"NEW" Race to Sub-30!

Tim Reynolds said:

ariasamie said:

someone please answer this guy:

TeddyKGB said:

Avg 29.52

30.13
(25.58)
26.97
28.83
29.02
(33.44)
29.46
31.44
30.47
29.34
29.78
29.78

What are the odds of the last two being exactly the same?

Click to expand...

this was originally posted on "NEW" Race to Sub-30!

Click to expand...

Let \( f(x) \) be this specific solver's probability of getting a solve of time \( x \). This is a discrete probability distribution since stackmats have limited precision. Then the probability is \( \sum_{x=0.00}^{\infty} f(x)^2 \), where the sum is taken over all numbers \( x>0 \) such that \( 100x \) is an integer. Maybe later tonight I'll try to write out a reasonable probability density and calculate this probability. But I'm kind of too lazy to do that.

The probability that any two consecutive times are the same out of an average of 12 is approximately 11 times this. Of course this overcounts a lot, but \( f(x)^2 \) is probably pretty small, so it's okay.

This also assumes each solve's probability function is independent of all the other times, which is in general a reasonably good assumption I would think.

Click to expand...

1. L2 U2 F2 D2 U2 L D L' F' U' B2 U' R' D B L U F L2 F' D U2 F L2 R
2. D2 L D' B' L' R2 B D' U2 B' F' U2 F' R2 F2 L B' F' U2 B' F2 D2 F' L2 B
3. B F U L R' U L R' B' F D F R2 D U2 L' R B2 D R2 B F' D2 U2 B
4. U2 B' D' U' B F' R' F' D' U2 B F R2 B2 D R2 D U' L R' B F2 D U2 F
5. B' F2 L2 R2 B2 U2 F R' B2 U' B2 F R B2 F L R2 B R2 B' F2 D B' F R'
6. F D2 L' R D U B' D2 B2 L2 F2 L' R' D U L' R2 F2 D2 U2 F' D B D2 B'
7. D U' L F D' R U F D U' F' D2 F' R2 B F D' U B L' R B2 F2 D' U2
8. D' R2 D U' L B' D2 F' U F' L B F' D U2 B' F' D U2 R' D' U' B' L' R'
9. D U2 F2 D' L' B' F D U' B2 F' L F D B2 F L2 D2 B F2 L' F' L2 R' F
10. D' B' F D L2 R U' B D' U' B2 D B' R B' R' D' U B' R B2 F' U' R2 U
11. L2 R' D2 L' R2 F L' R' D U' F D2 B2 U2 B2 F2 L R U2 B2 D L' R U2 R'
12. R B2 U R' B2 L2 B2 F2 D' B' R2 B F2 R2 B D' R D' U' B D' L2 R U' F2