Two Plus Two Poker Forums What can you relate a deck probability to?
 Register FAQ Search Today's Posts Mark Forums Read Video Directory TwoPlusTwo.com

 Notices

 Probability Discussions of probability theory

 05-28-2012, 05:14 AM #1 journeyman     Join Date: Jan 2010 Location: Bios Posts: 371 What can you relate a deck probability to? Can you relate to a coin flip, can never predict the future? Or is it like BJ? Or, after every shuffle your % of getting pocket Aces are the same? chances of getting AA is 1 out of ever 221 and on the same table at hand #220 you haven't gotten AA yet, what are the chances of getting pocket aces on the hand #221? is it 1/221 or its 220/221? If we changed the deck at hand #220 does it chance the probablity, if we didnt?
 05-28-2012, 07:30 AM #2 veteran   Join Date: Mar 2009 Location: In the wires Posts: 2,272 Re: What can you relate a deck probability to? Past events can't affect future random events. If we don't see AA for 220 hands, the chance on the next deal is still 1/221. And on every deal. Look up Gambler's Fallacy.
 05-29-2012, 02:18 AM #3 veteran   Join Date: Jun 2011 Posts: 2,263 Re: What can you relate a deck probability to? NewOldGuy is right, assuming a fair shuffle after every hand.
06-04-2012, 09:28 PM   #4
journeyman

Join Date: Jan 2010
Location: Bios
Posts: 371
Re: What can you relate a deck probability to?

Quote:
 Originally Posted by NewOldGuy Past events can't affect future random events. If we don't see AA for 220 hands, the chance on the next deal is still 1/221. And on every deal. Look up Gambler's Fallacy.
So after the every shuffle it's like tossin a coin past event don't have to do anything w the future not changing the seat?
Thanks

 06-04-2012, 09:33 PM #5 journeyman     Join Date: Jan 2010 Location: Bios Posts: 371 Re: What can you relate a deck probability to? I have flipped a coin before and out of 10 flips I could get 7 heads in a row however after a 100 flips its more like 45/55, after how many hands dealt we would see this even out? Let's say i haven't gotten aces in 600 hands or I have flopped a boat but the other guy flopped a higher boat. After how many hands we would see this line even out like the coin flip line evening out?
06-04-2012, 10:38 PM   #6
veteran

Join Date: Mar 2009
Location: In the wires
Posts: 2,272
Re: What can you relate a deck probability to?

Quote:
 Originally Posted by bluem3 I have flipped a coin before and out of 10 flips I could get 7 heads in a row however after a 100 flips its more like 45/55, after how many hands dealt we would see this even out? Let's say i haven't gotten aces in 600 hands or I have flopped a boat but the other guy flopped a higher boat. After how many hands we would see this line even out like the coin flip line evening out?
Neither of those is expected to ever even out, on average the gap will continue to get larger in both coins and cards. The proportion of the gap to the total flips is what gets smaller, not the gap size itself. Here's a simple example:

We flip 100 times. Our expectation is 50 heads with a standard deviation of 5. So when flipping 100 times repeatedly, the absolute mean deviation will be approximately 5 away from the expected number. *

Now we flip 10,000 times. Our expectation is 5,000 heads with a standard deviation of 50. So now on average we expect our result to be 50 away from the expected number. We flipped 100x more flips, yet now our average absolute deviation will be 50 away from even instead of 5 away from even. It get's bigger, see?

What does get smaller, is 50/10000 is smaller than 5/100. One is 5% off the mean, and the other is 1/2% off the mean. But that is not "evening out".

So again, not getting Aces in 600 hands has absolutely no effect on how soon you will get Aces again. How would the cards "know" that you were due? Look up Gambler's Fallacy for more detail.

* yes I know the SD is not always exactly the same as the mean deviation but it's very close

06-04-2012, 11:08 PM   #7
Carpal \'Tunnel

Join Date: Sep 2002
Posts: 8,899
Re: What can you relate a deck probability to?

Quote:
 Originally Posted by NewOldGuy We flip 100 times. Our expectation is 50 heads with a standard deviation of 5. So when flipping 100 times repeatedly, the absolute mean deviation will be approximately 5 away from the expected number. * * yes I know the SD is not always exactly the same as the mean deviation but it's very close
It's very close to 4, or about 80% of the standard deviation. The binomial distribution is well approximated by a normal distribution, and the mean absolute deviation for a normal distribution is sqrt(2/pi)*sigma or about 0.8*sigma.

06-04-2012, 11:28 PM   #8
veteran

Join Date: Mar 2009
Location: In the wires
Posts: 2,272
Re: What can you relate a deck probability to?

Quote:
 Originally Posted by BruceZ It's very close to 4, or about 80% of the standard deviation. The binomial distribution is well approximated by a normal distribution, and the mean absolute deviation for a normal distribution is sqrt(2/pi)*sigma or about 0.8*sigma.
I wasn't aware of that ratio so thanks (found a table of other interesting ones here). But using mean deviation makes it easier to explain the point imo (which doesn't change either way).

06-05-2012, 12:20 AM   #9
Carpal \'Tunnel

Join Date: Sep 2002
Posts: 8,899
Re: What can you relate a deck probability to?

Quote:
 Originally Posted by NewOldGuy I wasn't aware of that ratio so thanks (found a table of other interesting ones here).
You get that just by integrating x times the standard normal density from 0 to +infinity which is easy to integrate in closed form. That is, integrate

2/sqrt(2*pi) *x*exp(-x2/2)

where the 2/sqrt(2*pi) replaces the usual normalization factor of 1/sqrt(2*pi) since our effective density function is just the positive half of the bell curve which now must have total area 1 instead of 1/2 since our x can only take on positive values. But this just integrates to

2/sqrt(2*pi) * -exp(-x2/2)

and evaluating at the limits gives 2/sqrt(2*pi) = sqrt(2/pi).

Quote:
 But using mean deviation makes it easier to explain the point imo (which doesn't change either way).
I assume you mean using the standard deviation. The mean deviation is just another name for the mean absolute deviation.

06-05-2012, 12:22 AM   #10
veteran

Join Date: Mar 2009
Location: In the wires
Posts: 2,272
Re: What can you relate a deck probability to?

Quote:
 Originally Posted by BruceZ I assume you mean using the standard deviation. The mean deviation is just another name for the mean absolute deviation.
No, I meant mean. Everyone knows what an average is, and the mean deviation makes a nice clean example. Explaining standard deviation just complicates it.

06-05-2012, 12:32 AM   #11
banned

Join Date: Jan 2009
Location: Mesquite, TX
Posts: 5,584
Re: What can you relate a deck probability to?

Quote:
 Originally Posted by bluem3 Can you relate to a coin flip, can never predict the future? correct Or is it like BJ? a deck of cards is a deck of cards, regardless of the game being played Or, after every shuffle your % of getting pocket Aces are the same? correct chances of getting AA is 1 out of ever 221 and on the same table at hand #220 you haven't gotten AA yet, what are the chances of getting pocket aces on the hand #221? is it 1/221 or its 220/221? 1/221 If we changed the deck at hand #220 does it chance the probablity, if we didnt? no
....

06-05-2012, 02:32 AM   #12
Carpal \'Tunnel

Join Date: Sep 2002
Posts: 8,899
Re: What can you relate a deck probability to?

Quote:
 Originally Posted by NewOldGuy No, I meant mean. Everyone knows what an average is, and the mean deviation makes a nice clean example. Explaining standard deviation just complicates it.
You used them both, and you wrote:

Quote:
 Now we flip 10,000 times. Our expectation is 5,000 heads with a standard deviation of 50. So now on average we expect our result to be 50 away from the expected number.
If you're now saying that "average" here means a mean, which is the average that everyone knows, then on average we expect our result to be 40 away from the expected number, not 50. Moreover, this difference between the standard deviation and the mean deviation goes to infinity as the number of flips goes to infinity, so this statement:

Quote:
 * yes I know the SD is not always exactly the same as the mean deviation but it's very close
is no more correct that the statement that the numbers of heads and tails will be very close.

Last edited by BruceZ; 06-05-2012 at 06:18 AM.

 06-09-2012, 05:16 AM #13 journeyman     Join Date: Jan 2010 Location: Bios Posts: 371 Re: What can you relate a deck probability to? thanks everyone! I appreciate, for the answers.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are Off Pingbacks are Off Refbacks are Off Forum Rules

All times are GMT -4. The time now is 06:21 PM.

 Contact Us - Two Plus Two Publishing LLC - Privacy Statement - Top