But the head start doesn't change anything. At this point A is mining on their block, B is mining on theirs. There's no advantage.

I'd even say that B is slightly more likely to keep their reward because they started propagating their block earlier, so it's more likely other miners are mining on this block.

If A finds a second block between minute 1 and 2, then they win, but it would be the same if the didn't withhold their block.

When A is mining on their hidden block, they mine for a potential height of 2 that would win against a miner only able to push a height of 1. But by doing that they put the block they found at risk of being abandoned because another miner found a block in the meantime.

So if you find a block, you get almost 100% chance it'll stay if you publish it immediately. If you withhold it and find another one you get 100% chance of keeping your 2 blocks. If you don't find that 2nd one, you get <50% chance of your block to be the main chain (depending on time of reaction of another block being published, and connectivity). On the other hand, if you don't withhold it and find 2 blocks in a row, you also get almost 100% chance of keeping your 2 blocks. I fail to see how withholding is profitable.

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palata 2 hours ago | parent [-]

> I fail to see how withholding is profitable.

Because you keep ignoring the part where it is profitable :-).

> If A finds a second block between minute 1 and 2, then they win, but it would be the same if the didn't withhold their block.

Except that by withholding their block, they got a headstart so they are more likely to find the second block. So it's not the same.

And you keep ignoring the fact that they don't necessarily have to wait until someone else finds a competing block. Maybe a winning strategy is to always withhold the block for 5 seconds. If you slightly increase your likelihood to find the winning block, you increase your profit, and that's the whole point.

With the interesting consequence (and that's the game theory part) where if everybody starts withholding their block for 5 seconds, then it changes the winning strategy.

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copirate an hour ago | parent [-]

> Except that by withholding their block, they got a headstart so they are more likely to find the second block. So it's not the same.

Withholding their block (5s or whatever) doesn't make them more likely to find the second block. The probability of finding a block is always the same, given a hashrate.

They are the only ones mining on this particular chain, but that's not an advantage either. How mining on a hidden chain is an advantage?

On the other hand, withholding certainly makes them more likely to lose the reward of the block.

	▲	adgjlsfhk1 5 minutes ago \| parent [-]
		the key to realize is that this strategy only makes sense if you have a considerable fraction of total hashrate. If you have 10% hashrate, delaying for 1 block period gives you a 10% chance of finding another block on top (that no one else can search for because you haven't published the first one).