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?

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.

NewOldGuy is right, assuming a fair shuffle after every hand.

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

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

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).

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).


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.

....

You used them both, and you wrote:

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:

is no more correct that the statement that the numbers of heads and tails will be very close.

thanks everyone! I appreciate, for the answers.