Miner A can get 0, 1, 2, ... etc.  He could be lucky and get one block every 5 seconds, for example.

The actual odds are

0: 0.3673
1: 0.3685
2: 0.1842
3: 0.0612
4: 0.0152
5: 0.0030
6: 0.0005
7: 0.0001
8: 0.0000

If you work it out you get an average of 1 block.

For a miner with 10X the power, the distribution is

0: 0.0000
1: 0.0004
2: 0.0020
3: 0.0070
4: 0.0179
5: 0.0366
6: 0.0620
7: 0.0897
8: 0.1133
9: 0.1268
10: 0.1272
11: 0.1157
12: 0.0961
13: 0.0734
14: 0.0519
15: 0.0341
16: 0.0210
17: 0.0121
18: 0.0065
19: 0.0033
20: 0.0016

It is balanced around 10.  

Again, if you work it out, it averages to 1.

However, the more powerful miner gets lower variance.

All miners produce diff 1 shares at the same speed relative to hashrate (let's ignore the variance there). They do this no matter what share difficulty is wanted by the pool. Every one of those shares has 1/pool_diff chance of being accepted by the pool. Saying "it would've taken 31 seconds to finally get that share, but because the block took only 30 seconds I never had a chance" is just blatantly wrong.

Yes he can. He can also be extremely unlucky and have it take the equivalent of 1 minutes (although once the block his found the entire scenario resets, so he doesn't actually proceed to that minute).

And as I also already stated, the pool, as well, can get lucky and rapidly produce blocks, in such a case making it even harder for Miner A to get a share. The extreme right ends of the share/block scale work against each other.


If it takes 30 seconds on average to find a share, by the definition of an average, the distribution of "made it" or "didn't make it" when 30 seconds is the cut-off is evenly distributed between < 30 and > 30.

That doesn't make any sense. The whole point of a 512 diff rate is you send data to the server 1/512th of the time vs 1 diff. If they never get sent, how are they going to be accepted.

Interestingly, I didn't realize modern slot machines were programmed to change their odds depending on previous outcomes. Are you sure? That doesn't even really sound legal. I don't actually have much experience with them and was basing my hypothetical scenario on old-school mechanical slot machines, assuming they worked like that at some point. In any case, I'll stick with hypothetical, perfectly-balanced dice for any further analogies.

Unless I've been misunderstanding how a computer solves a block/share, it's not a solution in the same way a human would sit down and solve a differential equation by methodically working through it. Rather the computer just spams thousands to millions of potential answers until one works. This is were it is like throwing dice.

If you throw an endless stream of dice over and over again into a box and you get one point for every 6 that comes up, you will get one point on average every six rolls. This is actually very different from saying that you should expect every sixth roll to be a six. The actual sequence of rolls is random, but due to the six equally probable outcomes of each roll you should expect that in a large set, 6 will account for 1/6 of the total number of rolls (as would every other individual number). If I decide to swap your box every few seconds, it shouldn't matter. Sometimes a box will go by without you rolling a six, other times you'll roll one, two or more sixes into a given box and it will still average out to 1/6. If I swap the boxes even faster, it still doesn't change your chances on each individual roll. Unless you roll a six as I'm switching the box and it hits the side instead of going in, which I suppose is a rejected share in this analogy.

It's simple. The miner generates diff 1 shares. If a pool requests diff 512, the miner checks every share against that requirement. The miner ends up sending on average 512 times less shares, but every share is checked locally by the miner, and so has a chance. There is no magical 'buildup' to diff 512 that takes a random amount of time.

Um... I'm pretty sure that that - what you just said there - is what actually doesn't make any sense.
By the way, it's not ad hominem to point out when someone is wrong. And based on what you just said, I think you just lost what little credibility you had. I think you should go read up on how mining actually works before arguing any more.

And next round you might send way more diff 512 than expected with your hashrate. Yes, that round could turn out to suck by being longer having smaller PPS% from the coin. It could also be better than the round which you missed by chance. Is that what you're arguing is the problem?

It doesn't make sense because - here, let me spell it out to you once more. There. Is. No. Set. Interval. Between. Submissions.