Author Topic: Is Random.org truly random? (Read 4002 times)

Prof Underwood · « **on:** September 30, 2009, 11:59:02 PM »

I've seen people using this, and decided to test it out. It has a place where you can draw cards from a standard deck. I drew 10 each time, and below are the results.

1st - three 4's, two 6's, two Q's, two A's
2nd - two J's, two A's
3rd - run of 7 (A,2,3,4,5,6,7)
4th - three J's, two 10's
5th - three J's, two 2's
6th - two 3's, two 5's
7th - three 7's, run of 5 (7,8,9,10,J)
8th - two 2's, two 7's
9th - two 5's, two 10's, run of 5 (9,10,J,Q,K)
10th - two 4's, two 8's, two 10's, run of 4 (8,9,10,J)

Can someone who is good with statistics tell me whether it is normal to get such a distribution?

Colin Michael · « **Reply #1 on:** October 01, 2009, 01:13:35 AM »

That would be probability, not statistics since you are working with the entire parameter (52 cards).

It doesn't look normal to me, but I don't know what the motivation for stacking such a program would be.

sk · « **Reply #2 on:** October 01, 2009, 01:14:42 AM »

Isn't that the list of phases in Phase 10?

Anyhow, as to your question, random.org itself has an article that kinda explains randomness. Here's the gist of it:

Basically, random will never look random.

TheMarti · « **Reply #3 on:** October 01, 2009, 01:33:10 AM »

Quote from: Colin Michael on October 01, 2009, 01:13:35 AM

That would be probability, not statistics since you are working with the entire parameter (52 cards).

It doesn't look normal to me, but I don't know what the motivation for stacking such a program would be.

Probability is a chunk of statistical studies. He was just using the broad term.

It's 1:30 in the morning, but if I'm awake enough tomorrow (and have enough coffee..) I may (I use it loosely- I'd have to go back a little bit) be able to sit down and figure it out. At first glance, it actually does look alright.

~Marti

Prof Underwood · « **Reply #4 on:** October 01, 2009, 09:07:10 AM »

Just to add some more data points to your analysis...

11th - two 3's, two 6's, two A's
12th - two 6's, two A's
13th - three 8's, two 7's, run of 5 (5,6,7,8,9)
14th - three 2's, two 7's, two 10's
15th - three J's, two 7's, two Q's, two K's
16th - two 6's, two K's
17th - three J's, two 8's
18th - three 6's, two Q's
19th - two 7's, run of 5 (3,4,5,6,7), run of 4 (10,J,Q,K)
20th - two 3's, two 8's, run of 4 (A,2,3,4)

Prof Underwood · « **Reply #5 on:** October 01, 2009, 09:17:09 AM »

Here are some oddities that I notice.

With only 4 of each card in a deck, I seem to get 3 of them in 10 cards about half the time. (9/20)

I got a run of at least 5 cards about 25% of the time. (5/20)

With 13 different possible cards, it would seem that in 10 cards, most of them wouldn't match, but the opposite happens. Almost all the time there are multiple matches (17/20)

Certain numbers seem to come in clumps. For example there were 8 Jacks between trials 2-5. There was a pair of 6's and Aces in trial 11 AND 12. There were pairs of 7's in 3 consecutive trials (13-15).

TimMierz · « **Reply #6 on:** October 01, 2009, 10:11:59 AM »

I mean no offense, but after your very strange doubts on RTS's drawing, I think you may have a unique view on what randomness is.

I'm not going through all the calculations, but I think the odds of drawing 10 different valued cards out of a standard deck is 1.07%.

Prof Underwood · « **Reply #7 on:** October 01, 2009, 12:39:17 PM »

Quote from: TimMierz on October 01, 2009, 10:11:59 AM

I'm not going through all the calculations, but I think the odds of drawing 10 different valued cards out of a standard deck is 1.07%.

I agree that it would be rare to draw 10 cards and have none of them match. I would expect there to be a pair or maybe even 2 pairs most of the time. I would also expect runs of 3 consecutive cards often.

But I would not expect to get 75% of the Jacks in 2 consecutive draws (4th and 5th). I would not expect to get runs of 5 or more as often as I did. I would not expect to get 3 different sets of matches as often as I did.

I'm not expecting there to be an absence of pattern, but it seems like there is a bit too much pattern to truly be random.

TheMarti · « **Reply #8 on:** October 01, 2009, 01:18:06 PM »

I haven't used Random.org, but I have a question, if I am correct, each of these draws are as if you shuffled again and started with a fresh deck, right? The only reason I ask is because probability rules are different between the two instances.... therefore, making the probability of it being random more probable.

Like I said, I'll run numbers cause I do that for fun... but that's cause I'm a loser. :-D

~Marti

SirNobody · « **Reply #9 on:** October 01, 2009, 02:39:54 PM »

Hey,

If you look for a pattern in a small data set you can almost always find one whether the data set is random or not. It says more about your ability to identify a pattern than it does about the data set. Also consider that runs and sets have an inverse relationship. If you don't have a set it means you have a wider variety of numbers which makes you more likely to have a run.

There are 566,280 possible ten card hands (assuming the order and suit of the cards doesn't matter). You've listed 20 sample hands. So that represents about 1/30,000 hands or .0035% of the possible outcomes. That is such a small portion of the total number of possibilities that it is simply impossible to draw any conclusion from it.

For the record:

Probability of having a hand of 10 different cards: .05%
Probability of having three of a kind: 24.2%

Tschow,

Tim "Sir Nobody" Maly

Prof Underwood · « **Reply #10 on:** October 01, 2009, 03:33:03 PM »

Quote from: SirNobody on October 01, 2009, 02:39:54 PM

Probability of having a hand of 10 different cards: .05%
Probability of having three of a kind: 24.2%

That's the kind of numbers I was hoping someone could figure out. It's cool that I was able to get a 0.05% chance hand in only 20 draws (#3 having 10 different cards).

I am also glad to hear that there is about a 25% chance of getting 3 of a kind (since that is what I got). That still seems high to me though. Can anyone confirm Tim's calculation?

Can anyone figure out if the probability of getting a run of 5 is also 25%?

SirNobody · « **Reply #11 on:** October 01, 2009, 03:56:33 PM »

Hey,

I've done a little work on the probability of a run of 5 and in doing so I've become less confident in the numbers I got for three of a kind and 10 different cards. Doing Probability with limited quantities of identical objects can be extremely tricky. I'll see if I can come up with numbers that I'm more confident about later tonight.

Tschow,

Tim "Sir Nobody" Maly

The Schaef · « **Reply #12 on:** October 01, 2009, 04:48:55 PM »

I would also submit that runs aren't really more or less likely than disparate sets of cards, especially drawing 19% of the deck each test and the fact that each number occurs four times in the deck. The odds of getting 5,6,7,8,9 are the same as getting 2,4,6,8,10 or A,3,9,J,K. Our minds' own tendency towards order is what discovers the patterns in the draw.

I used something closer to a "real world" experiment, drew a hand of five cards from 9-A, basically, a euchre hand. I only ran the simulation maybe 15 or 20 times but I got a pretty broad mix of hands, from Right-King-9 to a hand full of kings and queens. I actually seem to get loner hands more frequently in "real" euchre than the simulated hands

The trick of combinatorics is to figure out the number of different ways your event can occur and the number of different total combinations. A scientific calculator that lets you hit the n! button helps a lot.

To figure out the odds of a flush, for example, you need the number of possible combinations of 5 same-suit, and the number of total possible hands. There are 13 cards in a suit, so to get the combinations, you take 13! over 5! * 8! (5 is the number you want to occur, 8 is the difference from your starting number.

13! is 6227020800, 5! is 120 and 8! is 40320, so 40320*120 is 4838400 into 6227020800 is 1287. So there are 1287 combinations of any five cards of the same suit, times four suits is 5148.

A five-card hand is 52! over 5! * !47, which without doing the math I will just tell you is 2,598,960. So you divide the number of possible flushes (5148) by the total number of 5-card combos (2598960) and you get 0.198%, basically 505 to one odds.

SirNobody · « **Reply #13 on:** October 01, 2009, 05:21:16 PM »

Hey,

Quote from: The Schaef on October 01, 2009, 04:48:55 PM

A scientific calculator that lets you hit the n! button helps a lot.

A calculator with a nCr(x,y) button is even better

Tschow,

Tim "Sir Nobody" Maly

ChristianSoldier · « **Reply #14 on:** October 01, 2009, 09:00:09 PM »

Not to mention a few instances won't give you a good idea of probabilities, maybe if you did 10,000 or 1,000,000 you might be seeing close to the actual probability

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Author Topic: Is Random.org truly random? (Read 4002 times)

Prof Underwood

Is Random.org truly random?

Colin Michael

Re: Is Random.org truly random?

sk

Re: Is Random.org truly random?

TheMarti

Re: Is Random.org truly random?

Prof Underwood

Re: Is Random.org truly random?

Prof Underwood

Re: Is Random.org truly random?

TimMierz

Re: Is Random.org truly random?

Prof Underwood

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TheMarti

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SirNobody

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Prof Underwood

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SirNobody

Re: Is Random.org truly random?

The Schaef

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SirNobody

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ChristianSoldier

Re: Is Random.org truly random?