Wheels And Odds, Wheel 2 if 6 with 45 balls

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draughtsman
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Wheels And Odds, Wheel 2 if 6 with 45 balls

Post by draughtsman » Sun Jan 27, 2008 7:44 am

TRANSFERED FROM OLD FORUM

Hi LA,

With the wheel match 2 if 6 with 45 balls in 15 combinations you will always
have 1 or more combinations with 2 right or higher.

I was wondering if the chance to have the other 4 numbers right, will the chance still be of 1 in 733 for a 6/45 game if you already have 2 numbers right (2+4=6 right)?

If this is truth you can fill the wheel with the 45 numbers in randomly order at least 733 times and you will have generated 10995 unique combinations. Theoretically there will be the winning (6 right) combination in the 10995 combinations..... The next job will be filtering the combinations and you'll have the Jackpot in 50 or so combinations?..

La, is this a right assumption???


(I checked this Wheel (15 combinations) for 500 drawings and there where to 2 matches of 5 right..)

Cheers,

Harmen

This is an interesting thought Harmen but many people make logical errors about what wheels can do in terms of jackpot and their guarantee under certain conditions. I'll try to explain some things here.

The 6/45 game has a total of C(45,6)=8145060 possible tickets (ouch!)

The C(45,6,2,6)=15 wheel in a 6/45 game indeed will have at least one ticket with 2 winning numbers or more, no matter which of the above 8145060 tickets will be drawn. Now, what matters here is that we play 15 tickets in total. The important thing to know about wheels is that every ticket in a wheel looks like a "random" ticket on its own, but when they are played together, they produce the desired guarantee which is the main reason of using a wheel. In the above wheel, not every 2 possible pairs (or a x=guarantee size combination in general) of numbers have to appear to ensure this guarantee. This is the case most of the time in abbreviated wheels. In full wheels, all pairs will appear.

Besides that, lets assume that the next draw brings a winning ticket.
We have played the above wheel with all possible numbers included, thus we are guaranteed to have a ticket in there that will produce at least a 2 numbers hit. As only one possible combination of the above 8145060 possible can match the winning ticket, you realize that your chance to hit the jackpot is exactly 1/8145060 =...0%! Because you have 15 tickets played, your chance to hit the jackpot raises to 15(tickets)/8145060=...0! Playing according to your calculations, your chances to hit the jackpot are equal to total played tickets/8145060. So, if you end with 10995 unique combinations, your chance is 10995/8145060 to hit the jackpot. It doesn’t matter if you play a wheel or a combination of wheels; the result is exactly the same.
Your chances do not increase if the winning ticket has all the numbers in your selection, but you can be certain that you'll not hit the jackpot if at least one number is not in your selection! In short, your chances do not improve neither go worse, in terms of jackpot, no matter if we use a wheel or play random tickets. This is a common mistake many people do not realize.
Your advantage of using wheels is the guarantee offered, even if you do not hit the jackpot. Your disadvantage of using wheels instead of playing random tickets, is that the wheel restricts the tickets you have to play (otherwise you ruin the guarantee!). If we are certain we can match the required match condition in a certain pool of numbers, go for a wheel. If not, we play random tickets! It is as simple as that really.

Your calculations are not correct because they assume
1) all 2 pairs will appear in a combination of the wheel, which is not true
2) for each of the above pairs, all other possible 4 numbers will be covered which is also not true

I understand intuitively how you conclude your assumption but this is a logical error unfortunately. The only way you can achieve the above two assumptions according to your example is by the use of a 2 Key wheel + a 4 size full wheel with the remaining numbers
2 Key + C(45-2,4,4,4) and remove duplicates (overlap)
All possible 2 Key wheels (or pairs more accurately) are C(45,2)=990
So, you have to generate 990 different 2 Key wheels, each one by attaching the 4 numbers size full wheel (around 123000 tickets). If you remove the overlaps that will occur, you'll end up with exactly... 8145060 tickets!
The above is not applicable to the C(45,6,2,6) wheel (we wish it could but maths are maths!)

cheers

Hi LA,

I ask same question but with wheel 6,45,2,2=72 tickets

In this case I only need 4 numbers to match jackpot, and the odds are 1 in 123410.

Could this wheel reduce odds or is other illusion as Harmen wheel? I ask this question because Stefan Valdeverde (Lotto Trix) thinks this type of wheel (2 if 2) improve odds.

Regards

Hi Hyperdimensional,

the case is exactly the same: we have an abbreviated wheel and all such wheels offer a chance proportional to their tickets size. They cannot improve the odds for a jackpot. If they do, we violate probability laws really.
As we move down the winning divisions, a balanced structured wheel does provide a better spread across the winning spectrum. An unbalanced one, provides more hits in certain conditions and fewer hits in other conditions, even if in both cases we match the same numbers.
What someone can claim is a phenomenal increase of odds to hit the jackpot. For example, no one wants to play the ticket 1 2 3 4 5 6 because simply never experienced (to my best knowledge) in any lotto game around. For the same reason, we do not want such tickets to appear in our wheels. Avoiding such tickets, we don't increase our odds actually, but at least we do not play tickets that we feel they will never come out, what I call "doesn't look like a winning ticket". Of course, there is no proof somewhere that says 1 2 3 4 5 6 has fewer chances to occur than any other ticket and there will never be one. Only statistical observation exists of history draws that reveal the "behaviour" of lotteries and suggest that 1 2 3 4 5 6 is a good ticket to skip anyway (it is by far too structured and organized than other tickets or other draw-related conditions hold). Some of these issues are exploited by WG and the re-arrangement feature of LA2.3.

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