Lottery pick3 odds?
So, I know just enough probability to get myself in trouble. For example: pick3 games (pick 3 digits from 09 inclusive) have 1 in 1000 odds of winning on a [I]straight[/I] bet, ie. I play 395 and the computer picking that number should happen every 1000 draws or so.
(I like to think) I'm not naive enough to think that if a number hasn't hit in 900 draws that it is more likely to hit than any other number (assuming a fair random number generator and unbiased code[SUP]*[/SUP]), but I don't know how to work out what the odds are that if I were to pick a number, say 734, and play it constantly that I will have to wait more than 1000 draws for it to hit. [SUP]*[/SUP] [SIZE="1"]California uses an "Automated Draw Machine" to pick winners for the Pick3 and other games.[/SIZE] 
[QUOTE=schickel;457985]So, I know just enough probability to get myself in trouble. For example: pick3 games (pick 3 digits from 09 inclusive) have 1 in 1000 odds of winning on a [I]straight[/I] bet, ie. I play 395 and the computer picking that number should happen every 1000 draws or so.
(I like to think) I'm not naive enough to think that if a number hasn't hit in 900 draws that it is more likely to hit than any other number (assuming a fair random number generator and unbiased code[SUP]*[/SUP]), but I don't know how to work out what the odds are that if I were to pick a number, say 734, and play it constantly that I will have to wait more than 1000 draws for it to hit. [SUP]*[/SUP] [SIZE="1"]California uses an "Automated Draw Machine" to pick winners for the Pick3 and other games.[/SIZE][/QUOTE] depends on if they can be redrawn etc. at last check if they can the odds of not picking n for y drawings is (999/1000)^y I think, which would put your odds of not picking it for 1000 at about 36.77% in theory. 
[QUOTE=science_man_88;457986]depends on if they can be redrawn etc. at last check if they can the odds of not picking n for y drawings is (999/1000)^y I think, which would put your odds of not picking it for 1000 at about 36.77% in theory.[/QUOTE]If you mean redrawn within each draw, yes, it's 3 independent fields of 10 digits. In fact just within the last week, the winning number was 555 (I think.....let me check)

[QUOTE=schickel;457990]In fact just within the last week, the winning number was 555 (I think.....let me check)[/QUOTE]Sunday April 23 evening [URL="http://www.calottery.com/play/drawgames/daily3/winningnumbers/?DrawDate=Apr 23, 2017&DrawNumber=14426"]draw[/URL]. Looks like it doesn't really pay to play triples.

At the risk of stating the obvious, the probability of picking any given 3 digits is
(1/10)^3, so from a theoretical point of view, given the large enough sample(of draws), you will get any given 3 digit combinations very close to 1/1000th of times. However studying historical lottery results you will find out that some numbers are biased and occur more often. There are two different factors at work. 1. The draw is not truly random 2. There is observed influence in random draws, which [U]probably[/U] has a quantum basis. In quantum physics it is a basic principle that just observing an experiment will affect the outcome of that experiment. For example in the double slit experiment, observing which slit a photon passes through will collapse its wave function and destroy the interference fringes which would be otherwise present. 
[QUOTE=a1call;457994]At the risk of stating the obvious, the probability of picking any given 3 digits is
(1/10)^3, so from a theoretical point of view, given the large enough sample(of draws), you will get any given 3 digit combinations very close to 1/1000th of times. However studying historical lottery results you will find out that some numbers are biased and occur more often. There are two different factors at work. 1. The draw is not truly random 2. There is observed influence in random draws, which [U]probably[/U] has a quantum basis. In quantum physics it is a basic principle that just observing an experiment will affect the outcome of that experiment. For example in the double slit experiment, observing which slit a photon passes through will collapse its wave function and destroy the interference fringes which would be otherwise present.[/QUOTE]Yeah, maybe, but if it was really easy, someone would have exploited any bias by now. According to the FAQ, they have two different draw machines and two different ways to pick the winning numbers, with both being chosen before the draws are run. I imagine there would also be a test draw or two before the winning draw, so it would seem to be impossible to figure out any effect there.[QUOTE=science_man_88;457986]depends on if they can be redrawn etc. at last check if they can the odds of not picking n for y drawings is (999/1000)^y I think, which would put your odds of not picking it for 1000 at about 36.77% in theory.[/QUOTE]Wow, that seems high to me. That's really why I'm asking, since my instincts could be wrong. So, if there's a ~37% chance of not drawing one number in 1000 draws, what would be the odds of missing a win in the following scenario: take 10 different numbers and play them for 100 draws. Intuition would seem to say that 10(numbers)x100(draws) = 1000 "trials" which would seemingly make it a certainty that you would hit once, but I don't know enough about how to calculate the odds in that case. 
[QUOTE=schickel;458073]Yeah, maybe, but if it was really easy, someone would have exploited any bias by now. According to the FAQ, they have two different draw machines and two different ways to pick the winning numbers, with both being chosen before the draws are run. I imagine there would also be a test draw or two before the winning draw, so it would seem to be impossible to figure out any effect there.Wow, that seems high to me. That's really why I'm asking, since my instincts could be wrong.
So, if there's a ~37% chance of not drawing one number in 1000 draws, what would be the odds of missing a win in the following scenario: take 10 different numbers and play them for 100 draws. Intuition would seem to say that 10(numbers)x100(draws) = 1000 "trials" which would seemingly make it a certainty that you would hit once, but I don't know enough about how to calculate the odds in that case.[/QUOTE] I think that would make it into (990/1000)^100 = 0.36603234127322950493061602657251738619 ( used PARI/GP both times I think) probability would depend on so many things see: [url]https://www.youtube.com/watch?v=lP58mP8Wchc[/url] standupmath video ( matt parker) [url]https://www.youtube.com/watch?v=U7f8j3mVMbc[/url] numberphile video [url]https://www.youtube.com/watch?v=BGfK9Bxl3OI[/url] another numberphile video that may help you. it's also why the monty hall problem stumbles so many as the video they made on that shows. 
they give example odds for one play at the bottom of [url]http://www.calottery.com/play/drawgames/daily3/howtoplay[/url] but there's a lot to think about some numbers it doesn't matter which you play etc.
numbers with all the same digit only have one way of sorting them so any= exact and the two main things become the same ( down to the prize money or using the straight/box option to win both prizes). those that have 2 digits in common ( something like 27% of the numbers total if you don't include the overlap with the all three digits the same in the set) have only 3 ways to arrange themselves, whereas numbers with no digit in common have 6 ways to arrange themselves. let x stand in for the same digits those with two or more digits the same include ( per digit x with some overlap e.g for x=6 xx6 x6x and 6xx are all the same number ( 666 the case where all three are the same digit technically)) x0x x1x x2x x3x x4x x5x x6x x7x x8x x9x xx0 xx1 xx2 xx3 xx4 xx5 xx6 xx7 xx8 xx9 0xx 1xx 2xx 3xx 4xx 5xx 6xx 7xx 8xx 9xx if you take away the overlap you have 28 possibilities remaining ( including 666 111 etc only once not three times). edit:doh I now see that this is already explained in that link. 
[QUOTE=science_man_88;458122]if you take away the overlap you have 28 possibilities remaining ( including 666 111 etc only once not three times). edit:doh I now see that this is already explained in that link.[/QUOTE]
Just to share, you do understand that the house always wins (statically)? There is a reason lotteries are not popular where gambling is legal. 
[QUOTE=chalsall;458142]Just to share, you do understand that the house always wins (statically)?
There is a reason lotteries are not popular where gambling is legal.[/QUOTE] my point was one of best case scenarios because some numbers get better odds in the setup than others do. xxx will have the best win with straight/box combo xxy xyx and yxx forms still have best win for them in straight/box combo but are at lower number of possibilities than the forms xyz, xzy, yzx, yxz, zxy, and zyx. 
[QUOTE=science_man_88;458143]my point was one of best case scenarios because some numbers get better odds in the setup than others do.[/QUOTE]
It's a bit like trying to teach calculus to a mouse. 
[QUOTE=chalsall;458142]Just to share, you do understand that the house always wins (statically)?[/QUOTE]
How about dynamically? 
[QUOTE=schickel;458073]So, if there's a ~37% chance of not drawing one number in 1000 draws, what would be the odds of missing a win in the following scenario: take 10 different numbers and play them for 100 draws.
Intuition would seem to say that 10(numbers)x100(draws) = 1000 "trials" which would seemingly make it a certainty that you would hit once, but I don't know enough about how to calculate the odds in that case.[/QUOTE] It doesn't matter what numbers you pick, the odds are the same. Whether you pick 734 a thousand times or 000 then 001 then 002 then ... then 998 then 999, the chance that you don't win any is ~37%, the chance that you win once is ~37%, the chance that you win twice is ~18%, the chance that you win three times is ~6.1%, the chance that you win four times is 1.5%, and so on. 
[QUOTE=CRGreathouse;458187]It doesn't matter what numbers you pick, the odds are the same ...[/QUOTE]... assuming a nonbiased digit selection process. In any physical device used to select the digits there will always be some bias. As to whether that bias is large enough to detect, or exploit, would need to be determined on a casebycase basis.
For most of these public lottery things the bias is probably very very small, and might be impossible to determine in any confident way. So I'd guess it is not an issue in this case. But if the number selection process is secret and hidden, or prerecorded, then all bets are off. Any number of shenanigans could be happening. 
[QUOTE=CRGreathouse;458187]It doesn't matter what numbers you pick, the odds are the same.[/QUOTE]
What I consider is the most sad is so few understand statistics. Take, for example, [URL="https://en.wikipedia.org/wiki/Monty_Hall_problem"]the Monty Hall problem[/URL]. So few people understand that when given additional information (by a door being opened) their random guess should change to the alternative door. And yet so many people continue to buy lottery tickets. Or, as it is also known, a tax on those who are bad at the maths. 
[QUOTE=chalsall;458229]What I consider is the most sad is so few understand statistics. Take, for example, [URL="https://en.wikipedia.org/wiki/Monty_Hall_problem"]the Monty Hall problem[/URL].
So few people understand that when given additional information (by a door being opened) their random guess should change to the alternative door.[/QUOTE] I'm loathe to draw conclusion based on Monty Hall. I've seen many formulations which are underspecified, and the actual practice on the show does not match the mathematical version generally/always presented, so this seems like a questionable example to generalize from. 
[QUOTE=chalsall;458142]Just to share, you do understand that the house always wins (statically)?[/quote]The odds are on the house side, true, but state sponsored games have the advantage that no pit boss will be showing players the door becuase they're winning "too much".[quote]There is a reason lotteries are not popular where gambling is legal.[/QUOTE]In the USA there are only 6 states that don't have lotteries. Nevada is a state that could be considered a big gambling state and they don't have a lottery, but New Jersey, which would also be considered a big gambling state, does. Utah should be understandable in not having a lottery or gambling.

[QUOTE=retina;458188]... assuming a nonbiased digit selection process. In any physical device used to select the digits there will always be some bias. As to whether that bias is large enough to detect, or exploit, would need to be determined on a casebycase basis.
For most of these public lottery things the bias is probably very very small, and might be impossible to determine in any confident way. So I'd guess it is not an issue in this case. But if the number selection process is secret and hidden, or prerecorded, then all bets are off. Any number of shenanigans could be happening.[/QUOTE]According to their procedures [URL="http://www.calottery.com/sitecore/content/ARCHIVE/media/factsheets/drawprocedures"]page[/URL], all California draws are conducted in the presence of a representative from an independent CPA firm, presumably contracted, so take that for what it's worth. The only game drawn mechanically right now is SuperLotto (5/47 + 1/27); everything else is done with computers. Therer are two onsite machines and an offsite backup. , For each draw one machine and one of two methods to generate the numbers is chosen. I would imagine that if some bias could be found, that would be the scoop of the decade (or some kind of pattern could be glaned from the cashing patterns.) 
So the real reason I posted this was to check how crazy I was for trying a system that I came across while looking for some pick3 tracking software (nothing that I found that was really recent or too capable, especially without having to plunk down $50 or more to try it out.) If there were bias to be found, 14,448 draws might be enough to have it start to show.
Anyway, I found this [URL="http://www.steveplayer.com/"]blog[/URL] with a couple of progressive systems; basically a martingale system where you play until you win, increasing bets when you lose, though the progression isn't "keep doubling until you win", since the odds on the game are not 50:50. For some reason I didn't choose the [URL="http://www.steveplayer.com/resources/progressivewagering/"]box prize[/URL] side of things (maybe the prize wasn't big enough to tempt my reptilian gambling brain enough) so I jumped right in with the [URL="http://www.steveplayer.com/lotteryblog/2016/11/04/general/lotterylearningcenterserieshittingstraightpick3numbers/"]straight prize[/URL] side of things. Starting back in February I played a bunch of Daily 3 games. The suggestion is to play either the afternoon or evening games only, but it's way easier to just play striaght through and use the advance feature. After three wins, I wanted to get a feel for what kind of risk I'm really running. Baesed on the chart, you can tell how far I was based on the amounts I was risking. First run, amount played: $1260, win: 3 @ $579=$1737, net win: $477 Second run, amount played: $290, win: 1 @ $409, net win: $119 Third run, amount played: $760, win: 2 @ $572=$1144, net win: $384 So after three wins in 3 months, I am up $980 over the series and this was with the same 10 numbers for the whole run. Also, since California pays all prizes parimutuelly, the first and third prizes were more than would have been wom with a fixed prize amount. And I could have netted slightly higher by playing each day, rather than using the advance draw feature noted above; all the wins were about in the middle of the series of 14 games you can play ahead, so I may have left $5060 on the table by being lazy. (The really nice thing is that the first win was 3 prizes under the cashing limit for a retail location, so no waiting and no 1099 at the end of the year!) Looking at the cummulative probability quoted in the thread above, it looks like I was really fortunate that I didn't get myself in a really deep hole, but I should quit while I'm ahead, huh? 
PS.
For a really bizarre game outcome, check out this 5/39 [URL="http://www.calottery.com/play/drawgames/fantasy5/winningnumbers/?DrawDate=1/14/2013 12:00:00 AM&DrawNumber=7009"]result[/URL]. The jackpot starts at $75,000 and rolls until it hits. Whenever I mention this one to someone, I always image the winners at home, jumping up and down because their numbers came up.
The real question to me is: [SPOILER]how many of the players picked these numbers themselves, and WTF were they thinking?[/SPOILER] 
[QUOTE=schickel;458327]Looking at the cummulative probability quoted in the thread above, it looks like I was really fortunate that I didn't get myself in a really deep hole[/QUOTE]
Fairly fortunate. If you play through this person's "straight" method for 103 days or until you win, you win with probability 64.48% with an average net winnings of $265.95, while you lose with probability 35.52% with the whole $1990 gone. Overall expected winnings are $535.27. The probability of winning three times in a row, as you did, is 26.81%. The expectations assume a prize of $500, as at the link. Your prizes were of different sizes, averaging slightly higher ($520); depending on how these numbers are determined the expectations will vary, but the basics will be the same. [QUOTE=schickel;458327]I should quit while I'm ahead, huh?[/QUOTE] Yes. Each additional game you play causes you to lose money, on average. 
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[QUOTE=schickel;458324]Nevada is a state that could be considered a big gambling state and they don't have a lottery, but New Jersey, which would also be considered a big gambling state, does. Utah should be understandable in not having a lottery or gambling.[/QUOTE]
The point I was /trying/ to make was that for the experienced gambler, the odds of winning via a lottery is *much* less than most games at a casino. As in, the state lottery "house" has much better odds. Don't let the *very* unlikely (but possible and occasional) big payoff you see others get distract you. I have never understood the thrill of gambling (other than in business calculated risks)  it just doesn't make mathematical sense to me. But if one must gamble (or enjoys it), I would argue a game of poker amongst independent agents (possibly also friends) makes far more sense. 
[QUOTE=CRGreathouse;458273]I'm loathe to draw conclusion based on Monty Hall. I've seen many formulations which are underspecified, and the actual practice on the show does not match the mathematical version generally/always presented, so this seems like a questionable example to generalize from.[/QUOTE]
Again, the point I was /trying/ to make is that statistics can be exceedingly counterintuitive. Humans are great at pattern recognition, but sometimes they perceive things which aren't really there. They make (sometimes bad) decisions based on this. This was fine when our ancestors ran from a field thinking they had seen a predator; in such cases a "false positive" didn't have a huge amount of downside compared to a "false negative". 
[QUOTE=schickel;458328]For a really bizarre game outcome, check out this 5/39 [URL="http://www.calottery.com/play/drawgames/fantasy5/winningnumbers/?DrawDate=1/14/2013 12:00:00 AM&DrawNumber=7009"]result[/URL]. The jackpot starts at $75,000 and rolls until it hits. Whenever I mention this one to someone, I always image the winners at home, jumping up and down because their numbers came up.
The real question to me is: [SPOILER]how many of the players picked these numbers themselves, and WTF were they thinking?[/SPOILER][/QUOTE]Hopefully they were thinking: "I just want to pick numbers that no one else chooses, so then I get the entire prize to myself and don't have to share it with anyone else." Otherwise that number sequence is just as good as any other. There is no reason in particular to either avoid or choose that sequence (except for the thought I posted above). 
This reminds me, there was a veryVERY good russian comedy long ago, called [URL="http://www.imdb.com/title/tt0084716/"]"SportLoto '82[/URL]", where the winning sequence was "1, 2, 3, 4, 5, 6", or so. No math in it, but the movie is extremely funny, nice to see, good Russian humour in it, and will make you laugh hard, assuming you can find En subs for it (the original version with original Russian sound can be easily found on torrents).
Edit: [URL="https://en.wikipedia.org/wiki/Sportloto82"]wki link[/URL] (no spoilers, safe to read) 
I haven't posted anything for a while so just to keep my stats up...
Xyzzy's post is one of the best in this thread. To address the question in general use the double slit analogy for coherence regarding what is random and what is not; Fermi, Bose Einstein.... Combinatorial methods discretize unique choices, probability paths develop a manner of choosing and statistically the multinomial distribution provides an overall picture of draws without replacement like the Canadian 649 lottery. Epstein's book, Hamming's "Numerical Reference for.." describing Herschel's derivation of the normal curve,Benford's Law (some excellent peer reviewed papers exist on this topic) are some good sources as well as some popular articles (ie. Southampton lottery analysis) give some tips like choosing "unpopular" numbers... . Recent results in AI/GPU research such as the GO and Poker tournaments and blackjack software such as what Qfit provides are good technological approaches to exploiting entropy for fun and profit. 
The insanity goes on....
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....or, "How to Develop a Problem Gambling Habit in 4 Easy Steps".
So, after reading everything here, I decided, what the hell, I'm up a little, let's just waste some money (up to what I've won), just for laughs. As I said, I like to put everything on autopilot, so I bought in again with the 14play (7 day) plan. It ran a week with no hits and had one draw left. For some reason that day, my OCD bone was tickling me more than usual, and since I had bought in starting with the evening draw, I decided to pull the trigger early and buy the next round starting on the afternoon draw, overlapping the last run by the afternoon draw. Luckily, I'm not superstitious or anything, because this was the result: 
[QUOTE=retina;458495]Hopefully they were thinking: "I just want to pick numbers that no one else chooses, so then I get the entire prize to myself and don't have to share it with anyone else."
Otherwise that number sequence is just as good as any other. There is no reason in particular to either avoid or choose that sequence (except for the thought I posted above).[/QUOTE]Yeah, well even before I got really heavy into this, I had read stories about the number of [URL="http://www.dailymail.co.uk/news/article2301360/TheLottonumbersavoidGoing123456bringtinywindfall.html"]people[/URL] who play (to me) "stupid" picks, like [I]the first X numbers[/I] or any [I]X sequential numbers[/I]. Granted, I've wasted a lot of money but we have several regulars who put me to shame. I just realized the other day that I have not seen one of our Fantasy 5 players who played every day to the tune of $35$40. And talk about optimism, he wanted all his played register receipts done separately from his cashing receipts, because he was going to use all of them to write off against any jackpot that he might win. 
Here are some facts which unfortunately are likely to cause some to ignore the first fact.
* In the long (enough) run thehouse will be the winner. * If the casinos did not have upper table limit, they would go bankrupt probably in a day by people with deep pockets (or on very lucky streaks ) playing double or nothing * In absence of an upper limit such as is the case with some daily draws the limit is set by the amount of money that you have * Due to the slight bias in favor of the house such as paying double on a probability of 18/37 in roulette, in the long run the house will always win( unless you can make them run out of money breaking the iterations). It is easy to verify this by computer simulation. It never fails to work in favor of the house given large enough number of iterations. 
I need to add the following:
* In double or nothing style gambling, where you play the minimum bid in the beginning and after each win and double your bid after each loss( assuming there is no maximum bid), the expected winner is the party with more money which is usually the lottery corporation. 
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6 minutes 9 seconds in is semirelevant to a1call's point 
This thread piqued my interest because it touches on the concept of randomness and other fundamental notions. The original post referenced a system with replacement of the draw numbers chosen. As a simple extension, miniaturize this system to the dimensions of a quantum state where Bell's theorem applies. (The added assumption of miniature people choosing their quick picks in this system may/may not apply.)

Please disregard the above post.
Aside from `magic` and `cheating` in gambling/gamesofchance, there is usually a working strategy or one doesn't exist. There are some excellent expositions on gamesofnochance. For poker, `The mathematics of poker, Chen`, is a good read. Complementing that are a few good sites that provide tips on building a decent pokerbot. Regarding lotteries, I found that an application of the gamma function that provided a quick way to establish a sample set of lottery numbers for the 649 relative to the jackpot size. Traversing the lottery database using historical winning numbers, the results were boom or bust. As with blackjack, every edge counts..so look at the subsidiary prize structure, extra bonus prizes, etc.. that may marginally improve your [url=https://betrig.com/compareodds/]betrig[/url] odds. Otherwise, give your designated dispensable funds to a charity or homeless person. 
While in NYC we picked up a Power Ball ticket and I just checked it online with the obvious results. I also clicked on the "Lottery Prediction" tab and saw this caption, "Astro Numerology Lottery Predictions."
You can't go wrong with that title! As an aside, we saw Dave Chappelle at the Comedy Cellar testing some material. The odds of that happening were astronomical so the trip was worth it for that alone. 
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So I stopped playing for a while because life caught up with me but I started playing around with this again and have caught both ends of the odds since the first of the year.
The first one is during a streak when I was ~$2400 in the hole and finally caught a winner. If it had hit at $480 instead I would have broken even. The second one just hit. For this one I was ~$900 in the hole playing the double ticket level. I also made a stupid side bet on this one: 040 had not come up since draw #10546 on 12/31/2011 and so I decided to make a bet on all three combos straight/box, even realizing that the odds were not any better of it coming up. Boy was that a nice surprise! Added bonus: cashing out $1700 with no 1099 involved. :smile: 
[B][COLOR="Purple"]hi schickel, i am a reseacher of pick three. I have found some solutions or system of probabilites. I would to like to share with sb. I am not native speaker but i am sure i can explain clearly.[/COLOR][/B]

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