Wright or Wrong? Let's read Craig Wright's "Selfish Miner Fallacy" paper together and find out

[cypherblock]

At t = -10 min, the expected time is still t = 15 min, but only because we have extra information. We know a priori that the honest miners won't solve a block between t = -10 and t = 0. So the question, when asked from t = -10, is equivalent to asking "what is the expected arrival time given that no block is find during the first 10 minutes of trying?"

Yes this is really the crux of the issue. However forgetting the bet for the moment, I'm not sure this is really what Wright wanted to model.

Let's look at it another way. Imagine we have a bunch of trials where the honest miner (at 66% hash) finds a block, and immediately SM starts trying to find their private block (HM keeps mining as well of course). Now sometimes the SM will in fact privately mine the very next block, and sometimes HM will beat them to it. If we now look at just the events where the SM was successful (they find the next block at t=s measured from the previous hm block) and look at the time interval from s to the next HM block, is that time 15min-s, or is it 15min, or some other value (7.5?) ?
|------s------|
|----------------s--|
|--s-------|
(where | = HM block, s=SM block found, and we are interested in the average time between x and the right hand pipe/block).

Anyway maybe that is a completely separate problem. But curious to hear thoughts on this.

 

[adamstgbit]

It would be interesting to measure how long it takes to find a block, when a block hasn't been found for 10mins.
and at the same time, measure the amount of time it takes on avg for each block to be found.
it would be mind blowing to hear that both these measurements turn out to be ~10mins.

 

[Peter R]

@cypherblock:

Great question. So the HM finds a block a t = 0, and then we focus on only the times when the SM finds the next block. Like you said, this is t = s (s could be anything).

The expectation value for the arrival of the next block by the HM is t = s + 15, because the HM always expects the next block 15 minutes from now.

The way I internalize this is that the SM gets an effective head start of 15 minutes by withholding the block.

 

[AdrianX]

@79b79aa8: the selfish miner finds the next block (height N) at time t = 0 (not an arbitrary time t). Because mining is memoryless, the honest miner always expects to find a block 15 minutes from now (and not from when he started). Since the honest miner is still looking for a solution at height N when the selfish miner finds his secret block, he still expects to find the next block 15 minutes from this event which occurred at time t = 0.

I am sure I found a statistical riddle based on what you are observing about invisible information - Oh yes it's called The Monty Hall Problem.

it seems to me Peter your statistical analysts is too simple, the next block is not based on "miner always expects to find a block 15 minutes from now" I can't explain it but I'm sure a mathematician can understand it's a variant of this The Monty Hall Problem, more information has been revealed while mining although a block was not found, so the chance of finding the next block is not like starting from scratch.

 

[Norway]

Thanks, @Peter R . I never took the time to dive into the selfish mining theory. I think your bet could be better worded (ref my "bugfix"), but it illustrates your point that the SM gets an effective head start of 15 minutes by withholding the block.

There is clearly also a risk related to witholding blocks, as it could be orphaned, And the orphan risk grows over time because the SM has less than 50%. Weather it pays off or not to be the only selfish miner becomes a question of math. But there is clearly an advantage here if we look at it isolated.

What if everybody are selfish miners? After all, miners are supposed to be selfish. Maybe there are some game theory at work here rendering the strategy moot.

I guess I have to do my homework if I should be able to really debate the whole selfish mining theory

 

[cypherblock]

It would be interesting to measure how long it takes to find a block, when a block hasn't been found for 10mins.

Yes this is what I proposed before (roughly). You can do this with real data on the blockchain. If you find all block intervals that took longer than 10min, and find the average interval of just those, the average interval is 20min.

 

[AdrianX]

@effectsToCause: This is not correct because mining is a memoryless process. No progress is made between t = -10 min and t = 0 for the honest miners. For the honest miners, the expected block is always 15 minutes away. At time t = 0, the honest miners still haven't solved a block (they are still looking for the solution for the block at height N), and so they expect to find a solution 15 minutes later (i.e., at t = 15 min).

the average time to find a block is from the moment you start mining on top of a public block, a SM block is no new information so why base of the average time off the SM block?
[doublepost=1501273764][/doublepost]

Yes it can. See here: https://gist.github.com/awemany/57b95a24b09b648bda1db9509f5dcba9

Less than a hundred lines of hopefully very easy to understand code.

Summary: @Peter R is right.

They small little keyword one quickly misses in the linked figure from Peter R (and I initially did as well) is the word next.

As in: A priori, there's no block in between the one from the honest majority and the selfish miner.

I don't understand what was modeled, and how and what is depicted

 

[lunar]

The Monty Hall Problem

@AdrianX

As far as I can see, this is exactly the issue. Great find.

 

[adamstgbit]

the average interval is 20min.

can someone confrim this.

altho it seems counter intuitive that whether the previous block has been found -10mins ago or 0seconds ago the expected time for the next block is always the same... i guess its possible.


dose this mean that the idea that since blocks come out on avg 10mins apart, on average you'll wait 5mins to get included in the next block(provided you have a nice fee and such...) is wrong? and infact when you make a tx even if the current block is 50mins old you're still expected to wait about 10mins for the next block.

 

[AdrianX]

@adamstgbit if it is 20 minutes, I would hazard a guess that the number of blocks found before 10 minutes bring that average down to 10 minutes.

on reason there may be more blocks found within the 10 minute window would have to do with the growing network. But the statistics are based on the published blocks and the average time tends towards 10 minutes.

@Peter R how is it that mining is memoryless, surly you don't need to remember past attempts as they are binary, they are remembers because they didn't work. Are you suggesting there is a probability miners are wasting hashing attempts duplicating the same equations?

 

[Zangelbert Bingledack]

 

[Norway]

@Zangelbert Bingledack

At t=-10, an HM with 2/3 of the total hashrate finds a block, and let us assume that the next network block is expected to be found by an SM at t=0.

This is very wrong.

At t=-10, The SM is expected to find a block at t=20. Because the selfish miner, with 33,3% of hashpower, is expected to find a block after hashing for 30 minutes.

At t=-10, The HM is expected to find a block at t=5. Because the honest miner, with 66,6% of hashpower, is expected to find a block after hashing for 15 minutes.

At t=-10, the combined miners are expected to find a block at t=0. Because the miners together, with 100% of hashpower, are expected to find a block after hashing for 10 minutes.
[doublepost=1501279948,1501279245][/doublepost]My interpretation:

"... and let us assume that the next network block is expected to be found under conditions that are not expected".

 

[Peter R]

This afternoon Craig Wright removed his paper "The Fallacy of Selfish Mining: A Mathematical Critique" from the SSRN preprint server.

I understand that he wants to make further changes and updates.

He has asked me to also end my ongoing critique of his paper in this thread. I am happy to oblige.

​

 

[Bloomie]

Locked per OP