suppose for the sake of argument that each individual miner has the same amount of hashing power of one hash per unit of time (a "tick").

the probability that a miner solves their block in the next tick increases with the number of hashes already checked, since the nonce space is finite.

colluding miners could agree to pay the coinbase transaction to the same address and thus work on solving exactly the same block. they could divide the nonce space amongst them and thus exhaust the nonce space faster than solo miners.

by agreeing to redistribute the rewards of their mining amongst them, the colluding miners have an expected payout for the next tick that increases faster than that of solo miners, since they are exhausting their nonce space faster.

so isn't it rational for miners to collude? could this create a tendency to monopoly in mining?


4 Answers 4


No. Your premise is wrong. There is no guarantee a solution exists in a range. If a miner exhausts a nonce range he changes other components of the block header. Mining is a Poisson process with each hash attempt independent of any others.

Hence, there is nothing to gain with this particular kind of collusion. Of course, pooled miners enjoy less variance than solo miners (which is legitimate), and there are other methods of attack.

  • And even if you knew a solution would exist in a particular block range, it wouldn't be a problem. Miners will be working on different block anyway (different time, different transactions included etc.).
    – Jori
    Commented Feb 15, 2014 at 17:44
  • @Jori my assumption here is that the miners are colluding, hence working on exactly the same block -- so the same creation time and the same transactions, including the same coinbase transaction.
    – popstack
    Commented Feb 15, 2014 at 18:01
  • Miners will be working on different block anyway, I never mentioned the colluded miners, there are other miners as well. Also the term 'colluded' is a bit misplaced here. These pacts don't have to be secret and in fact do exist, but just not for the reasons you prodvided
    – Jori
    Commented Feb 15, 2014 at 21:26

the probability that a miner solves their block in the next tick increases with the number of hashes already checked, since the nonce space is finite.

This is false. The probability that a miner solves their block has nothing to do with the number of hashes already checked. A block is solved if the nonce produces a hash less than the difficulty. Neither of these things are affected by prior hashes checked.

The nonce space is finite. But the nonce space can contain zero block solutions, one block solution or even two block solutions.

A typical miner exhausts their nonce space and starts working on a different block several times each second. I have a miner behind me that mines at about 300GH/s. Since there are only 4 billion nonce values, it can try the full range of nonce values 75 times each second. Needless to say, most blocks are unmineable with any nonce, and you must try again with a different block.

The odds of a block being mineable with any nonce are less than 3 billion to one.

  • 1
    Or, to put it another way, the faster you exhaust the nonce space, the worse. When you exhaust the nonce space, you have to do some extra work before you can get back to hashing. Commented Mar 10, 2016 at 10:13
  • Which other parameters are changed once the nonce space is exhausted?
    – Olshansky
    Commented Dec 26, 2017 at 0:46
  • 1
    There's a field in the coinbase transaction that you can set to any value you want that's sometimes referred to as the "extraNonce" field. Also, the time. And, of course, you can change the transactions. Commented Dec 27, 2017 at 19:28

Most of your question described a mining pool, and the motivation to form one.

Indeed it is rational to collude, and we have seen that as one of the earliest developments in the Bitcoin network. Also see: What is a Mining Pool, what is it good for?

Now, why don't we see only one mining pool? It's simple: Because it would be bad for the network! If one party controls too much of the network, i.e. 51% of the hashing power, they can control which transactions make it into the blockchain and get 100% of the mining rewards. This would quickly erode the trust in the network, and devalue bitcoins. For more information please refer to What can an attacker with 51% of hash power do?

Therefore miners, as people who are heavily invested in Bitcoin, are interested in keeping the mining power distributed. For example the mining pool GHash.IO has sent miners away when they were above 35% of the networks hashing power.

  • The motivations described by the questioner have nothing to do with the motivations of a mining pool (which is brought to live to ensure better distributed payouts).
    – Jori
    Commented Feb 15, 2014 at 17:45

The current hash rate of the entire network is in the order of 2^55 hashes/sec.; in 10 minutes (less than 2^9 seconds), we would be running through 2^64 hashes/second. This is 1/2^96th of the available space (between all of us), if EVERYONE colludes. The chance of randomly chosen nonces colliding is outweighed by the effort it would take.

Also remember that, in that 2^160 space, there are a LOT of answers.

  • The relevant figure is 2^640 rather than 2^160 since the block header is 640 bits. Addresses are 160-bit but that is beside the point. Commented Feb 18, 2014 at 15:28

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