Lottery pick-3 odds?

[LaurV]

Originally Posted by chalsall

Just to share, you do understand that the house always wins (statically)?

How about dynamically?

[CRGreathouse]

Originally Posted by schickel

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.

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.

[retina]

Originally Posted by CRGreathouse

It doesn't matter what numbers you pick, the odds are the same ...

... assuming a non-biased 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 case-by-case 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 pre-recorded, then all bets are off. Any number of shenanigans could be happening.

[chalsall]

Originally Posted by CRGreathouse

It doesn't matter what numbers you pick, the odds are the same.

What I consider is the most sad is so few understand statistics. Take, for example, the Monty Hall problem.

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.

[CRGreathouse]

Originally Posted by chalsall

What I consider is the most sad is so few understand statistics. Take, for example, the Monty Hall problem.

So few people understand that when given additional information (by a door being opened) their random guess should change to the alternative door.

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.

[schickel]

Originally Posted by chalsall

Just to share, you do understand that the house always wins (statically)?

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".

There is a reason lotteries are not popular where gambling is legal.

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.

[schickel]

Originally Posted by retina

... assuming a non-biased 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 case-by-case 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 pre-recorded, then all bets are off. Any number of shenanigans could be happening.

According to their procedures page, 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.)

[schickel]

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 pick-3 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 blog 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 box prize side of things (maybe the prize wasn't big enough to tempt my reptilian gambling brain enough) so I jumped right in with the straight prize 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 $50-60 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?

[schickel]

For a really bizarre game outcome, check out this 5/39 result. 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: how many of the players picked these numbers themselves, and WTF were they thinking?

[CRGreathouse]

Originally Posted by schickel

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

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.

Originally Posted by schickel

I should quit while I'm ahead, huh?

Yes. Each additional game you play causes you to lose money, on average.

[Xyzzy]