Test Results by Site:
Please note that this is the general discussion page for all pre-flop bad beat tests - for specific discussion of i-Poker preflop bad beat tests where a significant bias was detected in some samples please see the i-Poker page.
It should be noted that a 'Monte Carlo' method is used by poker tracker to calculate the 'all-in equity' of each hand. The Monte Carlo method works by running millions of simulations of the hand and converging towards a result. This produces sight errors in the 'all-in equity' figure that is output by Poker Tracker.
However, since the calculation is run for every individual hand the errors involved with the 'mean expected equity' or 'standard deviation' of a whole sample will converge as the size of the sample increases.
With the sample sizes that we have used we can expect errors in the final result (number of standard deviations of the sample from expectancy) up to approximately 0.25 standard deviations.
These could be reduced considerably by running the poker tracker report multiple times and averaging the results, but for these tests it would have no significant effect on the conclusions that we reach and so was deemed unnecessary.
One area of potential debate in this analysis is the assumptions about 'winning' and 'losing' players, i.e.: good players more often than not get 'their chips in ahead'.
In this regard the main point to be aware of is that this is one small aspect that makes a winning poker player. There are other important skills that make a 'winning' poker player (particularly in cash games), such as: the ability to bluff at the right time and adjusting to player types. However, making 'good calls' pre-flop is a factor that contributes to being a winning player, although it may not the biggest factor in cash game play at micro-stakes tables.
For sit and go tournaments the assumptions are likely to hold true due to the structure of the game which hinges around pre-flop decisions in the latter stages.
It is also clear that there are times when it is the correct play to call with a hand that is the underdog. For example, if pot odds dictate that enough money is in the pot already to make calling a small all-in bet profitable, a 'winning' player should call even if they are behind.
In the worst case scenario (i.e. the assumptions are incorrect) we have simply failed to define 'winning' and 'losing' players - these tests will still whether the cards fall as they should and if expectancy is met or not.
The more likely scenario is that the assumptions hold true for a proportion of the hands in the sample, but that there are a significant number of exceptions when they don't hold true. In this case a bias would show in the results if the sample size was large enough.
In further testing a priority will be given to different ways of defining 'winning' and 'losing' players.
The card removal effect refers to the fact that a player's own hand makes it less likely that their opponent has certain hands or certain hand combinations. For example, if a player holds AK for example, it is somewhat less likely that their opponent has A and K hands, since the player's own hand blocks two of the eight existing relevant cards (4x A, 4x K).
There has been speculation on the effects of card removal on bad beat tests results. It has been suggested by some that the card removal effect would cause a very small natural bias in the results towards the underdog and that effect of the bias would increase as the size of the sample increased. This has been disputed by others who believe that the effect of card removal would be negligible.
At this stage the effects of card removal are not fully understood and more research is needed before the card removal effect can be quantified.
It should be noted that card removal cannot have any effect on the results in Head's Up matches - Merge Network samples in these bad beat tests were taken from Head's Up matches.
Another area that has raised questions is the completeness and legitimacy of the original dataset. Hand histories were purchased from an independent 3rd party and although it is never possible to be 100% sure of the reliability of a 3rd party source there is very little reason to believe that the hand histories are anything but legitimate. The dataset is not complete.
Questions have been raised as to the effect of missing hand histories on the analysis. Obviously, if the hands were missed randomly then we simply have a slightly smaller sample size and this wouldn't change our results at all. However, it is possible that the missed hands were due to a software glitch when they were 'data-mined' and that there is a pattern behind why they were missed. For this to adversely effect the analysis the missed hands would have to share some characteristic which meant that their actual equities and expected equities were related differently from the rest of the sample. This is highly unlikely.
These bad beat tests was performed on specific game types (e.g. 10c/20c 6max cash tables) during a specific period (e.g. July/Aug 2011) at a specific poker site or network and the results can be considered true for these conditions only.
Although these results are relevant to online poker in general other circumstances were not tested. Other poker sites may use different methods for the distribution of cards and other game types (e.g. multi-table tournament hold'em) or levels (e.g. $2/$4) at the sites tested could also use different programs for the deal. It is also true that the method of dealing at a given site could change in the future as the site updates. Online Poker Watchdog intends to perform this test on other poker sites for a variety of games and levels.
Also, this analysis only tests one aspect of potential rigging, i.e. the 'Bad Beat' theory. In theory there are many other ways that a poker site could be rigged that this test doesn't examine, for example it doesn't test the distribution of hole cards between players in any way. Online Poker Watchdog intends to perform further analyses, designed to test other theories of potential rigging of online poker.