 - 37c3) which is 1 in 8145060 / 20 x 1369 or 1 in 297. The table below shows the 3 prizes which you need to get before getting the paying prize which must have the bonus ball. The odds for getting a Three only **which is not paid on** is roughly 1 in 45. To put that in perspective a good set of 22 structured numbers should average out to giving you a Three for every second draw played and the same set should give you a 3 + Bonus about every 14 or 15 draws. If you're not getting this then the explanation is that you are using stupid System plays such as System 8 which instead of using the 45 integers only uses 8 and is the second worse way to play! See my Comparison of 15 Lotto Structured Number Sets.

Essentially this is a partial 3if3 Cover which from 1 to 289 combs is as good as any other, each comb contributing a coverage of 20 from the 14,190 possible Threes. A 289 line 3if3 set with any distinct Threes is going to give a close to 99.9% 3if6 coverage. **However, if the Threes are chosen on the basis of maximizing progressively the coverage of the Sixes a proportionality is maintained especially up to around the 90% mark or 60 combs from where they taper off to about the 132 mark or 99% and from thereon it is practically a straight line.** By contrast a 3if3 without maximization of the Sixes at 60 Combs may only give about a 64% coverage a difference of around 26%.

A distorted 3if6 Cover with repeat Threes can be done in 131 combs. The methodology in constructing this way is to force low yielding combinations into the set at the expense of higher yielding ones. For 131 Combs played one should expect per probability calculation close to 3 prize Three wins per draw. The grouping of the possible winning combinations for the set played should reflect this by not having the group which delivers 1 Three win as dominant as is the case with the distorted Cover but the group that delivers 3 wins as is the case with my set. Even after sorting the 131 comb set by highest dependency the top 45 combs only give a coverage of 49% compared to my set with 57% and similarly only 37% for the top 22 compared to mine at 46%. In fact for the groups delivering greater than 1 win my set is ahead at every stage. Obviously, the obsession with guaranteeing a Three win every draw is pure folly and to advocate it as delivering better on average than Random Selections or my Unique 3's set with optimized coverage is no less than fraudulent.

Regards

Colin Fairbrother

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**Unique Threes 293 Line Progressive Cover, Matrix or Design 6/45 Lotto with minimum Three prize guarantee per draw but usually much, much more.**by Colin Fairbrother

Of the 8,145,060 Combinations of Six only 551 give just a single Three win ie 99.99% give more than a Three win.

The dominant group at 33.16% is 1 Four with between 0 and 13 Threes which is as it should be as your chances of getting a Four are 1 in 183 and we are calculating on 293 plays.

The chances of getting a Three are given by: -

1 in 45c6/(6c3 x 39c3) or 8145060/(20 x 9139) or 44.56.

So, for 293 combinations played we should be getting on average 6.58 Three wins. Looking at the chart we see that 14.53% of the possible draws form the dominant Three group give 7 Three wins as it should be. (None of this nonsense of distorting the set to get more lousy single Three wins as in "normal" covers; you want to play 18 lines then the first 18 give the best coverage and consequently best yield.)

1 in 45c6/(6c3 x 39c3) or 8145060/(20 x 9139) or 44.56.

So, for 293 combinations played we should be getting on average 6.58 Three wins. Looking at the chart we see that 14.53% of the possible draws form the dominant Three group give 7 Three wins as it should be. (None of this nonsense of distorting the set to get more lousy single Three wins as in "normal" covers; you want to play 18 lines then the first 18 give the best coverage and consequently best yield.)

Regards

Colin Fairbrother

Colin Fairbrother

6/49 Lotto with minimum prize guarantee

but usually much, much more.

by Colin Fairbrother

Qty of

Comb6

6 Prize 5 Prize 4 Prize 3 Prize To Pay Total% Accum %

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

- - - 1 446 0.00319 0.00319

- - - 2 7541 0.05393 0.05712

- - - 3 48793 0.34892 0.40604

- - - 4 181267 1.29626 1.70230

- - - 5 458528 3.27899 4.98129

- - - 6 868738 6.21245 11.19375

- - - 7 1290840 9.23096 20.42470

- - - 8 1488470 10.64423 31.06894

- - - 9 1359799 9.72409 40.79303

- - - 10 1046097 7.48077 48.27380

- - - 11 706894 5.05509 53.32888

- - - 12 449688 3.21577 56.54466

- - - 13 268036 1.91676 58.46142

- - - 14 134717 0.96338 59.42480

- - - 15 48393 0.34606 59.77086

- - - 16 17591 0.12580 59.89665

- - - 17 5343 0.03821 59.93486

- - - 18 1822 0.01303 59.94789

- - - 19 1208 0.00864 59.95653

- - - 20 5765 0.04123 59.99776

- - 1 0-16 4883034 34.91918 94.91694

- - 2 0-12 570552 4.08009 98.99703

- - 3 0-8 23704 0.16951 99.16654

- 1 0 0-10 116100 0.83025 99.99678

1 0 0 0__ 450__ 0.00322 100.00000

13,983,816

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

- - - 1 446 0.00319 0.00319

- - - 2 7541 0.05393 0.05712

- - - 3 48793 0.34892 0.40604

- - - 4 181267 1.29626 1.70230

- - - 5 458528 3.27899 4.98129

- - - 6 868738 6.21245 11.19375

- - - 7 1290840 9.23096 20.42470

- - - 8 1488470 10.64423 31.06894

- - - 9 1359799 9.72409 40.79303

- - - 10 1046097 7.48077 48.27380

- - - 11 706894 5.05509 53.32888

- - - 12 449688 3.21577 56.54466

- - - 13 268036 1.91676 58.46142

- - - 14 134717 0.96338 59.42480

- - - 15 48393 0.34606 59.77086

- - - 16 17591 0.12580 59.89665

- - - 17 5343 0.03821 59.93486

- - - 18 1822 0.01303 59.94789

- - - 19 1208 0.00864 59.95653

- - - 20 5765 0.04123 59.99776

- - 1 0-16 4883034 34.91918 94.91694

- - 2 0-12 570552 4.08009 98.99703

- - 3 0-8 23704 0.16951 99.16654

- 1 0 0-10 116100 0.83025 99.99678

1 0 0 0

13,983,816

This CoverMaster report should be looked at with due awareness that there is only **one **winning Combination which can pay out on more than one of the 450 lines. The minimum payout for 446, a very small percentage of the 13,983,816 possible Combinations is just 1 three. If you look you will see that some 1,488,470 or 10% pay 8 threes. Also some 4,883,034 or 35% pay a Four with a varying amount of 0 to 16 threes.

For the Cover people they just have to face the fact that this Cover, Matrix or design has the same features as their beloved C(22,6,3,3)=77 ie it is a set with the highest possible compacting of distinct threes. Worth noting is that distinctness percolates up so 9,000 distinct threes ensure that we have 6,750 distinct fours and 2,700 distinct fives.

For those that like to exercise the noddle you may care to ponder on why 450 of the 13,983,816 Combinations of 6 from a pool of 49 only give a possible Six win and nothing else? Don't post it as you'll spoil the thinking process for someone else! (Clue: Look closely at the previous paragraph.)

This** Lotto Structured Number Set**™ is an extensionof my Unique Threes Matrix although, obviously, arrived at programatically.

Ce´ la Vie!

Regards

Colin Fairbrother

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Colin Fairbrother