ASIC profitability equation

[reparto_temp]

Derived an equation that would predict the likely return of using a scrypt ASIC between two points in time. I put the equation in wolfram so there is no need to write any code to get results.

I derived the equation by using the profitability equation (https://bitcoin.stackexchange.com/quest ... ing-profit" onclick="window.open(this.href);return false;) and replace the difficulty variable with an exponential which strongly describes the litecoin difficulty increase so far. (Note: Bitcoin's difficulty is also increasing exponentially) This method can be used for bitcoin as well but it will not work for altcoins due to the impact of multipool mining.

just replace b with the expected bitcoin-litecoin rate (currently around 0.025, maximum was around 0.05)
replace h with the hashrate in hashes per sec (1MH = 1000000)
replace r with the block reward (currently 50 but will halve next autumn i think)
replace t_1 with the starting time (number of days since genesis block, currently around 940)
replace t_2 with ending time (number of days since genesis block)
https://www.wolframalpha.com/input/?i=- ... t_1%29+%29" onclick="window.open(this.href);return false;
the solution is the number of bitcoins you will earn in the specified time period
if you set the hash rate to 1MH then the solution tells you the hashrate/bitcoin rate required for a ROI within the specified time period

I have provided some solutions at the end of the post if you are having trouble with wolfram

factors to consider:
1.equation doesn't consider power costs but if you need to consider power then chances are it isn't going to be profitable. Also doesn't consider exchange fees or volatile exchange rates for altcoins
2.the historical difficulty data has periods when the difficulty increased super exponentially and linearly, these are most likely to do with the doge-lite feud and also the growing impact of multipool mining
3.i used litecoin because if multipool mining died then we are going to fall back to litecoin
4.scrypt asics are no more expensive than graphics cards so its not clear whether large miners will replace their gpu rigs or supplement them with ASICs, this will affect the rate of growth in the future and may invalidate the model. I also want to point out that, through moore's law, processing power is increasing exponentially therefore my assumption that the difficulty follows an exponential curve is valid
5.The overall profitability relies on the exchange rate between litecoin and bitcoin (or whatever coin pair) and hence is still somewhat subjective

Profitability rates:

Scenario 1:
Hash rate: 1MH/s (1000000H/s)
Bitcoin-litecoin rate: 0.025 (approx. current rate)
Reward: 50
Time period: 1 year starting from sometime around the time of this post (Days 950-1215)
Bitcoins produced: 0.38
https://www.wolframalpha.com/input/?i=i ... d+t%3D1215" onclick="window.open(this.href);return false;

Scenario 2:
Hash rate: 1MH/s (1000000H/s)
Bitcoin-litecoin rate: 0.05 (historical max.)
Reward: 50
Time period: 1 year starting from sometime around the time of this post (Days 950-1215)
Bitcoins produced: 0.77
https://www.wolframalpha.com/input/?i=i ... d+t%3D1215" onclick="window.open(this.href);return false;

Scenario 3:
Hash rate: 1MH/s (1000000H/s)
Bitcoin-litecoin rate: 0.075 (optimisitic future rate)
Reward: 50
Time period: 1 year starting from sometime around the time of this post (Days 950-1215)
Bitcoins produced: 1.15
https://www.wolframalpha.com/input/?i=i ... d+t%3D1215" onclick="window.open(this.href);return false;

Scenario 4:
Hash rate: 0.35MH/s (350000H/s) (Grid seed 5 chip ASIC, sells for 0.2 bitcoins)
Bitcoin-litecoin rate: 0.05 (historical max.)
Reward: 50
Time period: 1 year starting from sometime around the time of this post (Days 950-1215)
Bitcoins produced: 0.27
https://www.wolframalpha.com/input/?i=i ... d+t%3D1215" onclick="window.open(this.href);return false;

Scenario 5:
Hash rate: 5.2MH/s (52000000H/s) (Grid seed blade, sells for 3 bitcoins)
Bitcoin-litecoin rate: 0.05 (historical max.)
Reward: 50
Time period: 1 year starting from sometime around the time of this post (Days 950-1215)
Bitcoins produced: 4.01
https://www.wolframalpha.com/input/?i=i ... d+t%3D1215" onclick="window.open(this.href);return false;

As stated the profitability of scrypt ASICs is almost completely reliant on a stable exchange rate, I also want to point out that the ASICs are redundant after a year, and if you have to pay for power and mining/transaction fees then you will barely break even.

I could do extra work analysing the impact of ASICs on the bitcoin network but at first glance it seem that the ASICs had no impact, the difficulty was already rising exponentially and ASICs did little to change this. Also, using a mining contract service such as pyramining can produce approximately the same amount of profit as using scrypt ASICs.