## Why should a miner choose the longest blockchain if another chain has a higher expected reward?

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Why did miners/pools choose the longest chain for continuing it? Because with this strategy they have the highest expected bitcoin reward. The expected bitcoin reward is (new generated bitcoin (b) + transaction fees (t)) * probability (p) the block will not become orphaned.

Since today b + t is clearly dominated by b and b is kind of constant, today miners maximize p by mining for the longest blockchain. But what about the days when b gets close to 0? Then, right after a completed block, b and t are 0. Thus, a clever miner should ignore the latest block, since even with a small p he will end up with a higher expected reward.

But once miners become aware of transaction fees and will not build on the longest chain this could cause serious trouble? Did I forget something or are these assumptions right?

1The assumption that t starts out as 0 is wrong. Not all transactions will be included in every block. – Meni Rosenfeld – 2013-02-14T06:16:55.487

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I think it's conceivable that this could happen. But under realistic cases, I don't think it actually will. If you don't mine on the longest block, the probability that your block will ever be part of the longest block drops drastically. Unless a block you mine becomes part of the longest chain and stays that way, you never get any fees or reward at all.

ok, 5 seconds after a new block new t is 5/10*60 = 0.008333 (assuming 10 minutes blocks and an even distribution of transaction) of the old t or in other words the old t is 120 times bigger. So does it hold, that after 5 seconds the two p's also differ by a factor 120? This is for example not true if you hold more than 1/120 of the hash rate, is it? – user599464 – 2013-02-13T19:15:47.417

1You have to find a block just to be tied with the other chain in length but behind it because everyone saw the other block first. The odds that you'd find two in a row before the rest of the world finds one are so low that you'd need an incredibly lucrative transaction to make it matter. (Though it might matter occasionally in the future when the block reward is dwarfed by transaction fees.) The situation will resolve in a confirmation or two anyway. – David Schwartz – 2013-02-14T04:33:07.913

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You don't have to just find a block, but the blocks building on your block must reach a greater height than competing blockchain tips for others to reorganize their blockchain. In the easiest case that means you have to find two blocks before the whole network only finds one.

This is highly unlikely to happen, unless you have a) a significant portion of the network's hashrate at your disposal, or b) you find a block sufficiently near in time to the other block that each block reaches parts of the network first, and there are miners working on either to create a successor.

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If he doesn't choose the longest chain he would get nothing unless the next miners choose his block and not the latest, wich seems unlikely.

Also by the time that b = 0 if Bitcoin is not dead it will always be pending transactions with fees to be included on the next block (low priority transactions with small fees).