Informative, honest, indepth articles on Lotto and whether other than through sheer luck the odds can be bettered.
There is no way of telling the start or end of a Lotto history or whether it has been jumbled up without knowing the draw dates or draw IDs which means there is no intrinsic order to the draws - it is simply a bucket of numbers. For a particular time of the day you could set 100 machines or computers to start at exactly the same time and the chances are they will all be different numbers. No draw result is more valid than another and to resolve this scenario a random selection from the 100 results is needed.
The heyday of interest in discussing Lotto in on-line forums and in particular about using the history of draws to determine the numbers to play peaked around 2005. Practically all the many thousands of sites on Lotto number analysis are about assuming a relationship or constraint between the next draw and the draws previous to that, which as I will show is utter bunkum and is really the stuff of numerology with their penchant for errant ersatz science, mathematics and statistics.
You still have freaky people that actually believe that from the history of draws for a particular Lotto game the next jackpot number can be narrowed down. This of course is based on the erroneous assumption mentioned above that there is a relationship between the history and the next draw. Interestingly, give someone a single draw result or a set and a choice between a number of draw histories and they wouldn't be able to pick the relevant history without knowing the answer or looking it up. The point being that whatever is considered positive that one comes up with could be similarly achieved by using any like history.
There are two principles to keep in mind when discussing the history of draws for a Lotto game: -
In the following table for a Pick 6, Pool 49 Lotto game you can see the chances of success playing all the combinations for the respective Pool. Using only 42 integers from the Pool of 49 you have a 86% chance of success for the 1's but only a 62% chance for the 3's and 38% for the 6's.
The following table shows 34 draws for a 6/45 Lotto Game with the latest draw either at the top or the bottom of the table. Without looking it up the integers for the last draw could be anywhere and not show up as being untoward.
There is nothing to stop a Lotto operator from using blank ping pong balls and writing the integers on them prior to shuffling for the draw. Amazingly, on a forum that caters for the Lotto deranged they bemoan the fact that test runs by the Lotto operator are not revealed as if it would make a difference.
Often I have come across the shysters claiming such and such supports their spiel when in fact it it just the natural distribution. Consider a Pick 6, Pool 45 Lotto game. It is possible for all the integers to occur within 8 draws but this is highly unlikely. Here is a more likely distribution (in fact actual): -
Now, you may be tempted to think that the prior six draws has shrunk the number of integers by more than 50% to 24 from the Pool of 45. The important point to remember is that this is applicable to practically all six randomly selected lines not just the prior six draws.
There is a big question about the logic of making an association with an as yet non existent next draw. If you make the association it is made by you and then you must ask yourself the question, "Am I receiving anything extra from that of using any other random selection of six lines from the 8,145,060 possibilities?"
Lotto operators in the main still provide frequency or occurrence and absence or recency data and charts on their websites. The UK National Lottery gives for the 6/49 game the ball-set and machine used as if it mattered. Disclaimers such as this one from Tattersalls in Australia are not uncommon: -
From the articles there are two overwhelming facts - lack of repetition and inconsistency between ostensibly that which should be giving the best results if there was some correlation between history and the next draw.
The whole scenario of Lotto history analysis thus becomes farcical and results in the whole process being nothing other than a quaint way of jumbling the numbers to produce a set of numbers to play, which is more than likely inferior to random selections.
All the thousands of websites touting history analysis as being some guide to future draws are basing their "analysis" on a false assumption.
The good thing about signatures is that it handles both absence and occurrence or each considered separately.
Consider the oft used method of 5 categories (Repeat, Hot, Warm, Luke, Cold) for each integer with the following 5 signature examples: -
Alternatively, you could use just four categories and have the previous draw results in H, W, L and C with absence eg
The important point is that the combinations have not been reduced from 8,145,060 simply the convention used to represent the integers have extra complexity by carrying absence and occurrence data. As I will show the added complexity means the repetition of the subset combinations is practically non-existent, which is not unexpected but is not what we want. The gross inferiority of the subset repetitions when compared to integers alone is proof enough that no beneficial relationship exists in using history.
Adding complexity where it is not needed to get a win is illogical. Consider tossing a coin where you win if you get heads. You could add complexity by adding the quadrant compass direction the top of the head side or tails side is pointing towards when it lands. So, instead of two possibilities we now have 8 but the win is paid on only two possibilities and nothing is gained.
For the 10 draw previous history shown above we have 6 integers in P, 1 in H, 13 in W, 16 in L and 8 in C. The only consistent figure is P which is always 6 but the rest are random.
With 5 categories (Previous, Hot, Warm, Luke and Cold) and a Pick 6 Lotto game we have precisely 210 possible combinations with repetition allowed as shown in the table below.
However, this does not diminish the number of possibilities which for a Pick 6, Pool 45 Lotto game is 8,145,060. For the PWWLLC category alone there are 449,280 possibilities and for WWLLCC 262,080 for this particular history, too many to play thus requiring a random selection. This of course begs the question why bother as you could just as easily do a small random selection from all possibilities?
You probably understand my reluctance years ago when writing about signatures to release details of this system with its potential to be misconstrued. The problem is of the 210 Signature Combinations there is no basis for favoring one over the other and when this is combined with the varying number of integers in each signature all 8,145,060 combinations of six integers are possible as it should be, so it's back to randomness and a good template.
If you had 01 only in P00, 2 only in S01, 3 only in S02, 4 only in S03, 5 only in S05 and 6 only in S06 and you played P00 S01 S02 S03 S04 S05 you would have won if the winning number was 01 02 03 04 05 06.
To halve the possibilities in a 6/49 game remove just 6 integers and for a 6/45 game remove 4 or 5. Halving the Pool means just a very small fraction of all the possibilities are considered and this has a drastic effect on the yield. See Analysis of 15 Lotto Number Sets.
In other words you could have just as easily taken whatever number of combinations you wanted to play from the immediate previous draws and simply randomized it for the pool applicable to the game.
The likelihood of an integer repeating in the next draw main numbers can easily be miscalculated. In a 2094 draw sample for a Pick 6, Pool 45 Lotto game there are 2 occasions where 4 integers repeat (.1%), 49 where 3 integers repeat (2.3%), 296 where 2 integers repeat (14.1%) and 869 with just 1 repeat (41.5%). The likelihood of 1 or more integers repeating is then 58%, less than the usual figure given of around 74.5% (double counting?).
For a marginal improvement over random selections you can do no better than my online program LottoToWin available for a token $5.00 per year subscription.
My program ignores history and concentrates on producing a set of numbers to play by using all integers, not repeating paying subsets and maximizing without "optimizing" the coverage.
The reality is at every drawing everything is new and each integer has the same likelihood of being picked as any other integer.
When you stand back after applying all the sophisticated programming to extract something from history you may realize as I did that you're really just maximizing the best results obtainable from a small number of lines. The same template result for 9 lines in a 6/45 Lotto game can be obtained in a few seconds using pen and paper by randomizing the following lines: -
Using the 6/45 sample history above you could have decided to use: -
Consider the sobering fact that for a Pick 6 Pool 45 lotto game where getting four integers correct has odds of 1 in 733 more than two thirds of the integers are in the previous 10 draws but this only gives less than one third of the winning Fours. In other words two thirds of the winning Fours require near the full complement of the 45 integer Pool.
For the sample of 2094 draws in a Pick 6 Pool 45 Lotto game probability formula calculates that playing one line should give 2094/733 = 2.86 or 3 wins for a combination of four integers ie a Comb-Four. Each line has 15 CombFours and there are 148,995 possibilities of which only 31,890 occurred. Obviously, with 117,105 having no appearance you are better off randomizing the line played. If you were lucky and five of your plays had 06 24 26 36 you could have won the maximum repeat of five CombFours: -
Comb-Fours Count in 2094 Draws
SO, IN 2094 DRAWS OR RANDOM SELECTIONS 2980 COMB-FOURS REPEATED BY CONTRAST NOT ONE COMB-FOUR THAT WAS RELATED TO ABSENCE OR RECENCY AND OCCURRENCE OR FREQUENCY REPEATED.
BUT THERE'S STILL MORE!
For the sample of 2094 draws in a Pick 6 Pool 45 Lotto game probability formula calculates that playing one line should give 2094/45 = 47 wins (if paid on) for a combination of three integers ie a CombThree. Each line has 20 CombThrees and there are 14190 possibilities of which 13450 occurred. If you were lucky and twelve of your plays had 01 18 37 or 05 34 42 you could have won the maximum repeat of twelve CombThrees.
CombThrees Count in 2094 Draws
So, for a Pick 6, Pool 45 Lotto with 14,190 Comb-Three possibilities we have in 2094 draws 11,330 CombThrees that repeated, 2120 that occurred only once and 740 with no appearance.
BY CONTRAST JUST 2 COMB-THREES REPEATED ONLY TWICE THAT WERE RELATED TO ABSENCE OR RECENCY AND OCCURRENCE OR FREQUENCY.
Consider a simple example where you played the line 01 02 03 04 05 06 for the 2094 draws. Three combinations of four integers wins are expected and that is what you would have got 02 03 04 05, 02 03 04 06 and 03 04 05 06.
You're to be congratulated for thinking Lotto history analysis is as a way to beneficially produce numbers to play in Lotto, irrelevant and is a gigantic con played out by closet or brazen numerologists or despicable opportunists prostituting their integrity for a few lousy bucks and all using the usual trick of assuming something false is true by pandering to something intuitive but incorrect and then constructing a dung heap on thin air.