# zaphod

Senior Members

98

1. ## Small Experiment Demonstrating Randomness of Online Cardroom Shuffles

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?
2. ## New Ecosystem Found in Israel

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."
3. ## cardinality of subset of irrationals?

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

5. ## cardinality of subset of irrationals?

after thinking about it over lunch, i understand. thank you for the (somewhat patronizing) explanations, matt
6. ## cardinality of subset of irrationals?

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)
7. ## cardinality of subset of irrationals?

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?
8. ## cardinality of subset of irrationals?

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 )
9. ## cardinality of subset of irrationals?

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

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?
11. ## cardinality of subset of irrationals?

brilliant. thanks.
12. ## cardinality of subset of irrationals?

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: now, this set T is the set in question.
13. ## cardinality of subset of irrationals?

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?
14. ## Why are we naked?

sexual selection. would you have sex with a hairy girl? yeah, neither would i.
15. ## deck of cards

i am pretty sure the original poster was talking about perfect riffles, but you guys are on a roll, it seems
16. ## Canadian Federal Election 2006

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

18. ## I saw a nice proof today

i think its nifty
19. ## Four 4s ongoing challange!

yeah' date=' but if [math']\sqrt{4}[/math] isnt allowed, then $4!$ shouldnt be either because its like saying $4 * 3 * 2 * 1$ personally, i feel that people using 44, 4.4, .4, etc are bending the rules more than using $\sqrt{4}$ that being said, $4! + (4! + \sqrt{4})/ (\sqrt{4}) = 37$ (thanks to whelck for that one)
20. ## Four 4s ongoing challange!

$4! - 4*4 + 4 = 12$ well done on 11, by the way. i'm still looking for a single digit solution for 10. the best i had was $4!/4 + 4 = 10$
21. ## Four 4s ongoing challange!

$4 + 4 + (4/4) = 9$ or $((4! - 4) / 4) + 4 = 9$
22. ## Four 4s ongoing challange!

$( [4 * 4] + 4 ) / 4 = 5$ or $4 + ((4-4)/4)! = 5$
23. ## Four 4s ongoing challange!

$4 - ([4 - 4] / 4) = 4$ or $4! - (4*4) - 4 = 4$
24. ## Four 4s ongoing challange!

$[ (4 * 4) - 4 ] / 4 = 3$
25. ## Factoring Integers

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.
×