[copirate]

But by withholding you also increase the risk that your first block will never end up in the main chain (if the remaining 90% find a block while you're withholding).

And you would sill have 10% chance of mining another block if you don't withhold.

What advantage does withholding give you?

[palata]

> What advantage does withholding give you?

One last time. By withholding, you have a headstart on the next block. If you can mine for longer, you increase your chances.

[copirate]

Mining on the hidden chain is not necessarily a head start. It would be if it was certain that this hidden chain will become the main chain. But if it doesn't, then mining on it was a waste, not a head start. Of course you don't know in advance, but that's exactly my point. If you don't know whether you're on the right track, you can't say you have a head start. And in the described situation, it's not guaranteed at all that the hidden chain will become the main chain.

The hidden chain can easily be discarded if the miner of the hidden chain doesn't find a 2nd block and if the miners on the public chain find a block and propagate it before the hidden chain is published. In that case, the public chain and hidden chains will be 2 competing heads, and other miners will decide which one wins. They will generally take the first block they saw, so most likely not the (previously) hidden chain. In that situation, mining on the hidden chain was a waste, not a head start. We could even say that the miners on the public chain had a head start. That's why I say there's no such thing as a head start.

[palata]

I think that at this point, you would have to learn more about probabilities. You're stuck at "I don't understand how having 51% chances to win is better than having 49%, because you cannot know the result in advance and there is a 49% chance that you lose, in which case you have lost".

[copirate]

No, I'm saying it's not clear at all who is in a better position. I'd even argue that the miner hiding his block is in a worse position.

But I'll stop discussing that with you. It's pointless and you're way too condescending.

[palata]

> I'd even argue that the miner hiding his block is in a worse position.

That's just an intuition. You keep saying "having a headstart doesn't help, because those are independent probabilities". Which is wrong: having a headstart does help. How much does it help, and is it worth it? That's the whole question. And it would require more work to answer it.