Is online poker rigged? Research program

Hi all,


Some people say that online poker sites are trying to curb the flow of money from bad players to good players in order to boost their profits.
Is very hard to prove mathematically somenthing like that BUT I can do some math against specific situations.

THE PROBLEM:

Let's say I have hands H1,H2,....Hn where you are against one opponent and one of you two (or both) moves ALL IN.
Let's name your equities E1(H1),E2(H2).....when an ALL IN situation occurs before the river.

Let's define a function that returns the size of the pot when you WIN and 0 when you loose.
R(i)={ 0, if you loose
POTSIZE(i)/2, if we have a split
POTSIZE(i), if you are the winner
}


R(1)+R(2)+R(3)..................
and
E1(H1)*POTSIZE(1)+E2(H2)*POTSIZE(2)+.............. .

SHOULD CONVERGE!!!


The problem definition is somehow similiar with the one from 'all in luck/with total winnings' tab from Poker EV.
The differences are:
1. i dont take rake into consideration ..the game is considered 'ideal' (no rake)
2 only headsup 'all in's are considered in my program
3 In POker EV POTSIZE(i) represents the money bet only on the 'all in' street and not total pot size after all in like in my program


HOW TO RUN
The program is supposed to work with PT database (Access/Postgresql->ODBC access)
You also have the option to filter between 'big pot'/'small pot'/'all pots' ALL INs
The program will save 2 log files with the analyze and creates a chart with your result in ALLIN.png image file.

The conspiracy theory says that more than 80% of the winning players dont win their share of 'all in' pots.
With your help this theory can be confirmed or not.

I will appreciate if you can posts your results in this topic along with the mention
big/medium/marginal winner/looser

You can find the program here:
ALL IN PROGRAM

The following image is obtain by running the program against a 250k database and filtering after 'all in' pots>80BB

Thanks,
Valentin

Valentin, it looks like you have put a deal of work into this and I don`t mean to disparage your efforts, but I`m not clear what this proves. Some of your key concepts seem ill-defined. For example:

Where does the boundary lie between a big pot/small pot ? How does it affect the outcome, were we to choose a different boundary ?

And:

Why 80% ? Could we not as well choose any figure between 50% and 100% ? And, if we choose another figure, how does this impact our conclusion ?

And:

how defined ?

Out of curiousity, how does the program handle a split pot?

Misu, i'm not one of the yawns / no posters, i've seen enough clearly defined patterns over different sites and an extended timeframe to be firmly in the "rigged" camp. I do believe that pokersites skew the game somewhat towards the weaker players, in order to keep them at the site and therefore contributing to the rake.

Not really sure what you're trying to show here though. A simple "did I win 50% on my H2H all ins?" is pretty worthless if you dont take into the actual hands involved. for example

2 mythical players, playing 10,000 hands charted against each other.

Player 1 - moderate player, consistent loser. Plays MTT's much too tight. Never steals blinds (even late game). Doesn't call all-ins from short stack when he has huge pot odds, because he has junk. Only plays premium hands.

Player 2 - good player, consistent winner. Players MTT's well, stealing blinds, calling all-ins when he knows he has inferior hand, but has definate pot odds to do so.

The above 2 players, you'd expect player 1 to win a significantly higher portion of all-ins than player 2, but player 2 is a much more successful player.

(and, one O in lose!).

The big/small pot all in filter was created with the following in my mind:
- I was curious if small stacks (usually weaker players) are winning more than their share of pots when 'all in' situation occurs.
- If a site would want to skew the results the big 'all in' pots would be a nice place to start because it's harder to apply statistics on a smaller sample.


The outcome should not be affected by applying such a filter.



And:


The '80%' number is not relevant here. Statistics (standard deviation/confidence intervals) can be applied here and the result of a statistical analyze should be somenthing like:

If M% (e.g 80%) of N winning player databases analyzed are on the losing side of the coin then there is a 95% chance that the coin is not fair.


I'm not an expert in statistics but if I have a sample of databases analyzed I can formulate the problem and give it to other people smarter than me in statistic to solve it.

The R(i) function is

R(i)={ 0, if you loose
POTSIZE(i)/2, if we have a split
POTSIZE(i), if you are the winner
}


Also take into account that E(i) is hand equity ...this means it includes winnings or splits.

I'm not counting if you put your money in good when you move all in (or call all in). I'm trying to see IF you win your share of 'all in' pots.


AA has ~0.83 equity against KK preflop

But even if you win 83% of the pots with AA vs KK maybe you won the 100$ pot all ins and lost the 1000$ pot all ins.


That's why the equity is weighted with the pot size in my program.
Its not about who is winning player or not ..its about players getting their fair share of 'all ins' pot.

But what is their "share"? Even over a huge amount of cards, if hands are decided exactly as per the pre-flop percentages, different players have different shares, it wouldn't be the 50% you're probably presuming it is. A player like Doyle Brunson, winning loads of small pots by pushing with inferior holdings and losing a few big ones when he's called would never expect to win 50% of his all ins, so if the figures show he doesn't, what does that prove?

I compute only ALL IN situations for preflop/flop/turn with 2 players ( one moved all in and the other one called). When this kind of ALL IN happens I compute the equity of my hand at the moment the ALL IN happened.I know exactly at this moment how much I should win/loose in the long run.

The 'expected win' as I defined here its always positive because I dont take into account how much money I invested into the pot.

When an 'all in' happens and the other player calls the hands are face up.

I will take an example :

Hand1:
I move all in preflop and the opponent calls
Me:Kc Kh
Him:Ac Ah
Potsize : 1000$

My expected win is my equity multiplied by potsize:
EV(1) = E(1)*POTSIZE(1) = 0.18*1000 = 1800$

Result of the all in AA wins
R(1) = 0

Hand2:
I call an all in with 8c 8d on the following flop: 9h 8h 5h and the opponent turns Ah 2h for a flush
My equity in this 2000$ pot is 0.345 ( Poker Odds Calculator (twodimes.net) )

My expected win is EV(2) = 0.345*2000 = 690$

Turn is a 5d and river is a Jd and I win with a full house.
So result is R(2) = 2000$

Hand3:
I move all in on turn with 6c 7s on board: 9h 8h 2d As
The opponent calls my all in and he has Qh Qd
The potsize is 1000 and my equity in this pot is 0.182
( Poker Odds Calculator (twodimes.net) )
My expected win is EV(3) = 0.182*1000 = 182$

River is a blank and I loose the hand.
So R(3)=0

The sums
EV(1)+EV(2)+Ev(3)+ ..................
and
R(1)+R(2)+R(3)+ ................

SHOULD CONVERGE

Interesting post. Now i can whine some more about how i should have won more. The only problem is, I play on loads of different sites, how can i compact more than one player name into the same database (or the same nickname, but from more than 1 site). I would appreciate some help with that.

I can currently only see that i should have won about 180 and won 103. And yes, I am a winning player on average.

I would appreciate if you could post your graph in this thread.
At this moment the program will not agregate results from different nicknames but I am going to study this possibility the next days.

Tryed to upload it, hope it worked. There isn't a lot of value in my graph tough, because the sample size is only 60 or so. If I can combine all my different nicknames into one graph it will be a lot better, (about 30.000 hands currently in my PT database). Good luck with your research! I'll keep an eye on this thread, to see if you can make it possible to combine multiple nicknames (or the same nickname on more than 1 site).

Attached Images

ALL_IN.jpg (21.2 KB, 114 views)

And if there are more than two people in the pot? I.e. a three-way pot where the river makes a straight on the board or similar. Is the potsize then split with the amount of players in the pot? Does it take into account who wins what share if they don't all have the same stack size?

Interesting to see someone actually try to use the stats available to test a theory for a change.

That said the first graph isn't the largest sample <1000 pots analysed and seems to be within what would be expected variance from the "ideal" (which of course even in a truly random sample would still deviate from the "ideal").

Work a bit of standard deviation in there and you'll be able to assess the likelihood of that deviation. As I say from what I understand of your model (and there may be some gaps in it as FP says) the graph looks to represent a statistically probable deviation.

The word "should" is very loaded and is inaccurately used. If you toss a coin 100 or 10000 times you might expect the "average" number of heads to be 50% but there is no "should" about it. In fact 95 or 9950 heads would be nothing unusual.

And the larger the sample, the larger the probable deviation in numeric (if not %) terms.

9950 heads out of 10.000 times nothing unusual? I would retake my statistics exam if I were you . Anyway, it would be good to include standard deviation and a p-value (or whatever it's called, I have to retake statistics as well ) as 'proof'.

I take into consideration only 'all ins' with 2 players.
I do take into consideration the fact they might not have the same stack.

I won't even pretend to understand all the math jargon that has been discussed...I took all kinds of advanced mathematics in school, but once I passed the class, all knowledge flew right out of my head.

I will say this though. It seems that people tend to forget that poker is a game of odds, as in, there is a chance a certain event will happen. It's not an absolute. So of course there is going to be variance, despite what the odds say should happen.

Maybe I'm way off, but that's how I see it.

Here's a coin toss simulator

Probability Coin Toss


Here's my first go with 10,000 tosses

Coin Flips= 10000 Heads= 5065 Tails= 4935

My second (wow, spot on!)

Coin Flips= 10000 Heads= 5000 Tails= 5000

3rd

Coin Flips= 10000 Heads= 4943 Tails= 5057

and so on... have a go.

Then read this..

Statistical significance - Wikipedia, the free encyclopedia

Then analyse your data according to the principles.

Then get back to me about the 9950 comment.

Thanks

Rex

It would have been to easy if from 250.000 hands I have statistic discrepancy could be proved. In fact if you check the logs of my program you can see some statistics log messages(standard deviation/confidence intervals).

But you are not testing 250,000 hands, you are testing only those with two all ins, which is a <1000 sample from what I can see.

So can you demonstrate statistical significance? Which would be a starting point for demonstrating there was something going on.

The program was run only for all in pots >80BB
There are also around 2000 all in pots <80BB
I will post a chart with small all in pots included tomorrow.

I dont have statistical evidence on my database. Thats why I am here . Because I need 'aggregation' of results from different databases,

Ooops I just realised I typed 9950, where I meant 5050 (or 4950). Or possibly 9950 of 20000, below. Yes I need to retake basic counting if I think that what I said isn't nonsense. Sorry about that, I'll claim tiredness



If you are assuming a null model, then the size of the pot shouldn't matter (unless your hypothesis is that only the larger pots are rigged?)

You should be able to calculate the significance of deviation from the "average" given a sample size in order to work out how many hands you need to be reasonably certain of demonstrating some significance.

Yikes!! What a huge waste of time this seems to be . . . statistics may be useful here to a certain extent, but you simply cannot quantify luck (as it relates to each individual), nor can you come up with a large enough accurate sample to make this worthwhile; also, you simply cannot just take any PF all-in for another without looking at the context (such as position, stack size, tournament stage, read of opponents, table "climate", etc.) -- pure odds are simply not enough to decide whether or not an AIPF makes sense at any given time with a given hand.

I, for one, firmly believe that any legitimate poker room (online or live) has everything to lose (as in, their entire business) and absolutely NOTHING to gain by rigging anything towards anyone -- I see the same kind of "sick, crazy, unreal, rigged, whatever" stuff happen just about everywhere I play, and someone always ends up ranting about how it's the poker room's, dealer's, deck's, unlucky seat's (etc., etc.) fault . . . yet they always come back to play, anyway. (What does that tell you about poker players?)

Anyway, that's my opinion, and I'm sticking to it! (Oh yes, and I did just bubble out of today's CC Bodog tourney, yet you don't hear me bitching and moaning about the site, do you?!)

I don't think things are rigged, but I commend any effort to attempt to statistically analyse the way sites work. The data will show what it shows and you can get a big enough sample to make it worthwhile.

From what I understand of the model proposed here it seems to be taking account of most things that need to be considered. Beats people remembering things that fit their theory and calling anecdotes evidence hands down.

Credit to you for that Misu (even if I think you'll fail to find the evidence of riggign you are looking for).

Well it sure seems so, but we as card players remember the bad and not how incredibly weve all been in some spots, take sorel mizzi the best internet player, would he say rigged?, he's to busy stealing your pots...........

You`re not way off. In fact, that`s pretty much it in a nutshell. wp.


Agreed. Respect to Valentin for this thread. So much better than the usual "my AA got cracked, it`s a fix" kind of thing that we usually get.

Big time spended doing maths not always means great work,i like math(ì'm a big sklansky's fan)but,in my opinion when you search for a cheat,before starting an enquire you must think about the (presumed)cheater and ask yourself:has he any reason to cheat?
RESPONSE no he hasn't cause is the first interest of casino game(in poker of course,other games are another topic)that game flows crystal-clear.

I just realized I had yet another question regarding methodology: How do you go about dismissing the rake? If you're querying PT for the pot size, won't you get the raked pot size back?

The reason I ask is because the difference in convergence seems to be about $1.50 per hand lost.

In game table from PT there are pot & rake columns

real_pot_size = pot+rake - (any eventual overbet of one player or aniother - >absolute diff for total_bet columns from game_players table )

Okay, cool - just checking.