The mathematics of Bitcoin halvings: Cracking the equations and formulas

The Bitcoin money supply equation The Bitcoin money supply equation formula provides a theoretical maximum supply. In reality, some early mined BTC might be lost, resulting in a slightly lower circulating supply.The Bitcoin money supply equation formula can be seen in the image below:In the given equation, “Sigma” represents the total of adding up the Bitcoin reward amounts throughout all the bitcoin halving events.i: An index variable that represents each halving cycle.0: The summation’s starting point represents the first (genesis) block.i=0^32: This defines the range of the summation.^32: The summation’s upper limit, indicating the 32nd halving cycle. Since counting starts from 0, this includes a total of 33 halving cycles (0 to 32).50: This is the genesis block’s initial block reward (50 BTC).(1/2)^ (i/210000)): This represents the block reward for each halving cycle.(1/2): This represents the halving factor, where each reward is divided by two at each halving event. This is why it’s raised to the power of -1 (1/2 is equivalent to two raised to the power of -1).(i/210000): This exponent accounts for the number of halving cycles that have occurred. As ‘i’ increases with each cycle (from 0 to 32), the exponent ensures the reward is halved at the appropriate intervals (roughly every four years).

The math behind the Bitcoin halving A few core concepts like the block reward, halving equation and exponential decay form the basis for the mathematical foundation of Bitcoin halving.An intriguing illustration of economics being governed by code is the Bitcoin halving mechanism. Essentially, this concept revolves around the block reward – the amount of new Bitcoins granted to miners for verifying transactions and appending a new block to the blockchain. When Bitcoin was created, this reward stood at 50 Bitcoins. Over a period approximately every four years, this reward is reduced by half.A straightforward yet effective equation controls this reduction: The block reward is determined by the formula: 50 decreasing every 210,000 blocks mined since Bitcoin’s creation.The exponential character of this equation is what makes it enchanting: With each addition of 210,000 blocks to the blockchain, the block reward decreases exponentially. Consequently, the reward was reduced to 25 BTC following the first halving, then to 12.5 BTC after the second, and so forth. This built-in decline mirrors the increasing intricacy and expense of mining precious metals, where resource extraction becomes more challenging and costly over time.The Bitcoin system’s mechanism for cutting in half the number of new coins created over time has major consequences. It creates an inherent scarcity by slowing down the rate at which new Bitcoins become available. Furthermore, the value of Bitcoin as a long-term investment is strengthened due to its limited supply and consistent production schedule.