Mathematical theory
The rationale for Nakamoto's choice.
Calculation of the number of blocks in a four-year cycle:
6 blocks per hour
*24 hours per day
* 365 days a year
* 4 years per cycle
= 210.240
Which is approximately 210,000
The sum of all prize sizes for mined BTC block
50 + 25 + 12.5 + 6.25 + 3.125 + ... = 100
210,000 * 100 = 21 million.
One forum user stressed that this equation, however, could not explain the decision made by the creator of Bitcoin, as it was constructed on the basis of already existing parameters.
To go a bit further, and try a thought experiment, a value of 84 million coins could have been used. With the calculations occurring thus:
12 blocks per hour
*24 hours per day
* 365 days a year
* 4 years per cycle
= 420,480
Which is approximately 420,000
The sum of all prize sizes for mined BTC block
100 + 50 + 25 + 12.5 + 6.25 + 3.125 + ... = 200
420,000 * 200 = 84 million.
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With this amount of coins, and changing nothing else in the algorithm (and if my guesses are correct), the current circulation supply would be around: 74,640,000.
Given a market cap of 1.07 trillion, may put the price of one bitcoin at: $ 14,373.
The price of 14k is lower than the current 60k, but this only takes into account an increase in supply, it does not include the human's psychology surrounding prices of assets. That is, since the price would be lower for the 84 million capped coin, the FOMO would be less. People would have less fear of missing out over the life this 84 million capped coin since there are more coins in circulation. This effect may produce less interest, and therefore less buyers which produces an even smaller price than 14k.
Yet another psychological effect on the price, is simply that a lower price gives the impression of less value. People are less willing to purchase something that has less value. This seems counter intuitive, but this happens quite frequently in pricing.
One can see that having an even larger circulation number, like in the trillions, would produce even smaller prices for a coin, with even less psychological human interest, in which case it's possible to imagine that bitcoin wouldn't have taken off as it has.
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Given the above, there is no reason to think that Satoshi did not experiment with various caps, and block reward amounts, before a final implementation of what we have now.
