Dallas, Texas United States Member #4549 May 2, 2004 1689 Posts Offline

Posted: August 31, 2014, 2:55 pm - IP Logged

No Peter, I am not attempting to disprove anything. I find your theory interesting.

What I intended to do was establish some foundation for what I stated in my first response referring to the 10% +/- 2%. Since I made the statement, and truthfully it sounded outlandish (even to me) looking at the RP totals, so for my own satisfaction I needed prove it (even if it were only to myself. )

Seeing fresh ideas gives me that urge to see where and how far we can take it. Even now I can see where adding more code to show a skip/hit ratio. Might even add that Thoth differential to see where that takes the idea.

In my mind, the small games are fun to code. You can do so much more with 5K of code for them, when 5K of code for a game like MegaMillions or PowerBall won't get you out of the starting block.

I hope if I do anything it is give you something to think about, not something that says "HERE I AM TO CAUSE TROUBLE!" In any case, if anyone feels I am causing trouble, all they need do is ask me to explain myself. If I jump the shark, tell me and I'll check myself.

I did fail to check the CA Pick 3 for back to back hits using the same digits. Going by the .004 and considering there are 12490 draw, we should find approximately 50.

And I will work on that as soon as I get back from the market with baby back ribs for the grill. No person should ever have to think without grilled baby back ribs. That is, or should be, a crime in Texas!

BRB,

G

My greatest accomplishment is teaching cats about Vienna Sausage. When I need a friend, all I need do is walk outside, pop open a can, and every little critter in the neighborhood drops by to say "Hi!"

Dallas, Texas United States Member #4549 May 2, 2004 1689 Posts Offline

Posted: August 31, 2014, 6:05 pm - IP Logged

And heeeeeeeeere's California. Red represents the back to back straight hits. DR 105 and 106, etc. Most of the hits occur in the fat part of the delta curve. No repeats back to back to back.

G

My greatest accomplishment is teaching cats about Vienna Sausage. When I need a friend, all I need do is walk outside, pop open a can, and every little critter in the neighborhood drops by to say "Hi!"

Simi Valley, CA United States Member #156940 July 4, 2014 671 Posts Offline

Posted: August 31, 2014, 6:41 pm - IP Logged

Fascinating, Garyo! And if you remove the doubles, you get a pool of 45, of which 10 now are repeats. (I'm taking them out, because the straights vs. box odds for doubles is different than singles.) What percentage is 10 of 45?... Appx. 22%, very close to 1/6th... which is what we'd expect to shake out when it comes to boxes vs. straights (6 boxes, of which 1 would be a straight match). This fits my theory, then, that the numbers are (a) chosen first as to positioning, above/below/beside, and then (b) shuffled randomly to arrive at one of the 6 box final positions as played—of which appx. 1/6th would be straights, and the rest various boxes.

But as to "First, Second, Third choice" or "Position A, B, C"... these are non-abstract concepts, whereas the game works with the utter abstractness of numbers.

Still... if one was to assume a limited pool to begin with, for whatever reason—a pre-selected pool of numbers from which to pick which number's remaining digit—if one speaks temporally, one would want the limited pool picked first; that's because, it would have the least impact on the greater pool; it would diminish the end result least. If the limited pool were digits 0, 1, 2, 3, 4, you'd want that limited pool picked first, because it'd enable greater range of play (i.e., if second and third "positions" went first and second, you might get 1 and 4; this limits the scope of a limited pool, because now its choices are but three, 1, 2, 3; but if the limited pool is picked first, say 1, it limits the range of second and third picks no more than if the first pool were limited, or not limited).

Why do I say a pool is limited, and it's probably the first one? Because I just believe it, for one thing. But also, it would account for a very observable phenomenon in the game, that of digits being long absent.

If we have digits 0-9 (a-j); and then we have, as the pool for First choice digit (A), a limitation to say five digits (¹); then subsequent pick Second (B), has a range of:

B = A - a¹.

Favoring one way, means not favoring another. Choice Second (B) now has a full range of choices, including those of the original pool (minus A); but choice Third (C) becomes dependent upon the second choice, too, so its pool is diminished by two - A, and B.

Which means, if we assume a limited pool from which the First digit is chosen... then the Second Choice has the largest range of optional digits, and it's here that most of the long-outs would be sourced. (Because the limitations of A, mean their chance of dominating any individual play is greater than the impact of digits outside that pool—hence, you get so many repeats and often-playeds, and the long-outs, too. Under this system, you'd get less long-outs as a whole, than often playeds or repeats [indeed, you usually only get an average of about two long-out digits at any one time.])

Texas United States Member #150797 December 31, 2013 815 Posts Offline

Posted: September 1, 2014, 8:05 am - IP Logged

Quote: Originally posted by garyo1954 on August 31, 2014

Thanks for the kind words! Credit to where it is due. Married a geeky mathematician who couldn't open a pickle jar, but could do finances in her head faster than most use a calculator. Brilliant woman.

Somewhere on this LP site is a chart you should get your hands on. Likely in the Pick 3 encyclopedia's blog, Win D, if he still has a blog up. That chart shows how to cover every combination of one digit boxed for $42.50(?), or all the singles for $27(?). Some people refer to it as the "If You Know One Digit" system made famous by Steve Player.

Playing singles and using filters you can get it down to about $13. Been there. Done that. Using the "elimination" technique, 6 hit, so it won't hit again, I played.

&(&!@@#!!!! 6 hit two nights in a row! Can't happen three times.

%&^&@#@#!@@!!! 6 hit three nights in a row. But.......

%!&&&@@@@^^%$&#^#@!!!!!!!! NO WAY FOUR NIGHTS IN A ROW?

Ended up spending over $60 to win $40.

Still take a look at it. There is a lot of GOOD, SOLID INFO on Win D's blog.

But back to the original point of a number repeating 10% of the time. Went ahead and grabbed the CA Pick 3 drawings. Made some changes in the code, added another dozen lines to track repeats by position. Labelled Rep1 thru Rep 9.

Rep1 is the first digit repeating back to the first position. Rep2 First digit repeats to the second position. Rep3 first to third. Rep 4 second digit to first position. Rep5 second to second position, Rep6 second digit to third position. Rep7 third to first, Rep8 third to second, Rep 9 third to third.

You see there is only a one in ten chance of a given number repeating back in any position. Ten digits equals a one in ten chance of any digit falling in any position.

Certainly different than the bloated RP percentages. And a tad more realistic IMHO.

How does this affect your thinking?

Couple of other thoughts, interesting side notes if you will.....

1) The second digit (1245 total) has not repeated back to the first position in 34 draws. Might be worth looking at for a possible play.

2) I love working with numbers and I appreciate the thanks, but how about sending the winning MegaMillions instead? Don't have to buy anything, just send the numbers and I'll do the rest. TIA

G

Playing singles and using filters you can get it down to about $13. Been there. Done that. Using the "elimination" technique, 6 hit, so it won't hit again, I played.

&(&!@@#!!!! 6 hit two nights in a row! Can't happen three times.

%&^&@#@#!@@!!! 6 hit three nights in a row. But.......

%!&&&@@@@^^%$&#^#@!!!!!!!! NO WAY FOUR NIGHTS IN A ROW?

Ended up spending over $60 to win $40.

ROTFALMAO!

We've all been there Garyo!

Since this is the math board, I will add the chances of a number streak ending after x draws:

73% of numbers hit once and done,

92% of streaks end at two, i.e the number hits two draws in a row,

98% of streaks end at three, i.e. the number hits 3 times in a row,

99% of streaks end at four, i.e. the number hits 4 times in a row.

Longer streaks are very rare, but do happen -- the longest in the 2 plus years of data I am tracking is 8 in a row, but people who track their entire history will have longer streaks, no doubt.

"There is no such thing as luck; only adequate or inadequate preparation to cope with a statistical universe."

Simi Valley, CA United States Member #156940 July 4, 2014 671 Posts Offline

Posted: September 1, 2014, 10:03 am - IP Logged

Quote: Originally posted by Tialuvslotto on September 1, 2014

Playing singles and using filters you can get it down to about $13. Been there. Done that. Using the "elimination" technique, 6 hit, so it won't hit again, I played.

&(&!@@#!!!! 6 hit two nights in a row! Can't happen three times.

%&^&@#@#!@@!!! 6 hit three nights in a row. But.......

%!&&&@@@@^^%$&#^#@!!!!!!!! NO WAY FOUR NIGHTS IN A ROW?

Ended up spending over $60 to win $40.

ROTFALMAO!

We've all been there Garyo!

Since this is the math board, I will add the chances of a number streak ending after x draws:

73% of numbers hit once and done,

92% of streaks end at two, i.e the number hits two draws in a row,

98% of streaks end at three, i.e. the number hits 3 times in a row,

99% of streaks end at four, i.e. the number hits 4 times in a row.

Longer streaks are very rare, but do happen -- the longest in the 2 plus years of data I am tracking is 8 in a row, but people who track their entire history will have longer streaks, no doubt.

This is the fascinating illusion of numbers that this game runs on. Any three numbers - forget all the low/high, 01/89, etc. - any three numbers account for 71% of the available singles boxes, and 53% of the doubles.

Hence, if you think a double's coming up following a single, you have just a hair's better chance of basing that double on one of the last single's digits, than not. But just a hair. (However, going from double to double, you have a 47% chance of the digit repeating - a hair's worse chance of repeating digits.)

The reality is that any three numbers, at any given time, have a 71% chance of appearing (i.e., at least one of them does) in the next singles draw. Pick three out of a hat, the odds are the same.

But if you apply the streaks percentages Tia's added above, then when you see a repeating digit, one that's repeated only one time, your odds increase (i.e., of hitting the right digits) if you don't play that once-repeated digit into the next singles combo.

Dramatically...? Sadly, no. They increase only by about 3%.

Texas United States Member #150797 December 31, 2013 815 Posts Offline

Posted: September 1, 2014, 12:13 pm - IP Logged

Quote: Originally posted by PeerGynt on September 1, 2014

This is the fascinating illusion of numbers that this game runs on. Any three numbers - forget all the low/high, 01/89, etc. - any three numbers account for 71% of the available singles boxes, and 53% of the doubles.

Hence, if you think a double's coming up following a single, you have just a hair's better chance of basing that double on one of the last single's digits, than not. But just a hair. (However, going from double to double, you have a 47% chance of the digit repeating - a hair's worse chance of repeating digits.)

The reality is that any three numbers, at any given time, have a 71% chance of appearing (i.e., at least one of them does) in the next singles draw. Pick three out of a hat, the odds are the same.

But if you apply the streaks percentages Tia's added above, then when you see a repeating digit, one that's repeated only one time, your odds increase (i.e., of hitting the right digits) if you don't play that once-repeated digit into the next singles combo.

Dramatically...? Sadly, no. They increase only by about 3%.

Again, the weird illusion of numbers.

On the other hand, every little bit counts!

If you see that a number has repeated do you play it or not? My rule is no, but it does come back to bite me sometimes.

A safer rule would be to wait for 3 hits in a row before eliminating a number.

"There is no such thing as luck; only adequate or inadequate preparation to cope with a statistical universe."