From 2+2:

One of the predominant claims put forward by conspiracy theorists is that sites deliberately deal coolers and bad beats to "juice pots" and make them bigger so as to collect more rake. These conspiracy theorists never offer any actual statistical proof. Just their "feeling" that online poker has more "big hands" than it should. This despite the thousands of 2+2 users with large databases of millions of hands, particularly at FTP which is routinely datamined for all hands. Considering how well posters on this site have been able to spot real cheaters, be they bots or super-users, you'd think someone would have some concrete proof by now if there was any substance to any of these speculations.

Yet no one does.

No, the conspiracy theorists evidence consists entirely of the argument "It would be good for the site".

Except that's completely wrong.

They say it would be good for a site to juice the deck to ensure coolers. Big hands like quads over full house in order to maximize the rake. That the site would stand to make the most money this way.

This is wrong and it betrays a fundamental misunderstanding of the poker economy and how winning players and the house make money. This is exactly what a site would NEVER do. In fact, if sites were rigged we would never see quads over full house.

At most sites, the No Limit rake is 5% with a $2 cap. This means the maximum rake is hit when the pot reaches $40.

At a 50NL game if two players go all in, the pot is $100. At 100NL if two players go all in, the pot is $200. The site still rakes only $2.

In fact, the best situation for the house would be if the pot was always exactly $40. A $100 or $200 pot is actually bad for the site because they aren't getting their full share of the rake and there's a chance that somebody goes broke. Even worse if they go broke and never come back.

This is the worst case scenario for both winning players and the house - That losing players go broke too quickly, get frustrated with the game and never come back. You can shear a sheep many times but only kill him once.

It would actually be in a site's best interest to always have a $40 pot. That is, if a site were going to set hands to maximize profit from pot size, they would rig for medium sized pots.

Which of course is impossible since pot size depends too much on players. There's always some donk who'll overplay and get it all in. There's always some nit who will underplay and the pot will be small.

However, from the house's perspective clearly medium sized pots are optimum, small pots are second best since they still collect some rake and nobody goes broke. Large pots, particularly all-ins are the worst case scenario for the house. Both because they miss out on rake and there's a chance somebody goes broke and quits, even for a short time.

Since a site can't ensure that medium sized pots actually stay medium sized, if a site were rigged it would rig for small pots. Action hands and coolers would actually occur far below expectation.

So why do people keep coming back to the idea that there are more big hands online than live?

There are several reasons - Sample size and selection bias are the two most important. You get far, far more hands per hour online than live. At least twice as many hands per hour per table and as many as triple. In addition many online players multi-table. An online multi-tabler can easily see 10-20 times as many hands per hour as a live player. That's sample size. More hands of course means more big hands. Also, if you have the preconceived notion that there are more big hands online, then every time you see one of those big hands it's only going to reinforce that prejudice even if it's not that big of a hand. Whereas live you're not going to be making a note of every big hand. There's your selection bias, we tend to remember things that support what we already believe and discard whatever contradicts it.