(4) average XOR-correlation between bits and the previous 4 bits (not sure what this means -Eric)
This is simply XOR-ing each bit (starting with the 5th one) with the previous 4 and adding it all up. This test was to look for a possible tendency (or the opposite) to end streaks at medium range (other tests were either short range or looked at the whole string). I didn’t throw in more tests using any other numbers than 4 since using different tests with any significant correlation on random input would lead to overconfidence unless I did something fancy to compensate.
In response to:
“XOR derivative” refers to the 149-bit substring where the k-th bit indicates whether the k-th bit and the (k +1)-th bit of the original string were the same or different. So this is measuring the number of runs … (3) average value of second XOR derivative and (4) average XOR-correlation between bits and the previous 4 bits...
I’m curious how much, if any, of simon’s success came from (3) and (4).
Values below. Confidence level refers to the probability of randomness assigned to the values that weren’t in the tails of any of the tests I used.
Actual result:
Confidence level: 63.6
Score: 21.0
With (4) excluded:
Confidence level: 61.4
Score: 19.4
With (3) excluded:
Confidence level: 62.2
Score: 17.0
With both (3) and (4) excluded:
Confidence level: 60.0
Score: 16.1
Score in each case calculated using the probabilities rounded to the nearest percent (as they were or would have been submitted ultimately). Oddly, in every single case the rounding improved my score (20.95 v. 20.92, 19.36 v. 19.33, 16.96 v. 16.89 and 16.11 v. 16.08.
So, looks I would have only gone down to fifth place if I had only looked at total number of 1′s and number of runs. I’d put that down to not messing up calibration too badly, but looks that would have still put me in sixth in terms of post-squeeze scores? (I didn’t calculate the squeeze, just comparing my hypothetical raw score with others’ post-squeeze scores)
With (1) (total number of 1′s) excluded, but all of (2), (3), (4) included:
Confidence level: 61.8
Score: 20.2
With (2) (total number of runs) excluded, but all of (1), (3), (4) included:
Confidence level: 59.4
Score: 13.0
With ONLY (1) (total number of 1′s) included:
Confidence level: 52.0
Score: −1.8
With ONLY (2) (total number of runs) included:
Confidence level: 57.9
Score: 18.4
So really it was the total number of runs doing the vast majority of the work. All calculations here do include setting the probability for string 106 to zero, both for the confidence level and final score.
Whoops, missed this post at the time.
In response to:
This is simply XOR-ing each bit (starting with the 5th one) with the previous 4 and adding it all up. This test was to look for a possible tendency (or the opposite) to end streaks at medium range (other tests were either short range or looked at the whole string). I didn’t throw in more tests using any other numbers than 4 since using different tests with any significant correlation on random input would lead to overconfidence unless I did something fancy to compensate.
In response to:
Values below. Confidence level refers to the probability of randomness assigned to the values that weren’t in the tails of any of the tests I used.
Actual result:
With (4) excluded:
With (3) excluded:
With both (3) and (4) excluded:
Score in each case calculated using the probabilities rounded to the nearest percent (as they were or would have been submitted ultimately). Oddly, in every single case the rounding improved my score (20.95 v. 20.92, 19.36 v. 19.33, 16.96 v. 16.89 and 16.11 v. 16.08.
So, looks I would have only gone down to fifth place if I had only looked at total number of 1′s and number of runs. I’d put that down to not messing up calibration too badly, but looks that would have still put me in sixth in terms of post-squeeze scores? (I didn’t calculate the squeeze, just comparing my hypothetical raw score with others’ post-squeeze scores)
P.S:
With (1) (total number of 1′s) excluded, but all of (2), (3), (4) included:
With (2) (total number of runs) excluded, but all of (1), (3), (4) included:
With ONLY (1) (total number of 1′s) included:
With ONLY (2) (total number of runs) included:
So really it was the total number of runs doing the vast majority of the work. All calculations here do include setting the probability for string 106 to zero, both for the confidence level and final score.