Rigged: The AA test

i play exclusively on bodog, and while i dont have specific stats, i do notice aa kk, and qq dealt out in the same hand an abnormal amount of times

The numbers don't seem to lie here. Very interesting thread.

Wow just wow, wow just wow, wow, wow like wow.

Must be rigged then

I don't keep track of my play, but on Poker Stars I get more KK then any other pairs or any othe site, and I loose most of the time getting beat on the river by a draw.
May be the rigged part is that when a monster hand like AA, AK or KK is in play it provide other player with a flop that will give them good draw to beef up the pot. An with their usual reward on the river.
This coupled with loose player to call on draws, it would provide greater rake for the site.

Rohsweee

Id post my results if i knew how i need help ,,,, and dont call me names LOL

If you don't keep track, there's almost no chance you are remembering correctly. The human brain isn't wired for it.

I haven't read every post in this thread, so forgive me if this was covered.

How does the frequency of being dealt AA, or any other hand for that matter, prove that online poker is not rigged?

its a myth that will never be resolved, as there is no direct in proving such stats in-conclusivly that is.

Yes it does favour the sites to keep circulating $ for more rake etc etc.. but then again if it has over 100k players on it for the majority of the time does it need to do this?

I guess its just what side of the coin you see it from.

Over millions of hands, the probability of each card appearing in any given slot (your hand, the flop, the turn, the river) should reflect true randomness. If it doens't, then it's rigged. If it does, then it's not.

Full Tilt
15,567
Dealt Aces: 71 = 0.456%
Win= 94.37%

Dealt KK: 74 = 0.476%
Win= 93.24%

I can see how showing that the distribution of AA is improper would prove that the software is not working properly (“rigged,” although I think that sounds like there is some conspiracy at work, when all we are trying to prove is whether or not the software is selecting cards randomly).

But I don’t see how showing that your AA distribution is correct proves that the software is working correctly in every way. All it proves is that hand distribution looks good….and not even for other hands…just AA in this thread.

It would be great if someone could prove that any given online poker site was perfectly straight, but that would take a lot more than the analysis offered by poker tracker and other commercial software.

It seems to me that looking at AA distribution and claiming that it proves a site is not rigged is like looking at the breaks on a used car and saying it proves the car is in great shape….only you never checked the engine.

You can have perfect AA distribution, but what if you are losing 50% of the times you go all in pre flop heads up? That would be messed up, but your distribution would still look good.

Or what if your distribution is right, and you win the right percentage of hands all in pre flop heads up, but the pots you lost all fell within the top 25% largest pots you were involved in with AA? Then your distribution and win percentage would look good, but that would still be messed up.

Or what if your distribution looked good, your win rate looked good, and the pot sizes evened out, but every time you flopped set over set with another pair, your opponent made quads on the river to beat you? That would also be pretty messed up.

I might be missing something here, but it seems like AA distribution is a drop in the software bucket and it falls short of proving anything. An online poker site would have to be pretty dumb to skew the software on something as easy to see as hand distribution, considering they know what poker tracker can keep track of and they write their hand histories in such a fashion that poker tracker can easily convert them into data.

Personally, I’d like someone to analyze hands based on odds, which is something no commercial program can do right now. I’d like a program to take a large database of hands, group each situation by odds, like all the four to one hands in one group and all the three to one hands in another, and then analyze if players are really winning four out of five hands when they are four to one favorite.

I haven’t seen anything that can do that yet. But that would surely go a lot farther toward proving or disproving than hand distribution.

^^^^one of the best replies in a long, long time, ty

ahahah

ahahahahhaahahahah

WHAT? are you serious?

I found an article on Wikkipedia that gives hand ranking according to expected value.
I think it should provide some interesting statistics to add to the discussion.
It gave me the idea to do the analysis that follows.
This is the link: Texas hold 'em starting hands - Wikipedia, the free encyclopedia

I reproduced one of the tables here:

Tier.. Hands......................................... EV
1..... AA, KK, QQ, JJ, AKs........................ 2.32 - 0.78
2..... AQs, TT, AK, AJs, KQs, 99............... 0.59 - 0.38
3..... ATs, AQ, KJs, 88, KTs, QJs.............. 0.32 - 0.20
4..... A9s, AJ, QTs, KQ, 77, JTs............... 0.19 - 0.15
5..... A8s, K9s, AT, A5s, A7s................... 0.10 - 0.08
6..... KJ, 66, T9s, A4s, Q9s..................... 0.08 - 0.05
7..... J9s, QJ, A6s, 55, A3s, K8s, KT......... 0.04 - 0.01
8..... 98s, T8s, K7s, A2s......................... 0.00
9..... 87S, QT, Q8s, 44, A9, J8s, 76s, JT... (-) 0.02 - 0.03

It shows how hands have been grouped according to expected value.
The grouping was determined from statistics taken from actual play of a large number of hands.

What is interesting to note is the number of hands in each tier.
5 in the first, 6 in the second, etc...
The table only shows 52 hands.
Since we know there are 169 possible 2 card hands in Texas Hold'em
then we can add another row to the table, tier 10, showing the remaining 117 hands that have an EV less than -0.03.

If during a game, the hole cards are dealt randomly, we should expect, on average, to be dealt 5 hands from tier 1 for every 169 hands we have been dealt.
Similarly, we should be dealt 6 hands from tier 2, 6 from tier 3, etc...

The following table to shows that.

tier # hands in tier
1..... 5
2..... 6
3..... 6
4..... 6
5..... 5
6..... 5
7..... 7
8..... 4
9..... 8
10....117
total 169

Now, ideally, when we play a game, we would like all our pocket cards to be from lower tier numbers since these are the cards that statistically win most hands.
However we can see from the table that we are going to be getting most of our pocket cards from tier 10 and that they are most likely going to be losing hands.

I have over 10,000 hands recorded in my Poker Tracker database and I wanted to see how the hand distribution compares to the above tables.

I exported the hand data in a spreadsheet and came up with a set of charts.
One chart for the Poker Stars hands and one for the FullTilt hands.
The charts show that in general, I am being dealt more hands than expected from tier 10 and less hands than expected from tiers 1 to 9.

Here are some of the numbers for the PokerStars hands.
The numbers from the FullTilt hands are similar.

tier times_dealt..... expected # hands..... variance

1.......... 178............... 244......................... -0.80%
2.......... 217............... 293......................... -0.92%
3.......... 247............... 293......................... -0.55%
4.......... 256............... 293......................... -0.45%
5.......... 187............... 244......................... -0.69%
6.......... 179............... 244......................... -0.79%
7.......... 277............... 342......................... -0.78%
8.......... 95................ 195.......................... -1.21%
9.......... 360............... 390......................... -0.37%
10........ 6249............. 5708........................ 6.56%
total..... 8245............. 8245........................ 0.00%


Unfortunatelly I can't figure out how to insert the chart images in the post.
If someone can explain how to do it I will post them.

Does that indicate that these hands were not dealt randomly?
If the hands were dealt randomly, all the variance numbers should be close to zero and about half of them should be positive.
Why is there such a significant skew towards the negative EV hands?

I made the same analysis using only the hands from a tournament were I did well (placed 3rd).
It clearly shows that during that tournament, I was dealt more cards from the positive EV tiers and less from the negative EV tiers.
Of course, as a result, I was playing more hands and winning more hands than usual.

tier....... times_dealt... expected # hands....... variance
1.......... 7................. 9............................. -0.71%
2.......... 15.............. 11............................. 1.27%
3.......... 14.............. 11............................. 0.95%
4.......... 10.............. 11............................. -0.33%
5.......... 9................. 9............................. -0.06%
6.......... 4................. 9............................. -1.67%
7.......... 9................ 13............................. -1.25%
8.......... 3................. 7............................. -1.40%
9.......... 17............... 15............................. 0.73%
10........ 223............ 215............................. 2.47%
total..... 311............ 311............................. 0.00%

Here the variance is not as skewed towards the negative EV tier.
There is some positive variance for tiers 2 and 3.
The number of hands in tier 10 is closer to what is expected.

I think this shows a lot more than you would see just by looking at the single AA hand.
If anyone else wants to do that exercise, I can provide the Excell spreadsheet if someone explains how to post it.

Because its only 10,000 hands, we need a lot more to make a real attempt. Hence this thread

Been on vacation for a couple of weeks. It's nice to see some well thought out questions and answers as well as some new data from Richard7787. I'm a little busy getting things back in order but I'll try to update the table ASAP.

Welcome back FD, Im happy to contribute!

I'm not sure how to respond to your post. I have to assume you're asking if I'm serious about the entire post and not just about a specific assertion you disagree with.

Let me go take a couple of bong hits so I can respond in an equally intelligent post.....

....

CoughCough

CoughCoughCoughCoughCoughCoughCough

What were we talking about?

You are correct, 10,000 hands is not a very large sample.
On the other hand, it is not an insignificanlty small sample size either.
The larger the sample, the more the variance will tend towards zero.
However, even with a sample this size, one would still expect the variance to be more or less evenly distributed.
My analysis shows that it is definitely not evenly distributed.
I don't believe that the skew can be explained by the sample size.

Any other explanations?

Thanks to Richard7787 for this contribution

Full Tilt
15,567
Dealt Aces: 71

Results updated

Attached Images

Rigged AA.JPG (52.3 KB, 5 views)

Oo sorry never added.

Full tilt - 10945 hands -
AA - 47
KK - 45
QQ - 47
JJ - 54
10 10 - 45

Hi,
I am new to this site and couldn't get the point and meaning, to post a proper comment i wanna more details on it.
-------------------------

shawn


Full tilt poker bonus code and freerolls tournaments

shawn, if you go to the home page, and then click on general discussion, then Introductions, you can then click on 'new thread' and create an introduction thread for yourself, to tell us more about you.
Anyway, welcome to CC, and gl!


btw, thanks for the link in your sig, didnt know they had freerolls at Doyles, looks good!

There doesn't need to be an explanation. I see no statistical reason why the variance would have to be evenly distributed.

There may not be any statistical reason for variance to be evenly distributed.
However if the variance is a measure of high EV vs low EV hands, then it looks suspicious if it definitely favours the low EV side.
I just think it would be reasuring to see it "more or less" evenly distributed.

In any case, I found out why I was seeing this skew towards the low EV hands.
I was assuming that the 169 hands were all equally likely.
I later realized that, of course, they are not.
For instance, AA counts as one of the 169 hands, but in reality there are four different AA hands.
Taking that into account, I ran the spreadseet graphs again and got a much more reasuring picture of the variance.

ft_II.jpg
ps_II.jpg

Before, (with the flawed assumption) it looked like this
ft_-all.jpg
Hence the reason for my comments in the previous posts.

Since players are playing against each other rather than against the house, this measure of EV does not necessarilly indicate whether the deal is rigged or not. I just thought it was a convenient way to group the hands in order to get a picture that covers dealing of all the hands instead of just AA.

Its all random, everything.
KD

Sorry 'smak. I just saw this. Been a little busy lately. That and trying to drive my teenage daughter off of myspace has definately limited my 'puter time. Nonetheless, we all thank you for your contribution and without further delay, I present you with the updated table.

“Superstition is to religion what astrology is to astronomy: the mad daughter of a wise mother”

-Voltaire

Attached Images

Rigged AA.JPG (52.4 KB, 5 views)

Id like to see the variance when we pass the magic million...............because at the moment the figures look pretty spot on.
Thanks, FD, for doing this.
Like the Voltaire quote, btw.
KD

now i'm curious and need to check my PokerStars and Full Tilt Poker stats...

Dont have too many hands havent used Poker Tracker for very long but here is where I am at.

Full Tilt: 25100 hands 105 AA

Thanks widow. Nice run of Full Tilt donations lately.

Nothing has such power to broaden the mind as the ability to investigate systematically and truly all that comes under thy observation in life.

-Marcus Aurelius

Attached Images

Rigged AA.JPG (52.2 KB, 5 views)