luck.. what's wrong with this math?

[mdude77]

I'm overlooking something here, and I'm sure someone can point out to me where my error is.

If a pool finds a block on average every 60 minutes ("100%" luck), then...

1. If that pool finds a block in 1 minute, it's 60x better than expected? 
2. Therefore, at the opposite end of luck, 60x worse than expected is 3600 minutes?
3. However the average of 1 and 3600 isn't 60.

Is #3 the flawed premise, or is something wrong with #1 and #2?  Or all the above?

Thanks.

M

[1715034418]

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[1715034418]

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[OgNasty]

If a pool finds a block on average every 60 minutes ("100%" luck), then...

1. If that pool finds a block in 1 minute, it's 60x better than expected? 
2. Therefore, at the opposite end of luck, 60x worse than expected is 3600 minutes?
3. However the average of 1 and 3600 isn't 60.

The average shouldn't be 60, because on average it took you 1800.5 minutes each to find the 2 blocks.  

If it took 1 minute for the first and 119 minutes for the second, then you'd be looking at 100% luck.

[mdude77]

If a pool finds a block on average every 60 minutes ("100%" luck), then...

1. If that pool finds a block in 1 minute, it's 60x better than expected? 
2. Therefore, at the opposite end of luck, 60x worse than expected is 3600 minutes?
3. However the average of 1 and 3600 isn't 60.

The average shouldn't be 60, because on average it took you 1800.5 minutes each to find the 2 blocks.  

If it took 1 minute for the first and 119 minutes for the second, then you'd be looking at 100% luck.

Okay, that means #1 and #2 are invalid.

120 minutes is 2x as long 60 minutes. 
30 minutes is 1/2 as long as 60 minutes.

Why isn't a block in 1 minute 60x better than expected?

M

[QuintLeo]

The issue isn't that 1 or 2 are invalid, the issues is the mathematics of calculating an average.