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)

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?

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: 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