Test Results by Site:
This test is similar to the 'pre-flop and flop all-in, bad beat tests' that we have previously run, but is concerned with hands that are all-in on the turn. These tests set out to determine whether the river card is biased.
One common theory of how online poker could be rigged is the 'Bad Beat Theory'. In 'bad beat theory' good players receive more 'bad beats' than they should and poor players 'get lucky' too often when all the chips go in.
It has been argued that a site rigged in this way could increase its profit because the 'fish' would lose their money less quickly, the 'sharks' would win more slowly and therefore cash-out less often.
In this experiment we put some major online poker sites and networks to the test by analysing millions of hands to see if good players receive more 'bad beats' than they should...
Null Hypothesis: Each online poker site is fair. The cards are dealt randomly.
Alternate Hypothesis: Each online poker site is rigged. The river card is biased to favour losing players in 'turn all-in' situations.
In this test we anlaysed the results of 'heads up, turn all-in' hands, i.e. hands in which exactly 2 players were 'all-in' on the turn.
We compared the 'Expected number of hands won' with the 'Actual Number of hands won' over a large sample size.
If our null hypothesis was true (i.e. each online poker site is fair with respect to bad beats):
The 'Expected number of hands won' would have been very close to the 'Actual number of hands won' for a large sample of hands.
Since we wished to compare results for winning and losing players it was necessary to make an assumption:
Assumption1: good players more often than not get 'their chips in ahead', i.e. their hands will (on average) have an 'Expected Equity' of greater than 50%. Also, poor players more often than not get 'their chips in bad', i.e. their hands will (on average) have an 'Expected Equity' of less than 50%.
If our alternate hypothesis and assumption were correct (i.e. a poker site was rigged in this way):
1) Hands that are the favourite to win in an all-in situation would win less often than they should. Therefore the actual number of hands won would be fewer than the expected number of hands won for hands with an 'Expected Equity' of greater than 50%.
2) Hands that were the underdog to win in all-in situations would win more often than they should. Therefore the actual number of hands won would be greater than the expected number of hands won for hands with an 'Expected Equity' of less than 50%.