Here's one if you ever want to be someone in the poker world

[SmackinYaUp]

If you cannot solve simple problems such as this, you have no place in the poker room. Results will be posted after you reply (and show proof - I don't want any bullshitters in here!)

Let be sequences such that



Let and
Does the sequence { 8n } converge?

Also, how does this apply to poker?

Thanks


-Oh and there's a prize whoever answers it correctly and fully first without cheating.

[BobbySalami]

Ill get this given some time....i will just have some trouble with how it applys to poker........

[a500lbgorilla]

Done.

I laughed. R-D-R-R!

-'rilla

[Demiparadigm]

I hate you...
Maybe when I get off work I'll try and figure this one out

[hydroseeds]

Integral of f(b) minus integral of f(a) is the fundamental theorem of calculus.

And that's all I remember.

[BobbySalami]

hmmm......I may be missing the boat since it is late at night and I'm tired, but heres what I have.

Since a1>b1>c1>1....you are always adding a positive non-zero number to an (although it is theoretically zero.) Therefore since one of the subsequences (e.g an+1>an) diverges, 8n would never seem to converge?.....

Hmmm.....I must have missed something since I see no way this is related to poker. Am i warm?

BTW, nice Simpsons reference 'rilla

[ensign_lee]

{Sn} does NOT converge, because since a1, b1, and c1 are all bigger than one, and because they're bigger than one, this logically implies that they are all positive.

Because they are all positive, the 1/2^2548(variable + variable) part in each series will never dip below zero (i.e. become negative), and so the value will be forever increasing. Granted, it will be increasing at infinitely smaller intervals, but it will still be increasing. Thus, the series cannot converge.

Closest thing I can figure for this being related to poker is that this has to do with teh Fourier Transformation, which has to do with sinusoidal curves. The sinusoidal curves then would represent variance in poker. Because the series' don't converge, that would mean not all poker players will get to the same point in the long run (i.e. lose their money to each other to the point where everyone is exactly equal). The long run is infinity here, obviously.

Then, the series would prove that good poker players are able to deviate from losing their money to everyone in general by taking money from bad players. And because the series are continually going upwards, that as time went on (and presumably, good players moved up in limits), variance would get smaller and smaller.

That's the best I can do as far as a reference to poker. You'd better have something godo for making me solve those stupid series. Took me like half an hour.

[jmontis]

lol math

[Jeebus Kliest]

π

:nod:

Banana Cream..mmm

[Muxy]

π

mmmmm yummy pie.

[sinky]

42

Psssst, can you tell me the answer to question 1?

[Miffed22001]

no it doesnt converge
i have no idea how but it doesnt
is this the equation for AA vs KK
:P

[arkana]

Since a1>b1>c1>1....you are always adding a positive non-zero number to an (although it is theoretically zero.) Therefore since one of the subsequences (e.g an+1>an) diverges, 8n would never seem to converge?.....

Not necessarily, the the series 1 + 1/2 + 1/4 + 1/8 + ... converges to 2.
"To take a physical analogy, consider a student who is one yard from the wall of the classroom. He takes a large step to cut the distance to the wall in half. Then he takes another step to cut the distance in half again. He repeates this again and again, getting closer to the wall each time. He never reaches the wall, yet that is his limit postion."

This reminds me of the joke about the maths professor explaining to the engineer that if there was a beautiful girl 2m away from the engineer and he was to take a step closer equal to half of the distance between him and the girl every time he would never reach the girl, to which the engineer just replied: "I can get close enough"

But in this case i don't think the series converges because the term you are adding doesn't decrease fast enough...

[journey075]

no. fuck sequences.

N.

[BobbySalami]

Since a1>b1>c1>1....you are always adding a positive non-zero number to an (although it is theoretically zero.) Therefore since one of the subsequences (e.g an+1>an) diverges, 8n would never seem to converge?.....

Not necessarily, the the series 1 + 1/2 + 1/4 + 1/8 + ... converges to 2.
"To take a physical analogy, consider a student who is one yard from the wall of the classroom. He takes a large step to cut the distance to the wall in half. Then he takes another step to cut the distance in half again. He repeates this again and again, getting closer to the wall each time. He never reaches the wall, yet that is his limit postion."

This reminds me of the joke about the maths professor explaining to the engineer that if there was a beautiful girl 2m away from the engineer and he was to take a step closer equal to half of the distance between him and the girl every time he would never reach the girl, to which the engineer just replied: "I can get close enough"

But in this case i don't think the series converges because the term you are adding doesn't decrease fast enough...

Well, I had trouble with the addition of such small numbers onto an...therefore I went with one of the theorems from theoretical calculus in this case that if one of the subsequences get larger (e.g an+1>an) then the overall sequence does not converge.......but maybe it doesnt apply here for some reason....

[storm75m]

- I don't want any bullshitters in here!)

shit, I had this thing completely figured out, but I'm automatically disqualified. just lovely.

[Pizzaman]

Well, based on your original statement, I have no place in the poker room. BUT, I have a solution. Why don't we both go out back, you give me half the money you were going to lose, I'll kick you in the nuts, and we'll call it a day. Sounds like a plan.

[Greedo017]

this has gotta converge to something, because if it was divergent this question would be pointless.

arkana is right, just because you're adding an infinite number of positive numbers doesn't mean it never converges. ya gotta like, test it and stuff.

[BobbySalami]

Well logically it converges to something......but this is where I had problems....pick 3 numbers arbitrarilly where a1>b1>c1>1..and use them in the sequence of equations.....you keep adding smaller and smaller values sequentially to the next sequence.....

but thats where I get confused, your adding infintesimally small numbers so it "appears" to converge to a1+b1+c1...which doesnt make any sense so I am giving up.......lol

[hydroseeds]

LOCK THIS THREAD.

[SmackinYaUp]

Well, based on your original statement, I have no place in the poker room. BUT, I have a solution. Why don't we both go out back, you give me half the money you were going to lose, I'll kick you in the nuts, and we'll call it a day. Sounds like a plan.

I'll murder everyone you ever loved or have even seen.



Anyways, ensign_lee was the first with an amazing display of math superiority and somehow most of you came to the same conclusion as he did. I was hoping for some more math-oriented proof from you children besides your feeble-minded attempts at explaining this to me in laymen's terms. I am a semi-god on earth so there was no need to dumb it down for me.

Here is the answer:


No, it doesn't converge.

Clearly, each of , and is an increasing sequence. Thus, they are subject to the "monotone sequence alternative": either they converge or they tend to infinity.

Suppose each of them converges:

Then, taking the limit in the recursive formula,

This is impossible. Therefore at least one of the sequences tends to infinity and


Ensign, your diligent obedience will not be forgotten, and I have chosen to handsomely reward you with this nifty picture that can be used as an avatar, signature, display of your masculinity, printed and posted on your truck, used to scare children, or even copied and pasted onto the head of your favorite super model:




May my glowing radiance forever shine on you children and make your days bright. Goodbye.

[Greedo017]

Also, how does this apply to poker?

Thanks

[TylerK]

lol math

[TylerK]

lol math

(nerds)

[ensign_lee]

Yes; how does this apply to poker?

And the prize sucks.

[SmackinYaUp]

Wow, what happened to the excitement here? Everyone seemed to anticipate the answer to this question that I didn't think anyone even did anything except click refresh on their browsers. But now that the answer's out, everyone has moved on.

Yes; how does this apply to poker?

Closest thing I can figure for this being related to poker is that this has to do with teh Fourier Transformation, which has to do with sinusoidal curves. The sinusoidal curves then would represent variance in poker. Because the series' don't converge, that would mean not all poker players will get to the same point in the long run (i.e. lose their money to each other to the point where everyone is exactly equal). The long run is infinity here, obviously.

Then, the series would prove that good poker players are able to deviate from losing their money to everyone in general by taking money from bad players. And because the series are continually going upwards, that as time went on (and presumably, good players moved up in limits), variance would get smaller and smaller.

Good enough for me! Plus, if you're able to rack your brain with math stuff like this and not shove a 6 inch long railroad spike through your own spine, then you will be able to sit around the poker table for hours counting pot odds with no problems!

And the prize sucks.

The true reward should be the deep sense of accomplishment you gained from working a challenging problem...not to mention the girls that will undoubtedly flock to your front door step starting first thing in the morning.

Oh and I only lost 3.5 buyins tonight so you can take my word on these things.

[SmackinYaUp]

(nerds)

[arkana]

Please explain to me how these equations are associated with the Fourier transform. As far as i can remember the equations for the Fourier transform look nothing like this. Also saying the variance can be represented by sinuisoidal curves is meaningless because any function can be represented by a combination of sinuisoidal curves (and this is the basis of the Fourier Transform).

I was looking forward to some awe inspiring revelation but the actual answer was as disappointing and unsatisfying as teenage sex. It looks to me (feel free to prove otherwise) that you just picked some sequences at random that dont converge and use that as an argument for players being able to win money over the long run.

[SmackinYaUp]

the actual answer was as disappointing and unsatisfying as teenage sex.

Oh thats terrible to hear. What kind of teenage sex did you have?? Mine was the best.

[OopsYouLost]

Hey, this is my first post in the FTR community!
Ain't this topic proliferating GAAAYNESS?!?!?

[a500lbgorilla]

Ain't this topic proliferating GAAAYNESS?!?!?

This is clearly your first post in the community. Do you see why?

-'rilla

[ensign_lee]

Please explain to me how these equations are associated with the Fourier transform. As far as i can remember the equations for the Fourier transform look nothing like this. Also saying the variance can be represented by sinuisoidal curves is meaningless because any function can be represented by a combination of sinuisoidal curves (and this is the basis of the Fourier Transform).

I was looking forward to some awe inspiring revelation but the actual answer was as disappointing and unsatisfying as teenage sex. It looks to me (feel free to prove otherwise) that you just picked some sequences at random that dont converge and use that as an argument for players being able to win money over the long run.

I was pulling stuff out of my ass, arkana. Couldn't think of any rational way that this was related to poker, but I took a stab at it. Figured that SmackinYaUp would provide the real answer.

So don't insult me. :P

[OopsYouLost]

Ain't this topic proliferating GAAAYNESS?!?!?

This is clearly your first post in the community. Do you see why?

-'rilla

hmmm...you emphasize the word "clearly", is this some kind of mind games you're playing or am I just paranoid here?

[SmackinYaUp]

Clearly he was making fun of my word choice.

I did not make this problem up nor did I solve it myself. I copied it and I have no idea what it is or what it means, but it looked neat. I still give ensign_lee my award because he did good on the math and he did a good job bullshitting in a place where no bullshitting was allowed. I mean really, who in the real world is gonna ask you to please bullshit them? Nobody. How often do you need to bullshit? All the time!

Sorry to disappoint you arkana...

[CrunchyNuts]

Awww, I just found this thread and am now highly disappointed...thought I might have some more company in my math nerditude. ;(

[SmackinYaUp]

Yea I kinda feel like an asshole now. I didn't think I'd really get peoples' hopes up that high. I'm just a shell of a human being and maybe this is why my girlfriend hates me...