Dude, 8e-9 is not a little bit of maths. 1e-2 and 1e-3 could be, but perfection is not a little bit of maths...

But if it is like you are stating, let's wait for a Claude/GPT-based answer. Let's see if sota LLMs are able to describe this "a little bit of maths" and to let us able to replicate it. We are ready to learn

This is maths, If a remember they had 40 sites. It just takes 41 submissions to probe the actual mean of all 40 sites. So this is math, I don't need Claude for this. it is very simple. Start by a submission of all zeros. The Abs MBE will be the mean of means of station (S0). To probe one station, you submit le's say 10**9 for that station and zero for the other. The score will be the the (sum of mean of other station + 10**9 - probed station )/40 (S1). 40 (S0 - S1) will equal 2* mean of probed station - 10**9 and you can get the mean target of the probed station. I told you, this is maths 😄.

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You'll hit numerical precision issues with 10**9. Even with 10**4 and the 9 digits of floating points the Zindi LB gives you, you'd need to do a second pass to nail down the last few digits.

But since you're a math guy.. you might appreciate Hadamard matrices as a more numerically stable alternative for the same 41 submission cost.

You're right. The idea is not about 10**9 but using a value that is above the maximum possible value of the target. Here 10**4 is a better choice