statistical tests to show that online poker is not rigged

You could try the "Integrity" page -- they don't have literal published tests, but it certainly looks promising when you use hardware RNGs (not the pseudorandom, "seeded" software RNG that most home microcomputers use), which are officially verified by two security firms -- including one which hacked an online poker site in the past!

(Incidentally, I wish they did something kind of like PokerRoom's EV chart at http://www.pokerroom.com/games/evsta...php?order=card )

Seriously, the "OMG STARZ IZ RIGGED!!!1" people need to quit whining. No one seems to realize you hit an 80% shot, oh, say, 80% of the time. (which, honestly, is why I usually play limit poker)

What are the odds of a 989:1 shot hitting!?! It's like a billion to one!

The odds are 989:1.

[UCF THAYER]

This is a great 1st post.

[UCF THAYER]

[ QUOTE ]
The rake is the same at the upper level games I'll agree, but the majority of people playing at pokerstars aren't playing at those limits. They are playing at the .05/.10, or the .50/1.00, the average Joe I'm talking about. And at these low levels there is a pretty substantial difference in the rake depending on how much is in the pot. I'm not saying it is definately happenning, but if you look at some of the horrific online beats that we've all seen, and then consider this, I'm saying it logically makes sense.

[/ QUOTE ]

Actually, logically it doesn't make sense.
Poker sites want as many hands to be dealt as possible, more hands = more rake. Also, they don't want their players to go broke. What happens in huge pots with 4 of a kind losing to straight flushes? The hands take forever to play out, and a person loses a huge chunk of their money. Sure, the site may get max rake, but at a high cost.

Logically, if a site were to rig their site for max rake potential, they would ensure that all their pots involve the winner winning with top pair higher kicker. This way the hands takes a short amount of time, nobody loses all of their money, and there's still enough action to get alot of rake.

[AaronBrown]

There are three distinct issues.

First is whether the hands you get in on-line poker are distributed precisely as a theoretically perfect shuffle. The more transparent sites publish enough details of their methodology to reassure people that it should be almost perfect, and some publish sample outcomes which always conform to statistical expectation.

However, if I were hired as a statistical auditor, I would concentrate on the outputs (the cards dealt) not the inputs (the theoretical perfection of the random number generator). I wouldn't just look at the unconditional distribution of pocket and board cards, I would look at what matters to poker players, the distribution of hand strength; particularly the correlations between different hands at the same table and the same player in different hands. There are a lot of steps between random number generation and hand output that could have bugs. To my knowledge, no one has ever done anything like this. I'd also look hard to see if any player enjoyed superior luck, more than could be explained by random chance. This could be an insider or someone who figured out how to hack the site.

So, on this point I would say there is some published information, but less than a skeptical person would demand.

The next point is whether the sites deliberately skew the distributions, whether to push up the rake or attract players. I don't agree with the "it's only a few pennies in rake" argument. If you push up revenue by 1% while keeping costs constant, you can push up profit by a much larger percentage. Moreover, a manager under pressure to hit some target might well compromise the integrity of the business to make a few dollars, we've certainly seen enough of that over the last few years.

No site publishes anything that would refute this. It wouldn't matter if they did, because if you don't trust them to deal the cards fairly, why would you trust their reported statistics? Even if an independent audit firm did the analysis, it's hard to know what they would look for. You could easily rig things but keep the overall distribution of cards as expected by chance.

So on this issue, I'd say there is no information and not likely to be information. Trusting people will trust the sites, suspicious people won't.

While either of those types of non-randomness would bother me as a player, neither one is unfair. Assuming they're too subtle to notice, they wouldn't affect play much. So they're only theoretical problems, even if they exist.

The third kind of rigging is the really worrying kind. The site could have hired players, or bots, to win people's money by cheating. But here there is no evidence that could be produced. The cards and hands could be perfectly random, but the bot could know what they were. An auditor might discover that some players seemed much better than others, but unless she contacted individuals, she couldn't prove it was anything more than skill differences.

The bottom line is that people who believe the sites are rigged will never see evidence to disprove that. On the other hand, there's never been a shred of evidence to prove that any site is rigged in any of the three ways.

[Komodo]

[ QUOTE ]
[ QUOTE ]
The rake is the same at the upper level games I'll agree, but the majority of people playing at pokerstars aren't playing at those limits. They are playing at the .05/.10, or the .50/1.00, the average Joe I'm talking about. And at these low levels there is a pretty substantial difference in the rake depending on how much is in the pot. I'm not saying it is definately happenning, but if you look at some of the horrific online beats that we've all seen, and then consider this, I'm saying it logically makes sense.

[/ QUOTE ]

Actually, logically it doesn't make sense.
Poker sites want as many hands to be dealt as possible, more hands = more rake. Also, they don't want their players to go broke. What happens in huge pots with 4 of a kind losing to straight flushes? The hands take forever to play out, and a person loses a huge chunk of their money. Sure, the site may get max rake, but at a high cost.

Logically, if a site were to rig their site for max rake potential, they would ensure that all their pots involve the winner winning with top pair higher kicker. This way the hands takes a short amount of time, nobody loses all of their money, and there's still enough action to get alot of rake.

[/ QUOTE ]

why do you think players go broke on lower levels just because they lose one buyin? The player who lost will bring more and the player who won may create even bigger pots and more rake in the future.

[ianlippert]

Ok it took me a while to find it, but here is an RGP post from 2002, scroll down a bit to hand analysis, 2nd post from top.

http://www.playwinningpoker.com/rgp/02/

Not even 40K hands and everything seems to be pretty normal.

Aaron,

Excuse me for tossing a bouquet your way, but I just did. - You've given this thread a lot of insight and things to think about, as usual.

Now I've got a serious (burning?) question for you: Do you play online? I don't, having tried it a few years ago and not caring for it. But I'm thinking of giving it another go. I doubt your answer will affect my decision, I'm just curious.

Nut

[AaronBrown]

Actually, it does not show that everything is normal. There is a serious deficit of Aces and Kings, more than can be plausibly explained by chance. If this is really a random sample of hands, then the site has serious problems.

The trouble with this post is that it gives no consideration to standard deviation. It shows the actual and expected numbers of various types of hands, and concludes that they look pretty close. But over 37,867 hands, things should be a lot closer than this.

For example, there were 2,264 paired starting cards. 2/13 or 348 of them should have been AA or KK. In fact, only 297 were. That may not seem to be a huge difference, but if everything is random, getting 297 or fewer AA or KK out of 2,264 paired hands would happen only one time in 780.

That's not conclusive proof that the site has random number generation problems, but I wouldn't tout it as evidence everything is working perfectly. Combined with the strong deficit of AKs, it looks funny.

Of course, there are a lot of card combinations cited, and some of them are going to differ from their expected frequency. But AA, KK and AKs are among the most important starting hands. Missing 67 of them, even over 37,867 hands, could make a significant difference. If you are a 2 BB/100 hand average player, you expect to make 757 BB over this many hands. Your AA, KK and AKs might average 5 BB wins eacy, the deficit of 67 means you lose about half your expected profit.

[ QUOTE ]
What are the odds of a 989:1 shot hitting!?! It's like a billion to one!

The odds are 989:1.

[/ QUOTE ]

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