Ok this is not a school assignment. It is an ongoing debate on many forums.
Here is the abstract hypothesis as I would like to present it here:
We will limit the discussion to Texas Hold em for simplicity.
It is possible to rig poker game software to induce profitable* gameplay, without changing the testable variances and deviations from the expected statistics.
(*profitable to the website at the cost of the players)
Any and all anomelies would come up under analysis of the data therefore it is imposible to rig the software in this way without detection by standard analysis.
"the data" - hand histories
"analysis" - looking at 1 single players hand history
So the counter states that if the software is rigged, a single player will be able to prove it by running statistical analysis on just his hand history as long as there is sufficient sample size. It is important at this point to define the contents of a hand history. A hand history will alwyas show your own cards at minimum. It will show flops if they were played, and on to the river. It will only show your opponents cards if the game goes to a showdown either with you or 2 other players in it. Otherwise you cannot see any other cards but your own.
Ok so here are some of the specifics to consider.
The website charges a fee(called a rake) either by taking a portion of pots in money games or charging a fee to enter tournaments.
The hypothesis is based on the idea that the faster and bigger pots get and the faster tournaments play out, the more games will occur from which they can charge more rake. Therefore the goal is to quickly make players go all in or play high % of their pots often.
Although it is impossible to fully remove all psycholgical effects on the idea of pure poker maths, one must consider that hands like AA KK QQ will have a psychological affect on betting. There are also many other psychological that could affect betting and in truth the hypothesis would like to include these ideas into the coding since a programmer can in fact consider these things, however the math does not care about this. So the ypothesis wants to make it very clear that the software is not in any way increasing the frequency in which certain hands appear, but specificaly the order in which hands appear to induce betting agasint other strong hands. So rather than incrase the frequency that KK or AA comes up they would increase the times they come up agasint each other. Now KK AA is an obvious example and done so for simplicity. There are hundreds of hands that can be more easily masked from casual human detection.
I will stop here as i dont want to continue elongating the post but will add more if the conversation is picked up. But I would like to finish with an example of how I believe rigging can be hidden inside the statistics.
Consider 2 players with the following hands
Player 1 gets As Qd
Player 2 gets 10c 9s
both players go all in after seeing only these cards(preflop)
At this point the odds roughly say AQ will win 66% and T9 33%
So regardless of what the remaining card might be, if you ran the anaysis of how often AQ beats T9 you would expect to get 66 to33%. Fine the software doesnt "rig this"
But now lets consider the remaining cards. The flop brings Ad 2c 8s and the turn brings 6d. At this point the new odds are 92% for AQ and 8% T9.
So one manifestation of the Hypothesis is to increase the frequency with which this last card might win, say rather than 8% it hits a greater number approaching the allowable 33% of the time. You make your adjustments elsewhere to keep the 33% in tact, but now you have pigeonholed the 33% into the more exciting and bet inducing river(last card). Now in our case the players were already all in, but if they had not been, this set up might would affect the psychology the players, without changinging the expected odds.
Now I think it is obvious that I personaly feel it is riggable in this way. But I do not have the mathematical practice to present this argument in mathematical terms. Or I may flat out be wrong and would like to find out.