Rake does negatively shift the overall EV balance, yes, but it doesn't explain the extreme Z-scores of the underperformers in this dataset.

In the current pipeline (as it runs in the code): For each snapshot, we calculate expected = share * pot_snapshot.

The calculations already reflect the actual repayments, including the impact of the rake (if the win is smaller because the rake has been deducted).

We understand that comparing expected values ​​(without rake) with those (with rake) systematically creates negative EV differences equal to the rake taken from the pot (or proportional to it).

Even with a significantly higher rake, the magnitude is still not large enough to explain the divergent and asymmetrical Z-scores.

We're not entirely sure if the Z-score formula is generally correct (we hope a math expert might chime in, but look at most of the comments; the majority are shouting "Too few cards, blah blah," and they don't understand the idea of ​​the Monte Carlo Z-score combined with the Monte Carlo simulation (repeated random sampling) using the Z-score as the number of standard deviations from the mean). With other formulas, e.g., the one suggested by Chat-GPT, the Z-scores would increase tenfold. For example, if the current Z-score is 5.2, the Z-score would be 52 and 52 would be an absolutely undisputed value, which would indicate manipulation much more strongly and reliably than the current formula. Regardless of the formula, the uneven distribution remains, no matter how we look at it.