zaphod

if one wanted to make a quick and easy demonstration that online poker cardrooms' shuffles are indeed random, i guess it would be pretty easy, right? just use a little probability to state how many times a given even should happen, then compare data to the theoretical outcome, right?

the only part i'm iffy on, because its been so long since i've slept through a stats class is this: how much deviation from the theoretical outcome is considered acceptable error?

for example, here's the little experiment that i did:

while observing a texas hold'em game, i chose to observe how many times a flop (3 cards on the board) would contain no ace.

in theory, the probability of this happening is:

P(No Ace On Flop) = (48/52)(47/51)(46/50) = (4324/5525) = approx. 78.26%

now, observing 100 flops i ended up with this data:

after 15 flops: 12/15 = 80.00% no ace: +1.74% deviation

after 30 flops: 21/30 = 70.00% no ace: -8.26% deviation

after 45 flops: 32/45 = 71.11% no ace: -7.14% deviation

after 60 flops: 43/60 = 71.66% no ace: -6.59% deviation

after 75 flops: 55/75 = 73.33% no ace: -4.93% deviation

after 100 flops: 75/100 = 75.00% no ace: -3.26% deviation

would this be sufficient, statistically speaking?

whats the calculation to determine how close to the expected outcome i should be in order for it to be acceptable given the amount of data available?

Link

"Until now eight species of animals were found in the cave, all of them unknown to science." - Dr Hanan Dimantman, biologist at Hebrew University of Jerusalem.

While drilling rock at a quarry near Ramle, miners uncovered a cave that had recieved no sunlight in over 5 million years. There, Israeli scientists have uncovered an entire ecosystem adapted to its environment. Along with various bacteria, 8 different life forms which closely resembled scorpions were found.

"Every species we examined had no eyes which means they lost their sight due to evolution," added Dimantman. "This is a cave of fantastic biodiversity."

anyway, long story short: i respect you. thank you for everything.

i just feel that you got "exasperated" very quickly if your first response to one of my fairly basic questions was:

"And? There are 10^10 - 1 such, but what does that have to do with anything?" (implied emphasis denoted)

i apologize if your initial response was perhaps not as clear to everyone as it is to you, and that questions about it came up.

perhaps next time, you should add a disclaimer to your explanations stating that your line of reasoning has been double checked by god himself and that no questions about the integrity of your answers shall be tolerated.

i've never had any beef with you in any of my posts, and i didnt mean to "insult" you. i just think that as an official "math expert" of the board, it shouldnt be too much to ask to explain something that you wrote without giving off the very distinct tone of talking down to the person in question.

in closing, thank you for your help. good day.

after thinking about it over lunch, i understand. thank you for the (somewhat patronizing) explanations, matt

ok, so is there a way to re-define your set S that clearly defines how to cycle through the finite number of strings so as to make sure the cycles never repeat?

is there not only a finite number of combinations possible?

(be back in an hour, lunch time)

You don't see how to get irrational numbers from gluing together strings of finite length? Every irrational is gotten by gluing together strings of length 1 and there are only 10 of those.

to clarify my unease, lets pretend there were only 10 strings s(i).

s would look something like this: s = 0.s(0)ys(1)ys(2)ys(3)ys(4)ys(5)ys(6)ys(7)ys(8)ys(9)ys(1)ys(2)ys(3)ys(4)y....

which would not be very irrational, right?

You don't see how to get irrational numbers from gluing together strings of finite length? Every irrational is gotten by gluing together strings of length 1 and there are only 10 of those.

its not that i'm not clear on how you get a number that is infinitely long, but since the actual number of strings you're gluing together is finite, then i'm just not clear on how you can guarantee the "non-repeating" condition.

but i'm still reading over your "far far better explanation" right now, so i'll get back to you.

(and hey, by the way, i'm on your side. dont see this as a debate between me and you. its just math )

i'm just not clear on how you can guarantee that s is irrational given that the number of strings s(i) is finite.

hmmm.. however, i'm thinking about this part:

"where s(i) is any string of 10 digits except r"

this would be a finite number of strings, right?

brilliant. thanks.

hehe, yeah, i was kind of in a rush to leave work when i posted that last night. i realized after that i should have been more specific.

its quite a long story from another messageboard concerning whether or not your phone number could ever be found in pi. there was a website where you can search the first 2 million decimal places of pi to see if a certain string of numbers is in there.

anyway, debate started about whether or not it was absolutely guaranteed that anybody's phone number was going to be in pi eventually since the decimal expansion is infinite and non-repeating.

i got sick of the debate, so i kinda sketched out a little mathematical argument against it. here's the copy/paste of the post i made:

ok' date=' here it is, once and for all.

 

Is it possible that someone's phone number is not in pi? This question can be generalized by asking the following:

 

[b']Is it possible that a 10 digit string might not be found in the decimal expansion of a number that is infinite and non-repeating?[/b]

 

To answer the question, we will take the set of numbers which are infinite and non-repeating, which is commonly known as the set of irrational numbers, and call it J (which can be found by subtracting the elements of set of rational numbers Q from the elements of the real numbers R.)

 

We will show that there exists at least one element of J, say j, where a given 10 digit string of numbers x is not found. For the purposes of this demonstration, we will choose x to be the following phone number: 416-555-2372, or 4165552372.

 

How do we find this element j of J? We can actually use our imagination and "create" one. For example, if we choose the following irrational number:

 

j = 0.12120120012000120000120000012000000120000000...

 

Would you be able to find x in this string of numbers? The way j is constructed, it would be impossible to find x. We have therefore shown that is is indeed possible that a 10 digit string might not be found in the decimal expansion of a number that is infinite and non-repeating.

 

We can imagine now a subset of J, say S, which consists of all the elements of J that do not contain the string x = 4165552372. This new set S is known to contain at least one element, j.

 

Using the link earlier, we can do a quick search and find that the string x, "4165552372" does not occur in the first 200000000 digits of pi.

 

Now, does this prove that pi is an element of our set S? No, it does not. As far as we know, pi may or may not be an element of S since there is no real way to prove whether or not pi will eventually contain that string x.

 

However, what we have shown is that simply because pi's decimal expansion is infinitely long and non-repeating, this does not absolutely guarantee that everybody's phone number will be found somewhere.

 

-------------------------------

 

In other words, we take a 10 digit string called r. We can create a subset of J, called T, whose elements t are irrational numbers that do not contain the string r. It is not known if pi is an element of T for any given r. It may or may not be. However, what we do know that for any given r, that there exists a non-empty set T.

 

The very existence of this non-empty set T disproves the assertion that any string of numbers must eventually be found in the decimal expansion of an irrational number.

now, this set T is the set in question.

lets say i've got this subset T of irrational numbers that i want to prove is non-denumerable... how should i go about this?

i'm not seeing any way of diagonalizing without guaranteeing that the new number will still be in T.

any pointers?

sexual selection.

would you have sex with a hairy girl? yeah, neither would i.

i am pretty sure the original poster was talking about perfect riffles, but you guys are on a roll, it seems

I have a friend who worked in the previous government (that was ousted by Paul Martin's)

?

paul martin's gov't didnt "oust" anybody.

HUH? Your links are no big help to me. They are not even working! Plus' date=' it will only direct me to a crap dictionary.

 

What does the limit indicate for? Like lim x=pi/2. Does it mean only x value less or equal to pi/2?

 

Also, what does Devrivates mean? Give me examples won't hurt.

 

Thanks[/quote']

 

wow

i think its nifty

We are still stuck at 30... Sure there's an easy answer;

 

[math]4! + 4 + 4 - \sqrt{4} = 30[/math]

 

But [math]\sqrt{4}[/math] is [math]4^{-2}[/math] and it's like using a 2.

yeah' date=' but if [math']\sqrt{4}[/math] isnt allowed, then [math]4![/math] shouldnt be either because its like saying [math]4 * 3 * 2 * 1[/math]

personally, i feel that people using 44, 4.4, .4, etc are bending the rules more than using [math]\sqrt{4}[/math]

that being said,

[math]4! + (4! + \sqrt{4})/ (\sqrt{4}) = 37[/math]

(thanks to whelck for that one)

[math]4! - 4*4 + 4 = 12[/math]

well done on 11, by the way. i'm still looking for a single digit solution for 10. the best i had was

[math]4!/4 + 4 = 10[/math]

[math]4 + 4 + (4/4) = 9[/math]

or

[math] ((4! - 4) / 4) + 4 = 9[/math]

[math]( [4 * 4] + 4 ) / 4 = 5[/math]

or

[math] 4 + ((4-4)/4)! = 5[/math]

[math]4 - ([4 - 4] / 4) = 4[/math]

or

[math]4! - (4*4) - 4 = 4[/math]

[math][ (4 * 4) - 4 ] / 4 = 3 [/math]

does it really? i'll have to change that. haha i had a man-crush on feynman for a little while, and i was really getting into physics for a little while. but i've gone back to hating it.

thats interesting, i had actually started my BSc in Biology (Ecology Specialization), but i couldnt stay away from math. i might finish that off as a minor, though.