Topic: Bitcoin Halving - here's the math (Read 1171 times)

Very cool, however I think I just popped my last brain cell, following it.

In theory, adoption will grow and this increase in people using Bitcoin, would increase transactions and hopefully the scaling will keep up with that and then bump the block sizes to make room for more transactions. The more transactions you have, the higher the miners fees.

In some time in the future, these miners fees will be more than the block reward, because with every halving that is reduced by 50%.

As previous posters have pointed out, there seem to be a couple of flaws in the maths here. One is that block generation time will stay at 10 minutes (approx.), this cannot be true, as for Bitcoin to stay viable and increase in use, generation times need to be reduced drsamatically imho. Transaction reward is based on the value of goods purchased, and not on the value of a Bitcoin. If Bitcoin doubled in value overnight, people wouldn't be prepared to pay twice as much for a pizza just to use Bitcoin for payment.

You just slapped the face of those shill posters who are expecting an increase in the 21 million cap.
Some, if not most, of them are paranoid that at some point in the near future, we'll hit the 21 million cap when in fact, we're probably gone when we're nearing 21mil cap.

Well that is one of the ways you could explain Bitcoin halving. You could just say that every 210,000 blocks the block reward gets halved. It is pretty easy.

IMHO there are two matters to be considered in answering this question

(1) It is the total miner fees for all transactions in the block that is expected to be more than the block reward. Currently, there are between 1000 to 3000 transactions per block. This is expected to increase as bit-coin becomes more popular.

(2) This situation is expected to occur in the future and not immediately. Perhaps, when mining reward is less than 1 BTC (just guessing, it may be before, it may be after, but most probably not in the near future)

But if theoretically the miner fees will cost more than the block rewards and the price of Bitcoin gets very high, doesn't that mean people will spend fortunes in miner fees for moving even small amounts of money? How will this work out in the future?

Miners will continue mining, because in theory the transactions will increase and then the miners fees will be more than the block rewards. Miners will then compete for the bigger miners fees and not really for the block rewards. You will also find that big businesses will rely on the Bitcoin network and will build infrastructure to support mining to keep their other businesses going.

This is still a theory and that's why we still call it an experiment. ^smile^

but i dont understand anything what op wrote. i will try to learn math someday and increase my knowledge about how bitcoin system works.

The difficulty computation assumes that the expected hash rate for the next 2160 blocks is the same as the hash rate for the last 2160 blocks. So, if the actual hash rate is higher then blocks will be found more quickly than expected, and if it is lower then blocks will be found more slowly than expected. The hash rate has generally been increasing over time, so blocks have been found more quickly than expected, on average, resulting in a halving date earlier than expected.

isn't this related to the manner in which the difficulty target is recalculated, as defined by the developers ? am I correct in understanding that if the 10 minutes average is to be brought down, some change will need to be done to the code that recalculates the difficulty every 2160 blocks ?

I like math...... it is so sure and i like sure things.

The prediction of halving dates is based on an average block time of 10 minutes. So far the block time is almost all <10 min. Therefore the estimate of 2140 will come earlier if bitcoin keep on growing.

Transaction fees will take over. In any case, we will all be dead by then.
Btw you wrote 2041 instead of 2141.

A lot and usefull information you letting me know about all prediction and period in just one single post,well the concept of bitcoin distribution its amazing,and at the moment all people know thats there is a limit till 2140 but the question is what will happen in 2041 as the mine will be over,miners wont turn off,otherwise the security of bitcoin would be lost.

Yes, because of rounding down. 50 BTC * 100 million Satoshi is not product of 2 power, thats why rounding down comes in the play, like when halving from 9 Satoshi rounded down to 4 Satoshi.

But people like round numbers like starting 50 BTC * 100 million Satoshi block reward, proving Satoshi is just human afterall.

The Bitcoin system has been designed so that the reward for mining a block is halved after every 210000 blocks. When block 0 (also known as the genesis block) was mined in early 2009 it was 50 BTC (five billion satoshi) https://blockchain.info/block-index/14849/000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f

The first halving took place on reaching block 210000 towards the end of 2012, after which the reward for mining a block became 25BTC (2.5 billion satoshi) https://blockchain.info/block-index/270670/000000000000048b95347e83192f69cf0366076336c639f9b7228e9ba171342e It remains at this value today and will continue untill reaching block 419999. From block 420000 the reward will be 12.5 BTC.

It is generally mentioned that the total bitcoins that will ever be mined is approximately 21 million BTC. The math involved here uses geometric progressions (GP) . This is an ordered sequence of numbers where each number (or term) is obtained by multiplying the previous number by a fixed amount. e.g. consider the sequence 1,2,4,8,... here the fixed amount is 2. This is known as the common ratio of the geometric progression and is referred to by the letter 'r'. The letter 'a' is used to refer to the first term of a GP. So for the above GP a = 1 and r = 2.

If the common ratio (r) is a fractional value less than 1, this results in a GP where the terms decrease. e.g. 100000,50000,25000,12500,6250,... is a GP where a = 100000 and r = 1/2. GPs that have such common ratios are said to be convergent. It is a property of all convergent GPs, that the total obtained by adding any number of terms in such a GP (no matter how many terms) will always be less than a fixed value reffered to as the 'sum to infinity' of the GP. We shall refer to this as 'S'. It is obtained according to the simple formula given below

S = a/(1-r)

In other words, to obtain the 'sum to infinity' of a given convergent GP, subtract the common ratio from one, and then divide the first term by the answer obtained. Accordingly, for the GP 100000,50000,25000,12500,6250,... where a = 100000 and r = 1/2, S = 100000/(1-1/2) which gives 200000. What this means in practice is, that no matter how far we continue the above GP, the total obtained by adding together all the terms will always remain below 200000.

Now, let us see how this applies to Bitcoin. Here we will form a GP where the terms will be the total mining reward for a group of 210000 blocks.

for block 000000 to block 209999 total reward = 50 x 210000 = 10500000 BTC
for block 210000 to block 419999 total reward = 25 x 210000 = 5250000 BTC
for block 420000 to block 629999 total reward = 12.5 x 210000 = 2625000 BTC
for block 630000 to block 839999 total reward = 6.25 x 210000 = 1312500 BTC

and so on

It can be seen that we get a GP where a = 10500000 and r = 0.5 (or 1/2)
from this we can see that S = 10500000/(1-0.5) = 21000000

this means that the total reward obtained by mining all blocks that exist at any point in time (whether in the past or the future) will be less than 21000000 BTC. Since it is the bitcoins produced through mining that enter and circulate in the bitcoin economy, this means the total BTC in circulation will always be less than 21 million BTC. It should be noted that this also means that exactly 21 million BTC will never come into existence.

The table given below shows the mining reward in satoshis per block as the block chain grows
( 1 BTC = 100000000 satoshi )


Since 1 satoshi is the smallest unit of transaction in the Bitcoin system, when halving results in fractions of a satoshi, the fractional part is discarded. This will first happen on reaching block 2100000 and many times thereafter until ultimately the block reward comes down to 1 satoshi on reaching block 6720000. This means that from block 6930000 there will be no mining reward, and hence no new bitcoins produced through mining. At such a time miners will only get the tranaction fees, but it is expected that by such time the value of 1 BTC will be high enough for transaction fees alone to be sufficient compensation for miners.
If we use the above figures and calculate the total quantity of BTC produced, the figure obtained is 20999999.97480000 BTC, which is 2520000 satoshi less than 21 million BTC, and confirms the fact that the total BTC mined will be less than 21 million BTC as mentioned above.

The Bitcoin system has been designed so that new blocks are produced through mining at an approximate rate of 1 block per 10 minutes, which comes to around 144 blocks per day. So the time taken to reach block 6930000 should be 6930000/144 = 48125 days, which is a little less than 132 years. We know that the genesis block was mined, most probably by Satoshi Nakamoto himself, on 03-01-2009 as indicated on the blockchain at https://blockchain.info/block-index/14849/000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f. This means that by the end of 2140, block 6930000 would be reached. This is why it is said that the last satoshi would be mined in 2140, and that no new bitcoins would ever be produced thereafter.