Speaking Of Awesome Sets

[doc]

Here's an interesting set of only 11 numbers:
5-7-12-13-18-21-30-31-35-37-46

A full wheel of these numbers would of course produce 462 lines of 6 numbers. In only 37 draws from draw 1978 to draw 2014, this set of numbers would have produced an astounding 3 JP's and 6 5+B matches, as well as numerous lower prizes. The following report was produced by an excellent program that I now use regularly, Lottery Data Miner or LDM for short. Notice that draw 1978 had all 6 of the 5+B matches as well as a JP. LDM uses a unique scoring system to give a player some idea of how well a wheel or set of numbers has performed against random expectation. This set of numbers beat the random odds by a factor of over 1500 over a run of 37 draws.

Lottery: CA 649
Testing 462 lines against 37 draws

Match-5 + Bonus for Draw 1978 1/4/2003 At Line 199
Match-5 + Bonus for Draw 1978 1/4/2003 At Line 200
Match-5 + Bonus for Draw 1978 1/4/2003 At Line 206
Match-5 + Bonus for Draw 1978 1/4/2003 At Line 212
***MATCH-6*** for Draw 1978 1/4/2003 At Line 222
Match-5 + Bonus for Draw 1978 1/4/2003 At Line 237
Match-5 + Bonus for Draw 1978 1/4/2003 At Line 440
***MATCH-6*** for Draw 2002 3/29/2003 At Line 107
***MATCH-6*** for Draw 2012 5/3/2003 At Line 196

TOTAL MATCHES
Match 0 - 7,224 Expected is 7,452.385
Match 1 - 6,570 Expected is 7,060.154
Match 2 - 1,989 Expected is 2,262.870

Match 3 - 768 Expected is 301.716 Score is 43,511.750
Match 4 - 450 Expected is 16.558 Score is 464,578.600
Match 5 - 84 Expected is 0.308 Score is 4,661,272.000
Match 5+ - 6 Expected is 0.007 Score is 13,983,820.000
Match 6 - 3 Expected is 0.001 Score is 41,951,448
Total Plays - 17,094
Total Losses - 15,783
Total Wins - 1,311

Expected Total Score Is 39,600.040
Actual Total Score Is 61,104,630.000
This Wheel Scored 154,304.400% Of Random Expectation
Total Draws With At Least 1 Match3 - 6

But it gets better! The same 462 lines from the same set of 11 numbers shows the following results in only 13 draws, from 2002-2014:

Lottery: CA 649
Testing 462 lines against 13 draws

***MATCH-6*** for Draw 2002 3/29/2003 At Line 107
***MATCH-6*** for Draw 2012 5/3/2003 At Line 196

TOTAL MATCHES
Match 0 - 2,058 Expected is 2,618.406
Match 1 - 2,280 Expected is 2,480.595
Match 2 - 906 Expected is 795.062

Match 3 - 400 Expected is 106.008 Score is 22,662.370
Match 4 - 300 Expected is 5.818 Score is 309,719.100
Match 5 - 60 Expected is 0.108 Score is 3,329,480.000
Match 5+ - 0 Expected is 0.003 Score is 0.000
Match 6 - 2 Expected is 0.000 Score is 27,967,632
Total Plays - 6,006
Total Losses - 5,244
Total Wins - 762

Expected Total Score Is 12,680.100
Actual Total Score Is 31,629,490.000
This Wheel Scored 249,441.900% Of Random Expectation
Total Draws With At Least 1 Match3 - 2

Here we've lost the 6 5+B matches, but still 2 JP's in 24 less draws is quite acceptable in my opinion. Note that in this case, the set beat the random odds by a factor of almost 2500!

Of course there are a few problems with this. First of all, not many players have the bankroll to sustain the playing of 462 tickets for each draw. The real problem though is simply this---this set of numbers was found through the benefit of 20/20 hindsight. That's pretty easy to do. The hard part is in knowing this kind of information BEFORE the draws take place. Also, the question now becomes "Will these numbers CONTINUE to perform as well as they have for the NEXT 13 draws?". My guess is that they won't because these kinds of things have an extremely annoying habit of falling apart as soon as they become identified. Then again they might. That's the fun of this game isn't it?

 

[Beaker]

LDM gave you all that WOW I really need to check that pgm out more closely.

Will they continue to hit? You bet. I never fight a trend - its your friend - even in the lotto.

What I would like to do is find the sets that are hot like your example.

Funny, many of those numbers will end up in my set for May 14th

 

[Dennis Bassboss]

This is a hot set....but many sets are much more awesome than this one....

 

[doc]

This is a hot set....but many sets are much more awesome than this one....

For example?

When working with sets of any size, one must realize that there are very many other sets of the same size. Using a set of 11 numbers for example, there are 29,135,916,264 different ways to choose any 11 numbers from 49. If you would like an awesome set of 25 numbers, you would have 63,205,303,218,876 to choose from. Perhaps someone would like to make an attempt at explaining which ones are good or bad.

 

[peter]

For example?

When working with sets of any size, one must realize that there are very many other sets of the same size. Using a set of 11 numbers for example, there are 29,135,916,264 different ways to choose any 11 numbers from 49. If you would like an awesome set of 25 numbers, you would have 63,205,303,218,876 to choose from. Perhaps someone would like to make an attempt at explaining which ones are good or bad.

I'm not a math wizard, but from what I understand all possible combinations for the Can 649 equal 13,983,816 possibilities. 11 numbers has 462 combinations, I have a complete chart listing all of the combinations from 6 numbers to 49 numbers. Am I missing something?

 

[doc]

I'm not a math wizard, but from what I understand all possible combinations for the Can 649 equal 13,983,816 possibilities. 11 numbers has 462 combinations, I have a complete chart listing all of the combinations from 6 numbers to 49 numbers. Am I missing something?

You are correct. Choosing 6 numbers from a pool of 11 results in 462 combinations. It is also correct that choosing 11 numbers from a pool of 49 results in the figure that was posted. They are different but related things that are calculated with the same mathematical formula.

 

[peter]

But Doc, if you played all possible combinations, using all 49 numbers, which is 13,983,816 combinations, how then can you arrive at 25 numbers , which total (your fiqure) 63,205,303,218,876. combinations. I calculate playing 25 numbers to get 6 of them, at 177,100 combinations.
Help me out on this Dennis, your the Math teacher, and the student needs your input.

 

[Beaker]

But Doc, if you played all possible combinations, using all 49 numbers, which is 13,983,816 combinations, how then can you arrive at 25 numbers , which total (your fiqure) 63,205,303,218,876. combinations. I calculate playing 25 numbers to get 6 of them, at 177,100 combinations.
Help me out on this Dennis, your the Math teacher, and the student needs your input.

Peter, he is talking about combinations of 11 from 49 not combinations of 6.

Recall: (n,r) read 'n choose r' is n!/(n-r)!r!

so (49,11) is 49!/38!11! which is that big number he put.

He is not talking about combinations of 6 he is talking about combinations of 11 numbers from 49 which was the initial topic of this thread ie what set of 11 is awesome.

Got it?

 

[Dennis Bassboss]

Yes ...Just arrived late here...I was....trying to study....He is not talking about the numbers of lines from 11 numbers here...Which is 462 lines or combinations...
but Beaker has already answer this one....Got to work on my double announcers grid for tomorrow's draw folks!

 

[andrew3698]

Hi Peter

Was just browsing. The figures seem very confusing but I think the math logic rests on solid foundations.

If you're looking at blocks/pools of 6 numbers each, then there is only one pool (out of a possible 13 983 816) that holds the jackpot winning combination.

When you examine 11-number pools, the perspective changes in a great way. The field of 11-number pools subsumes the field of 6-number pools, many times over. There is thus more than one 11-number pool that holds the jackpot winning combination.

 

[doc]

I'm not sure why there is confusion over the difference between the number of combinations in the game (13,983,816) and the number of sets resulting from a set of size N, where N >6. To go back to the original example, if I pick any set of 11 numbers (in the hopes that 6 of those 11 will match the jackpot), it is useful to realize that there are well over 29 billion different ways to choose any 11 numbers. Beaker already explained this pretty well.

To make things more interesting (or more confusing ), there are 962,598 sets of 11 that would contain the same 6 winning numbers + any other 5 numbers from the 43 remaining numbers. The set that I posted here is just 1 of those.

This is all just a way of looking at the "hidden" odds. In this case, the odds of having 6 correct numbers within your set of any 11 numbers is exactly 30,268 to 1.

 

[Beaker]

Yes, the odds of hitting all 6 are very high. Thankfully, we get paid for hitting 3.

All of those numbers, and more, can be verified at the link below.

http://www.lottostat.com/odds.html

 

[doc]

Yes, the odds of hitting all 6 are very high. Thankfully, we get paid for hitting 3.

All of those numbers, and more, can be verified at the link below.

http://www.lottostat.com/odds.html

Quite right Beaker. The odds of hitting 3 numbers out of 11 are still a little over 10:1. If you were to play all 462 lines from the full wheel and had 3 numbers correct, you would be holding 56 tickets that win $560 for a profit of $98. I'm not so sure that risking $462 in order to win $98 is a wise bet. Of course there's always the chance that you'll do much better than that.

As a further point of interest for anyone who cares, in order to have a better than 50% chance of matching at least 3 numbers, you have to use a minimum pool of 21 numbers.