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When bitcoin forks, does anyone know how many blocks ahead one chain gets before the miners on the shorter chain concede?

I am doing a research project on modeling Bitcoin, and I am wondering how realistic it is for miners to abandon their chain as soon as they receive a chain that is one longer than the one they have.

I imagine that as chains get longer (and more money/computational work is at stake) miners are more likely to try to catch up from a 'deficit' of one block.

There is also the fact that a miner with sufficient hashing power (40+ percent) has a reasonable chance of catching up from being behind.

Any thoughts on this stuff?

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Miners are incentivized to always mine at the longest valid chain tip. If there were incentives to not mine on the longest known chain, then we would expect the network to be unable to maintain consensus on the blockchain's state. And without that, it would be impossible to build a reliable financial system.

So it isn't about 'miners conceding a shorter chain', its just that miners will always all be mining at the chain tip. Currently, the majority of the block reward is constant (the newly minted coins), so a miner should not really care if they mine block X or block X+1: their reward will be ~the same in either case. As such, a miner is incentivized to just mine at the chain tip, because the chance of finding a valid block at either height is equivalent, but the potential reward for finding one at the chain tip (thus extending the longest chain) is much larger. Finding a block at a height that has already been found will likely mean the miner gets no reward, since that block will be rejected by the network as not being a part of the longest chain.

All of the above concerns situations in which there is not a fork due to a change in consensus code, just the regular competition between miners. If you mean to ask about forks caused by changes in consensus code, you'll need to be a little more specific, as the nature of the code change will affect the game theory. But in general: Bitcoin works because miners are incentivized to mine at the chain tip. Without this incentive, the system would likely not achieve the stability required to give any sort of reliability guarantee.

  • I understand what you are saying, but I am worried about this situation: Two miners find a block around the same time. Both get a bitcoin block reward. One extends his chain, so the other either has to concede that his bitcoin reward is no longer considered valid, or attempt to "catch up" and make his chain longest again. I may be misunderstood, but I believe this could happen in real life. – user97236 Aug 2 at 23:38
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    @user97236 This indeed happens all the time, and it's the reason why mining exists in the first place. The answer is that in this case the miner is still incentivized to switch, because if he observes the other fork being extended, he can assume that the rest of the network also switched to that fork, and thus even if he would succeed in extended his own fork, he is less likely to succeed to find 2 blocks in the same time as the rest of the network can find one. – Pieter Wuille Aug 2 at 23:57
  • @user97236 yes, that situation is possible and expected, the losing block is commonly referred to as an ‘orphan block’. If you search for that term on this site you’ll find lots of info. The losing miner’s most profitable play is to abandon their block and continue mining at the chain tip. Unless they have a majority of hashing power (>50%), they would be incurring a massive opportunity cost by attempting to outrun the rest of the network, with a low chance of success. – chytrik Aug 2 at 23:57
  • Thanks for the input guys, I think I understand now. The only people who wouldn't switch over to the longest chain right away are those who have blocks in the orphan chain. So this is at most k people if the fork is k long. – user97236 Aug 3 at 0:11
  • @user97236 even miners who found the block(s) on the shorter chain will maximize their expected profit by immediately switching to the longest chain. Note that it is exceedingly rare for an orphan block chain to be longer than one block. – chytrik Aug 3 at 2:27

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