Chess SPRT Calculator

  • The fields Elo0 and Elo1 represent the bounds for an SPRT test with error probabilities α and β. If the true Elo is less than Elo0 then the probability of the test passing is less than α. On the other hand if the true Elo is more than Elo1 then the pass probability is more than (1-β).
  • If the Elo model is Logistic then the pass/fail probabilities are independent of the auxiliary data Draw ratio and RMS bias. On the other hand if the Elo model is Normalized then it is the expected duration of the test that is independent of the auxiliary data.
  • The Draw ratio is mainly a function of the opening book and the time control. The draw ratio can be found on the live_elo page of a test with typical URL https://tests.montychess.org/tests/live_elo/666cac63746a4248d2b64a4d or the raw statistics page with typical URL http://tests.montychess.org/tests/stats/666cac63746a4248d2b64a4d.
  • The RMS bias is the Root Mean Square of the biases of the openings in the book where the bias of an opening is defined as the conversion to Elo (using the standard logistic formula) of the expected score for white between engines of "equal strength". Explicitly the RMS bias is the square root of the average of the squares of the biases expressed in Elo. The RMS bias appears to be relatively independent of time control and Elo differences. It can be found at the bottom of the raw statistics page, but it should be noted that the value reported there is only reliable for tests that have at least a few tens of thousands of games. Also note that for non-functional simplifications or small speed-ups, correlations between games in a game pair cause the (virtual) RMS bias to be much higher than normal.
  • More information on the mathematics behind this web page can be found on the Fishtest wiki.
  • The original version of this web page was written by Henri Wiechers.