coin is fair?

[T50_Omaha8]

[ QUOTE ]
What if 80% of the winning poker players ( 5%-20% from total) are in the "unlucky fifth of poker players" ?

[/ QUOTE ]Then there is some 'riggedness.' Since luck and skill should be independent (ie the same expectation applies to everyone), 20% of winning players and 20% of losing players should be in the 'unlucky fifth.'* I'm afraid your data doesn't say anything about anyone besides you, so this sounds like speculation. If you came up with data for other people we'd be more than happy to check it out--I'm quite curious myself.

Let me just note that I find your claims of riggedness to be more interesting than most claims. Most 'rigged' claims come from (1) DonknGo players who see wide preflop disparities very often and (2) cash game players who think the deck is slanted to create more action. The problem with theory #1 is that poker sites have no incentive to carry out such a plan, while the problem with #2 is that starting hand and flop anylsis is extremely easy with a lot of statistical programs available. You claim a much more subtle kind of riggedness which would be a lot harder to detect on a statistically significant level, and which sites actually have some incentive to carry out (ie to curb the flow of money from winning players to losing players). The problem is simply that your anomaly does not appear to be statistically significant. Analyze the hands for other people or play 40k more hands and come back. Results will either converge to the mean or diverge to 'riggedland'.

Addressing your second post--I don't know, and I usually just wait for AaronBrown to chime in again when something confuses me.

*This is not exactly true. Some of the 20% of winning players who are part of the unlucky fifth will have negative winrates, causing them to appear to be losers even though they have a positive expectation at the poker table. That is, the unlucky fifth will have a lower ratio of winners to losers than the whole poker playing population, just as the 'lucky fifth' will have a higher ratio of winners to losers than the whole poker playing population. Here winner and loser means net amount won/lost, not whether the player has a positive or negative expectation at the poker table.

[gaijinuronin]

I have a "feeling" that on the pot gets big I 'm outdrawn more that it should.
Also possible that I'm just bad at poker and instead of trying to test the card randomness I should learn the game better.

So I'm a programmer having some "common sense" math knowledge.
I 've made a program computing my aggregated expected value and aggregated actual result from ALL IN hands that went to showdown.
I'm not a statistician to really interepret the data so I came on this forum seeking for help.

After the math part will be done I intend to add some nice user interface and create a site where the results to be uploaded.
In the end the results will be filtered by site & blind level & BB/100.






[ QUOTE ]

I'm afraid your data doesn't say anything about anyone besides you, so this sounds like speculation


[/ QUOTE ]

Sure it is only speculation.
But the math/statistics can put an "end" to the speculation...or not.



[ QUOTE ]
*This is not exactly true. Some of the 20% of winning players who are part of the unlucky fifth will have negative winrates, causing them to appear to be losers even though they have a positive expectation at the poker table. That is, the unlucky fifth will have a lower ratio of winners to losers than the whole poker playing population, just as the 'lucky fifth' will have a higher ratio of winners to losers than the whole poker playing population. Here winner and loser means net amount won/lost, not whether the player has a positive or negative expectation at the poker table.

[/ QUOTE ]

I think I can weight everything with the number of hands analyzed.So a 20PTBB/100 winner on 200 hands will not matter a lot in the analyze.

[T50_Omaha8]

[ QUOTE ]
But the math/statistics can put an "end" to the speculation...or not.

[/ QUOTE ] Right...that's the point of all this. You should really just include SD of $E as one of the statistics the program gives you automatically--it's really one of the most important stats (right up there with E$ and A$).

You could also program a confidence test right into the program. But I'm afraid you'll need someone with more knowledge of statistics than myself to help you with that. I'm much more fond of probability.

[gaijinuronin]

I'm reading about The Central Limit theorem
(http://en.wikipedia.org/wiki/Central_limit_theorem)

I don't understand how can this theorem be applied here.

It says there that it works with "independent and identically-distributed random variables"

But here each discrete random variable has its own "Discrete probability distribution"

What we have here is a set of discrete random variables R(i)

The discrete random variable is the outcome of an ALL in move
R(i) = {
Potsize(i) , with a W(i) frequency ; W(i)=chance of winning
Potsize(i)/2 , with a S(i) frequency; S(i)=chance for a split
0, with a (1-W(i)-S(i)) frequency ; I loose
}

So I have a set of outcomes R(i) (i=1,N) and also know the W and S.

Huh ..I think it's a total mess in my head about statistics...maybe i should post less.

[T50_Omaha8]

[ QUOTE ]
It says there that it works with "independent and identically-distributed random variables"

[/ QUOTE ] Good point--these aren't identically distributed. Intuitively, I think it or something extremely similar to it still works here (since avg winnings should be normally distributed around the mean), but I'll hold off until one of the statistics pros speaks up.

[Under dog]

Theres a link to this thread on Aba's blog

No doubt posted by a .10/.20 "pokers rigged" washout

Get your tinfoil hats out!!

EDIT: to say left in the comments section obv

[ama0330]

run it over 500,000 games and you might get my attention

[T50_Omaha8]

[ QUOTE ]
come up with some statistically significant results and you might get my attention

[/ QUOTE ]This is how outsiders should be treating OP's claims. As I've said earlier, I don't believe these results are significant (I'm awaiting a stats pro's analysis to be certain), but they certainly diverge from the expected mean over a decent sample. If there is ANY difference in the expected mean and actual mean there exists some sample size large enough (may be more or less than 1/2mil) to detect the difference at a high confidence level. We shouldn't challenge OP to analyze a certain number of games, just to come up with a sample with statistically significant results.

BTW I'm pretty sure he's analyzed far more than 280 hands, these are just big all-ins. If you want half a million all-ins for >80BB, you're asking for an unnecessarily huge sample.

[gaijinuronin]

finally the statistic part of the problem was solved with some help from JakeD

This is the way I defined the problem:
---------------------------

N is the number of some games logged in a database.
In each of these games there was a chance W(i) to win an amount of money P(i)


So in each game I can win R(i) dollars:

R(i) = {
P(i), I win ......W(i) chance to happen
0 , I lost .......1-W(i) chance to happen
}

0<=W(i)<=1

Theoretically after all these N games I should have win something like E = sum after i ( W(i)*P(i) ) with i=1,N

In reality I have won S dollars.

How likely is to have such a big abs(E-S) value??
------------------------------------------
The answer:
- computing the "standard deviation S of the actual payoffs":

the mean is M = S/N
and SD = sqrt (( sum after i of pow( R[i]-M , 2) ) / (N-1)

Then I apply Central Limit Theorem I get a
X% confidence interval (range) for my actual total win.
-----------------------------------

An example:
I've run my program against a 40k hands database and filtering the ALL INs after potsize>80BB

I've got:
Analyzed games: 154
aggregate should_win= 5527.73
aggregate actually_win=4647.30

tau = 1.98 SD = 36.30
Chance of not being rigged: 5.00%

I take z = 1.96 that coresponds to a confidence level of 95%
This means there is a 95% chance that S satisfies:
5527.73 - 1.96*36.30*sqrt(150) <= S <= 5527.73 + 1.96*36.30*sqrt(150) <=>
5527.73 - 871.38 <= S <= 5527.73 + 871.38 <=>
4656.35 <= S <= 6399.11

But S (actually_win) is 4647.30 in our case.

This means there's at least 95% chance to be rigged in big pots.


The interesting part happens when I run the program for small pots ( < 80BB )

Analyzed games: 342
aggregate should_win= 3632.40 aggregate actually_win=3654.20
Average pot:16.80

As you can see the difference 3654.20-3632.40 is very small.



It seems strange things happens when the pot gets big.

If anyone is interested in testing this program on bigger databases please 'private message" me.Thanks.

[gaijinuronin]

One small mistake in the above post:
5527.73 - 1.96*36.30*sqrt(150) <= S <= 5527.73 + 1.96*36.30*sqrt(150) <=>
There should be sqrt(154) instead of sqrt(150) ...but anyway it doesn't significantly the result.