How big of a Sample Size needed for a legitimate concern of game fixing

This the cut and paste of what I sent to wizard of odds and I was told to start a thread on the forum.

"I am curious on how to become a confirmed 'wizard' player.
>
> As well, I am starting to get very frustrated with bodog blackjack and have
> recently started requesting my daily hand breakdown so I can crunch some
> numbers. Specifically Im comparing dealer to player blackjacks, % of hands
> dealer get 20/21, and simply % of hands won/lost. The numbers are really
> starting to back up my thoughts. I am at a sample size of about 6000 hands,
> how big of a sample size is necessary to really be suspicious of faulty
> "randomized cards" and if I reach this sample size with the same skewed
> results, would you be of any help. Thanks for your time. "

Quote: danielb

This the cut and paste of what I sent to wizard of odds and I was told to start a thread on the forum.

"I am curious on how to become a confirmed 'wizard' player.
>
> As well, I am starting to get very frustrated with bodog blackjack and have
> recently started requesting my daily hand breakdown so I can crunch some
> numbers. Specifically Im comparing dealer to player blackjacks, % of hands
> dealer get 20/21, and simply % of hands won/lost. The numbers are really
> starting to back up my thoughts. I am at a sample size of about 6000 hands,
> how big of a sample size is necessary to really be suspicious of faulty
> "randomized cards" and if I reach this sample size with the same skewed
> results, would you be of any help. Thanks for your time. "

There is no set number of hands you need. For any number of hands of data you collect, you can figure out the standard deviation and expectation for that, and simply measure how far out on the curve your results are.

For example, if you recorded 10 hands, and the dealer got 10 blackjacks, it wouldn't really matter how many you got. That's already pretty crazy. So, 10 hands could be enough.

The most important thing to do is not pick and choose data. You need complete data log files for some period of play.

If you've done this, please just post #of hands, #player BJ's, #dealer BJ's and I'll crunch a number or two for you. But again, DO NOT SELECT a range of data. You must give this for all data you've collected.

It depends on how far away your results are from expectation. For example with flipping a coin:

Flip a coin 15 times. If you get 10 heads, that's pretty normal / within reasonable expectation. If you flip the coin 15,000 times and get 10,000 heads....now you're onto something weird.

Now if you were to flip it 15 times and got 14 heads, you don't need to do another 15k flips, 14/15 is already very far out of expectation. Doing 50 or 100 more flips, if you're still flipping heads at a rate of 14/15...it doesn't take long to figure out things are awry.

Or if you were to do 8/15 heads. Now doing it 15k times and getting 8k heads (same %)....it's not all too out of the ordinary. If you were to get 800k heads out of 1.5M flips, then you may be getting somewhere weird.

I know a cat who claimed he got ripped of at the bodog bj games. Of course they came back and said his reult was "statistically possible". I said it again and I'll say before, a cat has to be coconut for doing anything other that play poker online, hey hey.

To be a "Wizard player" you need to click through a banner on one of the Wizard sites and sign up for an account at that casino. Don't surf around in between.

As teliot said, there is no magic sample size you need to make a case of cheating. If the dealer got 100 blackjacks in a row, then that would be enough. However, for more subtle forms of cheating, it might take tens of thousands of hands. I could teach a whole college course in answer to the question.

Quote: Wizard

To be a "Wizard player" you need to click through a banner on one of the Wizard sites and sign up for an account at that casino. Don't surf around in between.

As teliot said, there is no magic sample size you need to make a case of cheating. If the dealer got 100 blackjacks in a row, then that would be enough. However, for more subtle forms of cheating, it might take tens of thousands of hands. I could teach a whole college course in answer to the question.

if only 99?

OP
in my opinion, do not pay attention to this poster (RS) behind the curtain
run and run fast and far

of course, after you post all your data

hope you reveal the crimes where they are
they are every where
we are all every where

Quote: RS

<snip>
Or if you were to do 8/15 heads.
Now doing it 15k times and getting 8k heads (same %)....it's not all too out of the ordinary

OMG!
nice trash!
AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

SD = 61 (rounded from a square)
500/61 = it's not all too out of the ordinary

in my opinion again, must be a shill (huh?)
right so

Sally, what IS a shill?
Mully

Quote: soxfan

<snip>I'll say before, a cat has to be coconut for doing anything other that play poker online, hey hey.

hey hey
looks like you B another shill, imo!

in my opinion, go to your God, OMG!

NEVER play online poker for real cash or money! way too much of a gamble
(points count)

only sports betting online
and that can be a gamble too because it (the sports bet) was made too late

sweet!
shills every
where?

hey hey soxfan, I hear (from good people in the US, you won over $16 million US at Baccarat
too bad you still owe over $31 million US for your losses

taxman

Quote: danielb

<snip>% of hands dealer get 20/21,<snip>

for this example over your 6k bets
say the probability of a dealer getting 20 or 21 after checking for a natural = 27% (6deck-H17)

so
p= 0.27
q= 1-p
n= 6000

do this

(p*q)/n
then take the square root of that
i get
0.00003285 for (p*q)/n
0.005731492 <<< this is what i was after
the standard deviation of p (sd of p)

now take .27 and
add 4.417*sd of p (i get 0.025316) to .27

then subtract 0.025316 from .27

now you have a range around p
29.5316% to
24.4684%
the chance of NOT being in that range = 1 in 100,000

that is a small #
but it is a start
you can use 5.327*sd of p for only a 1 in 10 million chance of being outside a range

Oh
i have a biology degree
and was forced to take math

so i suggest you check any answer given
we all have good and no-so-good days

Sally

Quote: RS

Now doing it 15k times and getting 8k heads (same %)....it's not all too out of the ordinary.

I know MS already answered this, but in case you didn't get her rather artistic way of expressing herself, let me be a bit more prosaic.

The expected number of heads is 7500.
The standard deviation is sqrt(15000*(1/2)*(1/2)) = 61.24

Getting 8000 heads then corresponds to a z-Score of (8000-7500)/61.24 = 8.16. That is, getting 8000 heads is about 8.16 standard deviations above expectation. The probability of this result (or more heads) occurring purely by chance is 0.000 .... as far as any calculator or spread sheet can compute that I know about.

The limit with Excel is 7.87 standard deviations. Events that are 7.87 SD's (or more) above expectation occur with probability 0.0000000000000017764, or about 1 time in 562,949,953,421,312. You are at 8.16 SD's with 8000 heads.

So, now maybe you will revise your "not all too out of the ordinary" claim.

Quote: teliot

Events that are 7.87 SD's (or more) above expectation occur with probability 0.0000000000000017764, or about 1 time in 562,949,953,421,312.
You are at 8.16 SD's with 8000 heads.

So, now maybe you will revise your "not all too out of the ordinary" claim.

Oh
i see
thank you

i see this too

Quote: mustangsally

i see this too

Nice. 1-in 5,970,149,253,731,340.

Quote: teliot

Nice. 1-in 5,970,149,253,731,340.

and if OP comes back and shares his data (6k hands played)

maybe you will find similar values

"with bodog blackjack"

bodog will say "no way", imo

round 2
ding!

Quote: mustangsally

Picture

http://www.wolframalpha.com/input/?i=z+score+calculator

I always forget about Mathematica. I programmed using Mathematica on a NeXT station running NeXTSTEP back in the early 1990s. Now, it's so easy.

I decided to experiment to see how far out I could make this work. Here are the results from 68300 standard deviations (it could happen!):

Okay, I didn't do the math. That wasn't the point of my post.

Quote: RS

Okay, I didn't do the math

sure
no math was needed to do

this is done in one's sleep

15000 divided by 2 = 7500
7500 divided by 2 = 3750
SD abouts 60
2SD = abouts 120

maybe the example i show so the OP can grasp this concept
is to use 7,620 and not 8000

















NOT!

Quote: RS

That wasn't the point of my post.

your post had no point, in my opinion
because your examples were, again in my opinion,
ugly and awful (yes, in that order. looks like my examples i used to make way back in school)
you can do better than that
so you must have been having a not-so-great moment


"now you're onto something weird"

thank you for sharing that part

and only weird
and not about improbable

spank me