And you would sill have 10% chance of mining another block if you don't withhold.
What advantage does withholding give you?
And you would sill have 10% chance of mining another block if you don't withhold.
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.
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.
But I'll stop discussing that with you. It's pointless and you're way too condescending.
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.