Complete Tests:
Test Results by Site:
We have listed a summary of the relevant results for each bad beat test.
For completeness the spreadsheets containing the outputs of the Poker Tracker Report and the results of the analyses are available. They can be viewed in PDF format by clicking on the links below the results for each site. Please be aware that the documents are large as they contain thousands of hands.
First we compared the actual number of hands won with the expected number of hands won in each case - the difference between these figures is the actual deviation.
The actual deviation of the 'ahead hands' was subtracted from the actual deviation of 'behind hands' to give the actual deviation of all the hands in the whole sample that were the underdog (i.e. equity < 50%). We also calculated the standard deviation for these hands - it is slightly different from the standard deviation of the whole sample because the hands that have a 50:50 chance of winning were not included.
We then calculated the 'actual deviation/standard deviation' of these hands - this number has been highlighted in each table. If you only look at one figure... this is the one to look at! If the number is positive it shows that throughout the sample the underdog has done better than expected, if it is negative the favourite has done better than expected.
Note that the margin for error for the 'actual deviation/standard deviation' in these tests is up to approximately +/-0.25. For more detail on the margin for error see the discussion page.
If the 'actual deviation/standard deviation' is less than 2 then this is strong evidence of no bias in the sample.
If the 'actual deviation/standard deviation' is greater than 5 then this is strong evidence of a bias in the sample.
Sometimes results will occur where the 'actual deviation/standard deviation' is slightly greater than 2 (and occasionally greater than 3). This will occur from time to time due to variance. It does not necessarily mean that a bias has been found, although it may be grounds to run further tests on a particular poker site (for example, if it was greater than 3)
For more information on interpreting deviation see this article.
We can see from the tables below that the actual deviation is just 1/4 of a standard deviation - well within 2 standard deviations.
Data Group | Equity Range (%) | Total No. Hands | Expected No. Hands Won | Actual No. Hands Won | Actual Deviation | Standard Deviation |
---|---|---|---|---|---|---|
All Hands | 0-100 | 19807 | 10505.7 | 10507 | +1.3 | 55.0 |
Ahead | 50-100 | 10605 | 8401.1 | 8394 | -7.1 | 39.6 |
Behind | 0-50 | 9001 | 2004.1 | 2010.5 | +6.4 | 37.5 |
Data Group | Actual Deviation | Standard Deviation | Actual Deviation/Standard Deviation |
---|---|---|---|
All 'underdog' hands | +13.5 | 54.6 | +0.25 |
View full results in PDF format: All Hands, Ahead, Behind.
We can see from the tables below that the actual deviation is 2.17 standard deviations from the expected result in favour of the underdog. This result should occur due to variance in approximately 3% of tests (or roughly once in 33 tests).
Data Group | Equity Range (%) | Total No. Hands | Expected No. Hands Won | Actual No. Hands Won | Actual Deviation | Standard Deviation |
---|---|---|---|---|---|---|
All Hands | 0-100 | 12170 | 6547.9 | 6420 | -37.9 | 42.1 |
Ahead | 50-100 | 6553 | 5249.3 | 5184 | -65.3 | 30.5 |
Behind | 0-50 | 5460 | 1130.2 | 1155 | +24.8 | 28.3 |
Data Group | Actual Deviation | Standard Deviation | Actual Deviation/Standard Deviation |
---|---|---|---|
All 'underdog' hands | +90.1 | 41.6 | +2.17 |
View full results in PDF format: All Hands, Ahead, Behind.
We can see from the tables below that the actual deviation is just 0.15 of a standard deviation from the expected result - well within 2 standard deviations.
Data Group | Equity Range (%) | Total No. Hands | Expected No. Hands Won | Actual No. Hands Won | Actual Deviation | Standard Deviation |
---|---|---|---|---|---|---|
All Hands | 0-100 | 13898 | 7615.7 | 7609.5 | -6.2 | 46.3 |
Ahead | 50-100 | 7812 | 6167.1 | 6160.5 | -6.6 | 34.1 |
Behind | 0-50 | 5957 | 1384.1 | 1384.5 | +0.4 | 30.9 |
Data Group | Actual Deviation | Standard Deviation | Actual Deviation/Standard Deviation |
---|---|---|---|
All 'underdog' hands | +7.0 | 46.0 | +0.15 |
View full results in PDF format: All Hands, Ahead, Behind.
We can see from the tables below that the actual deviation is just under a quarter of a standard deviation from the expected result - well within 2 standard deviations.
Data Group | Equity Range (%) | Total No. Hands | Expected No. Hands Won | Actual No. Hands Won | Actual Deviation | Standard Deviation |
---|---|---|---|---|---|---|
All Hands | 0-100 | 3674 | 2042.0 | 2030.5 | -11.5 | 24.7 |
Ahead | 50-100 | 2101 | 1620.1 | 1617 | -3.1 | 18.0 |
Behind | 0-50 | 1550 | 410.4 | 402 | -8.4 | 16.6 |
Data Group | Actual Deviation | Standard Deviation | Actual Deviation/Standard Deviation |
---|---|---|---|
All 'underdog' hands | -5.3 | 24.4 | -0.22 |
View full results in PDF format: All Hands, Ahead, Behind.
We can see from the tables below that the actual deviation is just over a half of a standard deviation from the expected result - well within 2 standard deviations.
Data Group | Equity Range (%) | Total No. Hands | Expected No. Hands Won | Actual No. Hands Won | Actual Deviation | Standard Deviation |
---|---|---|---|---|---|---|
All Hands | 0-100 | 16609 | 8622.8 | 8582.5 | -40.3 | 51.0 |
Ahead | 50-100 | 8678 | 6780.5 | 6745 | -35.5 | 36.5 |
Behind | 0-50 | 7763 | 1758.3 | 1751.5 | -6.8 | 35.1 |
Data Group | Actual Deviation | Standard Deviation | Actual Deviation/Standard Deviation |
---|---|---|---|
All 'underdog' hands | 28.7 | 50.6 | +0.57 |
View full results in PDF format: All Hands, Ahead, Behind.
We can see from the tables below that the actual deviation is just under 2 standard deviations from the expected result in favour of the underdog. This result should occur due to variance in approximately 5% of tests (or roughly once in 19 tests).
Data Group | Equity Range (%) | Total No. Hands | Expected No. Hands Won | Actual No. Hands Won | Actual Deviation | Standard Deviation |
---|---|---|---|---|---|---|
All Hands | 0-100 | 10526 | 5481.7 | 5500 | 18.3 | 39.7 |
Ahead | 50-100 | 5481 | 4355.2 | 4326 | -29.2 | 28.2 |
Behind | 0-50 | 4918 | 1063.0 | 1110 | +47.0 | 27.3 |
Data Group | Actual Deviation | Standard Deviation | Actual Deviation/Standard Deviation |
---|---|---|---|
All 'underdog' hands | +76.3 | 39.3 | +1.94 |
View full results in PDF format: All Hands, Ahead, Behind.
More information on these bad beat tests can be found on the Explanation, Dataset, Method, Results, Conclusions & Discussion pages.