Kelly Criterion Applies Exquisitely to Mining
When the mathematical proof & paper behind the Kelly Criterion (optimal bet) was published (90's), there existed no real-world scenario where this mathematical principle could be applied with expected effectiveness.
It Does Not Apply Well to Trading & Markets
Why? Simple answer = asset prices are not dictated by probability. Perhaps you could model an estimate, but that would only be based on prior data.
The Kelly Criterion shines in instances where the payout/profit AND the % of obtaining said payout are BOTH KNOWN.
PoW Mining Fits Like Cinderella's Glass Slipper
1. The literal mechanism used by miners to obtain the 'winning' nonce value relies on hashing data using an algorithm that's designed to map inputs to a set of outputs stretched across a universe spanning from 0 to ∞.
2. Bitcoin provides a target for the hash output that calculates how long it should take the network (aggregate) to find an eligible nonce for a given block height. Every 2016 blocks, the difficulty is re-adjusted based on prior performance to meet this target.
3. Based on #1 and #2, we can mathematically derive the % that the nonce is found.
3a. The 10-minute target instantiates a Poisson distribution (% of successful trial shifts based on time elapsed since start).
3b. The nature of SHA256 as a hash algo makes each hash (guess) a bernoulli trial (binomial outcome; either you found a winning nonce [success] or you didn't [fail])
4. Since probabilities are based on the entire network's aggregate expended efforts, mining pools can estimate their deployed hashrate % relative to the rest of the network with the same level of reliability (no guess on upper bound limit for time elapsed before estimates become stale [# of blocks confirmed since last calculation].
5. Every block pays out a fixed reward of 6.25 $BTC (we will leave fees out of this entire construction since those are nominal compared to coin base payout ... for now).
6. A large mining op requires some contract w an electricity provider (generally priced down to the $$/wattage for some fixed period of time). The estimated # of hashes/second per machine should be known too (exclude overclocking, software mods etc. for simplicity's sake). Storage/warehouse overhead should be constant (lease/rent) & known.
^^ With all of our costs known, our probability of success known and the value of our reward also known - the Kelly's Criterion fits perfectly.
I'm not in the back office at a large mining firm. So I'm more than confident they've likely long since come to the same conclusion as myself. Notably, there exists nothing online alluding to such a calculation. That's not surprising though as its unlikely that all participants have made this deduction in optimal output (example: Marathon Mining + Riot Blockchain + Core Scientific made absurd purchase orders w massive delayed delivery times at the height of the bull market + deriving profit estimations in $$ for investors they debt financed from that unrealistically projected $BTC value >1 year later & resource consumption costs even before relevant contractual agreements had been established).
They're either dumbasses or dumb asses. Hard to figure which. Either way, Bitmain & Foundry (DCG) ended up laughing to the bank.
When the mathematical proof & paper behind the Kelly Criterion (optimal bet) was published (90's), there existed no real-world scenario where this mathematical principle could be applied with expected effectiveness.
It Does Not Apply Well to Trading & Markets
Why? Simple answer = asset prices are not dictated by probability. Perhaps you could model an estimate, but that would only be based on prior data.
The Kelly Criterion shines in instances where the payout/profit AND the % of obtaining said payout are BOTH KNOWN.
PoW Mining Fits Like Cinderella's Glass Slipper
1. The literal mechanism used by miners to obtain the 'winning' nonce value relies on hashing data using an algorithm that's designed to map inputs to a set of outputs stretched across a universe spanning from 0 to ∞.
2. Bitcoin provides a target for the hash output that calculates how long it should take the network (aggregate) to find an eligible nonce for a given block height. Every 2016 blocks, the difficulty is re-adjusted based on prior performance to meet this target.
3. Based on #1 and #2, we can mathematically derive the % that the nonce is found.
3a. The 10-minute target instantiates a Poisson distribution (% of successful trial shifts based on time elapsed since start).
3b. The nature of SHA256 as a hash algo makes each hash (guess) a bernoulli trial (binomial outcome; either you found a winning nonce [success] or you didn't [fail])
4. Since probabilities are based on the entire network's aggregate expended efforts, mining pools can estimate their deployed hashrate % relative to the rest of the network with the same level of reliability (no guess on upper bound limit for time elapsed before estimates become stale [# of blocks confirmed since last calculation].
5. Every block pays out a fixed reward of 6.25 $BTC (we will leave fees out of this entire construction since those are nominal compared to coin base payout ... for now).
6. A large mining op requires some contract w an electricity provider (generally priced down to the $$/wattage for some fixed period of time). The estimated # of hashes/second per machine should be known too (exclude overclocking, software mods etc. for simplicity's sake). Storage/warehouse overhead should be constant (lease/rent) & known.
^^ With all of our costs known, our probability of success known and the value of our reward also known - the Kelly's Criterion fits perfectly.
I'm not in the back office at a large mining firm. So I'm more than confident they've likely long since come to the same conclusion as myself. Notably, there exists nothing online alluding to such a calculation. That's not surprising though as its unlikely that all participants have made this deduction in optimal output (example: Marathon Mining + Riot Blockchain + Core Scientific made absurd purchase orders w massive delayed delivery times at the height of the bull market + deriving profit estimations in $$ for investors they debt financed from that unrealistically projected $BTC value >1 year later & resource consumption costs even before relevant contractual agreements had been established).
They're either dumbasses or dumb asses. Hard to figure which. Either way, Bitmain & Foundry (DCG) ended up laughing to the bank.