Recent content by BennyT

Maybe I'm not thinking about this problem correctly, but for the question I'm asking, I don't believe I need a match to be found. I'm just looking for how many shuffles it takes for the probability of shuffles after this number of shuffles matching prior deck arrangements to be 0.5.

I'm sorry, but I don't quite understand why the question I asked isn't just the birthday paradox with 52! as the number of days. I may have said something earlier to convince you otherwise. So what exactly is the difference between the birthday problem and the other more complicated one? I am...

I found that p(no match)=e^(-(N^2/(2n)) where n is my number of combinations. Then 1-p(match)=p(no match) and taking the log I get ln(1-.5)=-(N^2/(2n) so N=(-2ln(1/2)*N)^(1/2).

Would that constant by any chance be (-2ln(1/2))^(1/2)?

EDIT: I also would like to take the time to figure out the actual answer to this question on my own, but what I'm really looking for guidance for is looking at the probability as a function of N so that I may be able to translate its expression into a way Mathematica or another computational...

Oh, by subsequent shuffles I think I meant the next shuffle after N shuffles will have a probability of 0.5, and then shuffles further on would be greater than or equal to 0.5. So I guess subsequent was just referring to the shuffle at which the probability after N shuffles is at least 0.5, or...

I was expecting an answer around order 10^34, so that sounds spot on. Thank you for clarifying my issues with probability. That's actually what I wanted to check more than anything as I'd like to try the problem, the actual solving of it, on my own. May I ask how you ended up finding that in...

After looking into the birthday paradox, it appears to be the same problem but instead of 365 options, I have 52! options. So, I am a bit skeptical as to whether, approximations or not, I will be able to produce a number answer.

Also, the overall goal is to find an expression which I can give to Mathematica to determine the number of shuffles I need to meet this condition. Honestly, I don't know if I'll actually be able to considering the size of these numbers and Mathematica's number limit. But I'm also considering...

Do you mean that it should be (1/32)+(31/32)(2/32)+(30/32)(31/32)(3/32) instead? I'm not quite sure I'm thinking properly about my probability.

I'm definitely going to give this a read. Thank you for your help. To clarify, I'm looking to find the number of shuffles (with the assumption no successful deck match has been found prior) necessary so that the probability of subsequent shuffles matching anyone of the unique combinations...

Homework Statement The problem I'm having involves looking for a specific formula for the probability of matching a deck of playing cards via the result of a shuffle. I want to know how many times I must shuffle for the probability of the shuffle matching one of the past resulting decks to be...

I think I do. Its the function f (x,y) equal to some constant, say k. Maybe this is right, maybe not. But when k=f (x,y), k=arctan (x/y) or y=x/(tan (k)), right? So I believe it is the function set so that the set of x and y values must equal the value k. I don't know, thank you for your...

See that's the thing. I know this is a simple question, but I'm having a total blank. Thank you for your help and I understand if you can't show me more.

Homework Statement Let f(x,y)=arctan(x/y) and u={(√2)/2,(√2)/2} d.) Verify that ∇fp is orthogonal to the level curve through P for P=(x,y)≠(0,0) where y=mx for m≠0 are level curves for f. Homework Equations The Attempt at a Solution ∇f={(y)/(x^2+y^2),(-y)/(x^2+y^2)} m=1/tan(k) where...