There's More to Picking Winning Lottery Numbers than Clicking On Enter

by Joe Roberts / CDEX Lottery Director

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. . .

Joe Roberts CDEX Lottery Director software

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