this analyzis makes no sence .. The hands are from variuos poker rooms, and its from cash games.

The one I posted is from a single major poker site (I found out). Yes, it's cash games.

How many of your 80k SNG hands were played on the bubble? My guess is your sample size isn't sufficient to be confident in any of these results.

About 5000.

But of course, of these hands I was personally all in only about 800 times and of those times there was a showdown only about 300 times. So, yeah. Not a huge sample size.

On the other hand, if I flip a coin 300 times and it comes up heads 200 times, are you ever going to bet tails? I can't find the link to my confidence level calculator, but I'm guessing it's still a pretty grim outcome.

I seriously doubt you had 300 all-ins exactly on the bubble (last non-paying spot) that were all favorites and you lost 200 of them. Saying the average equity was 57% is not the same as them all being favorites. A few 80-90% favorities in the set can bring up the average, and you might have had 200 underdogs in the set. You need to look at how many lost when they were the favorite, that were also exactly on the bubble. In 80,000 games I could find lots of subsets of 300 all-ins that lost more than expectation, but you said yourself that the total of all your games came out to expectation. By definition you are all-in to get eliminated in every single game that you didn't take first place, so there are a lot of subsets of 300 in there. Be careful how you define them.

Does your database take away rake? Truly breakeven players who play a lot will lose tons.

My point here was not to suggest that my (limited) results "prove" that I was cheated. The OP offered data that he believed proved that the shuffles were unbiased. I was just illustrating that it ain't necessarily so.

FWIW, as I said in my OP, my EV on the bubble was NOT 57% but only 51%, and the distribution of equities was normal so the average EV was not higher as a result of a few outlier hands.

My point was this:

If you're going to try to "prove" a fair shuffle you can't just take a simple model (in OP's case, gross all in equities) and assume it applies to all sub situations. For example, the average temperature of the entire Earth remains pretty constant over 365 days. But obviously it is pretty variable when you look at specific places.

If you're going to test for "fairness" you have to test all sorts of hypothesis. Some of them might even be pretty wacky. Because the bottom line is it's easy to design a system of "rigging" a deal that is very difficult to detect unless you test specifically for that system.

I'm skeptical of people who claim they are being cheated when they have no evidence, but I'm also skeptical of people who claim that the deals are indisputably random when these types of analysis (eg. positional equity in sng's or pots size equities in cash games) haven't been done on a large scale.

This thread should be in the sticky so that it doesn't get lost and can be easily referenced back to, imo.

Poker Tracker calculates pot size as net of rake. And that is why it seems so remarkable to me. The actual figures are 55% losers and 45% winners.

355,000 total hands, $21,800 in total rake paid by 2487 distinct players.

I think that maybe what's going on here is we have some very tight games with a lot of blind stealing so not a lot of rake (obv) being paid which would generate less net losers that I would expect.

I'm curious what other's databases show. My stats are from 1/2 NLHE games on PS.

Whoops, my bad. There were only 43,000 distinct hands played (I don't play a lot of NLHE) , NOT 355,000. I was looking at the summary for all players which obviously duplicates hands by players at the same table.

Still, only about 50 cents per hand paid in rake, so pretty tight games.

You're absolutely right. I am the OP, and this was just a gross first pass and checking to see if the deal overall seems random, and it does. There's several people doing a lot more analysis, including me, now that we have some large databases to work with. More to come.

I have a proof that pfai are rigged in Ongame.

Ongame network. SnG.

I analized pre-flop allins taking into account stack size of the opponents.
I recorded preflop equity and outcome of all-ins I seen at the SnG tables.
Short stack win recorded as 1.
Short stack loss recrded as 0.
Tie recorded as 0.5.
The cases shortstack vs 2 or more bigstacks recorded as well.
Equity taken from the poker client, or calculated using PokerStove.

RESULTS:

Tournaments: Double or Nothing SnG $22, $33 and Double or Nothing Turbo SnG $22, $33.
Time: from Nov 20th to Dec 18th, 2008.
Number of experiments: 1582 pfai
Average short stack equity 46.7%
Short stack win 42.4%.

Big stack wins more often than it should.
The standard deviation is 3.39*SIGMA.
PROBABILITY OF THE DEVIATION IS AS LITTLE AS 0.03%.

That proves that ongame software gives advantage to the bigstack,
making the shortstack leave the tournament earlier.
Thus the average time of a tournament shortens, players sign up to more
tournament, hence the site collects more rake. This practice is most lucrative in DoN SnGs there 6 players finish the tourney after small stack loses all-in on bubble.

You can check any ongame database and make sure.

After leaving ongame scam site, I've been playing DoNs at Stars.
Here I found something strange as well.

I analyzed 1150 preflop allins. Big stack had average equity 53.1%, actually won in 54.5%.
Especially, big stack sucks out a small stack's pocket overpair too often. Like AK>AA, 55>TT, JTs>QQ, etc.
I recorded 93 such allins, big stack had average equity 16.7%, and won 27 allins (29%).
The standard deviation is as high as 3.2*sigma, the distance is short though.
On the other hand, I had 122 allins then short stack was dominated by pocket overpair (short stack ave. equity 16.4%). And short stack sucked out big stack in only 17.5 cases (0.5 is one split pot) - 16% as it is supposed to be.

Also I have a feeling that in post-flop all-ins big stack get their outs more often than short ones do.
And flush and straight draws close a little bit more often then they should, encouraging bad players.

The above makes me believe PokerStars is rigged. To prove it mathematecally, one have to analyze ten times more hands. I cannot do it manually. But I have hand histories of more than 2,500 tournaments I played (in .txt format). These can provide at least 25,000 all-in hands.

So, custom software needed to analyze big vs shortstack all-in luck, draw probability, etc.

Can anyone offer or refer to such sofware? Pls mail to ROONEY put "@" in between BK.RU

Interesting.

It is sort of charming to see the difference between a properly conducted statistical analysis and one that uses a more creative interpretive approach.

The distribution implies HU allins, yet on 102 million hands I would think there would be some multiway allins.

You're correct. This particular run which Indiana did for me, filters for 2 players all-in preflop and one won (ties excluded), 6-handed cash tables only, all on one major poker site. It was more of a proof-of-concept for the hand analysis software he's been working on.

I have the code myself now and I'm working on some refinements to do a more complete analysis.

You don't think 93 hands is a large enough sample size?

the fact that 40-50% and 50-60% don't line up on their total number clouds this analysis big time

in addition, you have no null hypothesis and alternative hypothesis
there is no statistical test here

is this "[0.42 - 0.44): 47204 21103 0.447%" fair, unfair, other?
all you have is an eyeball test right now

that's not true, he has a "feeling" too.

1 day a mod and got an attitude already.

MyTurn2Raise - This was mostly a proof-of-concept for Indiana's database and analysis code, and I'm working on refining it now that he released the code. There are some things that need to be cleaned up on this test.

If we assume that average equite is in the middle of each interval we get:

[0.34 - 0.36): 22147 7530 0.34%
average equity 0.35. Deviation 3.12*sigma.
[0.54 - 0.56): 52804 28537 0.54%
average equity 0.55. Deviation 4.42*sigma (!!!)
[0.44 - 0.46): 52790 24259 0.46%
average equity 0.45. Deviation 4.4*sigma (!!!)

I calculated only 3 intervals.
Are you saying this data proves all-ins are not rigged?


Moreover, I can say the data are sensless because you excluded ties.
Equity formula is (percentage of wins)+1/2*(percentage of ties). So, it's incorrect to count only wins and compare result with equity. Must count ties as well.

following the previous post:
I tried to estimate ties influence.
It's obvious that ties will add to the wins number.

[0.28 - 0.30): 44814 13266 0.296%
ties add min 0.2% to the equity (in case of dominations up to +0.8%. PokerStove)
percentage if ties included: 29.6%+min 0.2%=29.8%
Average equity 0.29. Deviation minimum 3.74*sigma.

[0.30 - 0.32): 40589 12854 0.317%
ties add min 0.2% to the equity (in case of dominations up to +2.2%(!) like AKo vs ATs. PokerStove)
percentage if ties included: 31.67%+min 0.2%=31.87%
Average equity 0.29. Deviation min 3.78*sigma.
I took minimal figure for tie influence. But if we assume that actually ties add 0.4% i/o 0.2%, we get deviation 4.66*sigma. This makes the result impossible unless the site is rigged.


[0.44 - 0.46): 52790 24259 46%
ties add about 0.2% to the equity (PokerStove)
percentage if ties included: 0.45954+0.002=0.46154
Average equity 0.45. Deviation 5.33*sigma which is really impossible.


Now tell, is this statistics from PokerStars?
Suckouts like AK<Ax, AQ<Ax, etc. and lost 55/45 flips are often there.


Ironically, your "proof that preflop all-ins are not rigged" proved contrary.

This study is meaningless for proving all-ins are not rigged and I'm somewhat surprised nobody's pointed this out yet.

The typical rigging theory is that fish run good, at the expense of 'good' players. If you let a fish win his twenty percents 25% of the time, and you only let the 'good' player win 15% of the time and tweak the results of good player vs good player all ins as necessary for balancing, you still end up with the proper net run of 20% on the aggregate results with no visible oddities.

Basic example with three players: Fish, Tag1, Tag2:

Fish1 vs Tag1 in spot where Fish1 should win 20% but instead wins 30%

So current aggregate results so far in the format of expected | actual

20% | 30%
80% | 70%

Now Tag1 faces Tag2 in a spot where Tag1 should win 80% but instead instead wins 90%

20% | 20% (from 30%+10% / 2 = 20%)
80% | 80% (from 70%+90% / 2 = 80%)

And the data looks perfectly normal when just considering the aggregate.

Statistical analysis without segregation of data is 100% useless in basically any scenario. You need to split these numbers up based upon player type, player profitability, stack sizes, etc to really test anything. So, for instance, this basic example would be detectable by noticing a generally upward trend in the fish's all-in EV net run and a generally downward trend in the tags' graphs - assuming the imbalance between the tags was equally imbalanced. eg - tag1 gets his 80% as a 90% in equal proportion to the times he gets his 20% as a 10%. Other detection methods would include running the all-in equity segregated by player type.