Here is another viewpoint to add to the fine ones already in this thread.



I would just like to step back from the numbers for a minute, and then we'll
come back to them.  We'll touch on game histories, and a bit on subsets, but
the main point is something unrelated to numbers altogether.



There is an intangible part to playing.  It's beyond the numbers.  It does
not yield to quantification.  It doesn't even yield to logic, because if we
look just at the game's raw odds versus its prizes, then there is no logical
value in playing at all.  



The odds are high and the prizes low by comparison.  There is something beyond 
that, intangible. I think it's possible to talk about the intangible side 
without making it sound vapid or wishy-washy.  It's a real factor in why and 
how we play.



The intangible side of playing is partly imagination (lifestyle and
adventure, among others) and partly a combination of entertainment and
challenge (tough odds? so what? the play is cheap and affordable).  Those
things don't have anything to do with the absolute numbers, nor with the
odds.  They are intensely personal.  They vary by player, and similar
motivations in various players can work their way into very dissimilar ideas
for what numbers they want to play.



I am just suggesting that the idea of using some kind of method to grab some
numbers for the next draw, is OK -- provided it is seen as one of the
intangible, personal elements, and not otherwise.  Within that boundary,
there is no basis for criticism -- within that boundary.  The trouble often
in dialogue, however, is that that boundary line is not mapped very well.


The idea of using any personal method to select numbers has nothing to do
with any kind of accuracy in forecasting.  It's a personal stamp that the
player puts on the game.  So for example, when a player uses a game's
history to get new numbers, that does not mean that that game history has
some kind of intrinsic, built-in forecasting accuracy that was just waiting
for the player to discover it.  Nothing like that.  It is simply one kind of
personal method the player can adopt, and it is his no-fault option to do so
as long as no intrinsic predictive value is ascribed to it.



There is nothing quantifiable in a number that says, 'play me'.  The
decision is in the player's motivation according to how he sees the game.
The decision might be able to be pinned down, but it would have to be done
so by a psychologist, not by a mathematician.



The reason for using game histories as a basis for getting numbers is simply
this.  I do not think it is much more than this.  The most universal lottery
information we have, that is given to us daily by the game commission itself
as well as by radio/tv reporters, newspapers, websites, at the supermarket,
and everywhere else -- is the game's history of winning numbers.  It's on
every evening newscast, and is on page 2 of every local newspaper (sometimes
on page 1).  The game is indistinguishable from its numbers, and the media
make sure that we see the numbers constantly.  We are already pretty well
saturated in the recent winning numbers.  We could play dates, dogtags,
license plates, shoe sizes and the like, and many folks do.  But the media
are feeding us with a kind of running history of 'facts' about what numbers
have been winning.



So I think it is natural for a person to see the history, and to recognize
numbers he or she 'would have' played, or 'should have' played.  It's a
natural instinct.  I don't think that kind of absorption with the numbers is
weird or misguided.  It's a natural human reaction to something seen after
the fact, often a startling reaction.  Outside of the lottery, it's the same
kind of reaction that happens at other times in a person's life, in much the
same manner.



Again, all of this stays out into the intangible personal area.  The
selection of numbers for the next draw is the outcome of all of that
intangible personal activity.  And that selection remains intangible,
whether it was done in an instant or else took hours of thought.  At that
point the numbers are chosen.  And at that point an individual person's
selections are 'right' to that person.  It becomes 'wrong' only if someone
states that there is a tangible (i.e. predictive) value in the selection of
numbers.



This whole thing is hard to pin down because the line between 'preference'
and 'prediction' gets blurred in semantic shortcuts we sometimes take in the
language.
It has already been shown here in RGL, a couple of years ago by Karl and
Mario, and more recently by Steve P and Thad, that the probability of
winning is not affected by the past history of a game (each new draw is
independent), nor by the use of subsets to reduce the field of play (the
probability of matching the subset is inverse to the probability of matching
the winning member of the subset).  So the tangible part is immutable.



Yet let's plod through a couple of subsets, because that is one way we can
see (and cross) the line between the tangible and intangible parts of
playing.



Take a simple game that has only 10 combinations.  Eight (8) fit some kind
of subset definition, and the remaining two (2) fit some other kind of
subset.  It does not matter how we classify those subsets, or what we call
them.  This is just for the example.
So there are two of those subsets, making an 8/2 split of the game's 10
combinations.



Over the long history of the game, the "8" subset will show up about 80% of
the time.  The "2" subset will be there about 20% of the time, obviously.
I can play just one combination.  If I play it from the "8" subset, I will
be in the correct subset 80% of the time.  But I then have only a 1/8 chance
of having the correct winning combination.  Inversely, if I play my one
combination from the "2" subset, I will have the correct subset just 20% of
the time.  However, when that happens I will have a 1/2 chance of having the
winning combination.  The two probabilities are exactly inverse to each
other, and my overall winning chance in steady play is still 



1/10:

      p(0.8 * 0.125) = p(0.2 * 0.5)
      0.1 = 0.1



That's in steady play.  But now we are going to wax philosophical, just for
the lark of it.



We are still in our 10-combination game.  Suppose we say that there is no
tangible value in using (backward) multiple-draw game history to make a
selection of numbers for the next draw.  OK, we accept that.
Then why should we not be able to say, as a corollary, that there is no
tangible value in using (forward) multiple-draw probabilities to make that
selection?



In better words.  What happened in the past 10 draws (or any amount of past
draws) has nothing to do with what will happen in the next coming draw.



There is no cause and effect in the game, past to present.  Then what
happens in the next coming draw will have nothing to do with what will
happen in the next 10 draws (or any amount of future draws).  There is no
cause and effect in the game, present to future.



Every draw is simply the one, isolated, "next" draw.
So when I choose numbers for the next draw, I do not need to consider the
probabilities of anything happening beyond that one next draw.  Each draw is
a single, independent event.  And it has its own independent probabilities
of what will win in that one event, regardless of what has gone on before
and of what will go on afterward.



Going back to the 10-combination game above.  In the next draw, there will
be an 80% chance that the winning number will come from the "8" subset.  If
I play my combination from one of those eight, I take my chance that I have
the 1/8 winner.  I may not have the one winner, but if my combination has
numbers which match some of the common characteristics of the winning
subset, then I may have chances for minor prizes (if the game awards them),
because my chances are present of matching some winning numbers.  



On the
other hand, if I simply choose one combination from the "2" subset there is
a 20% chance that I will match it in the next draw.  The chances are
therefore less that there will be minor prizes in the next draw.



The reality in Lotto games is that the 1/10 game never pays enough at any
prize level to put a steady positive money flow into the player's pocket.



It will take luck, beyond the tangible part of the game's odds and prize
amounts, to make money.  The ongoing flow direction will be outward, unless
and until some major luck happens.  But the main idea is to play a ticket
into the next draw which has a percentage chance which the player
understands and accepts, of being an "active" or "live" ticket in that draw.



If the player does it with a game history or a dartboard -- it does not
matter which -- he is not 'wrong' and cannot faulted for his 'method' --
because that is the intangible personal part of playing.  If on the other
hand he claims to have a game history or dartboard with predictive value,
then he is 'wrong' -- because he is now dealing with a tangible,
quantifiable process that yields to the definition of parameters and
measurement, and he ultimately will not be able to prove it.



- - -



A nice little exercise from Draw 1 of the new California SuperLotto Plus
game, for a wrap-up example.



The winning numbers were:



      2  4  11  15  28  (Mega: 16).



There is no history, because it's Draw 1.  So we'll play with subsets.



There are millions of ways to make subsets.  We will just use the old
warhorses:  Sums,  Even/Odd,  Low/High,  Consecutives,  and  Matching Final
Digits.   (Please don't let eyes glaze over, hold palm over mouth when
yawning, graciously.)



The CA game is a 5/47, with 1/27 Bonus.  Subsets are usually made on the 5
principal numbers, with the Bonus number tacked on in wheeling.  These are
**very**  liberal and broad filtering ranges for isolating subsets in this
kind of game:



      Sums:  60 to 180    (Central Sum +/- 50%)

      Even/Odd Numbers:  4/1 to 1/4

      Low/High Numbers:  4/1 to 1/4

      Consecutive Numbers:  None

      Matching Final Digits:  No matches.


We'll take only the subset of numbers which matches *all* of the above
filtering (i.e., each combination must have *all* of the above
characteristics).

A Full wheel (5/47) has 1,533,939 possible combinations.  Wheeling a 5/47
with the above filtering gives just 327,325 combinations.  That is a
reduction of 78.66% from the Full wheel.


Good news, bad news.  If a player played the subset, together with each of
the possible Bonus numbers (1...27), it would have cost him (327,325 * 27)
$8,837,775.  But he would have won the game's first draw Jackpot, at
$21,000,000 -- which went unwon.  The good news is, he would have won $21M.
He could have taken the lump sum at about $10.5M, deducted the $8.8M as
expense, and netted $1.7M before taxes, for an evening's work.  (Dick, if
you read this, help on this one if you like.)


The bad news is, no one could have afforded the $8.8M cost.  Nor could
anyone think of printing out 8.8 million combinations on playslips.  He
would need the prize money to buy inkjet cartridges.
The  _intangible_  news is, no one could have forecast that the winning
numbers would fit inside the subset shown above, in the filtering. 

 Even
though those are very broad ranges, with nothing extraordinary to them. 


Even though there is no history to study (because it was the first draw).


The other intangible bit is, if there were  *anything*  that were
predictable about that first draw, then everybody's lottery software program
would have figured it out and everybody's PC screen would have had the same
combinations to play.  And the Jackpot prize would be split into thousands
of tiny chunks, one chunk for each player.



- - - - -



We can leave room for the intangible part of playing, because that is what
makes it 'playing'.  If there were nothing but the plain numbers and the
odds, there would be nothing to discuss (and no RGL).  It would be cut and
dried, wager and loss, all money.



The tangible part is solid and does not move, no matter how we push and
shove.  But the other part is the real human side, and so far no one has
quite put a full wrapper around what it does for us, good or bad, as a form
of enrichment (no pun) in our lives.



Trying to drive with the foglights on. . .