All gas token versions share three common parameters — cost of minting, cost of burning and burning discount. The most effective gas token is cheap to mint, cheap to burn and provides huge burning discount. CHI parameters are as follows:
fixed_mint_cost = 30147 per_token_mint_cost = 36032 fixed_burn_cost = 14895 per_token_burn_cost = 6148 per_token_burn_discount = 24000
With these constants we can come up with cost functions for mint, burn and discount:
mint_cost(n) = 30147 + n * 36032 burn_cost(n) = 14895 + n * 6148 burn_discount(n) = 24000 * n
CHI burning efficiency is the ratio between bun discount and burn cost.
efficiency(n) = discount_burn(n) / cost_burn(n)
Due to the presence of fixed costs, CHI efficiency goes to maximum when number of tokens approaches infinity.
efficiency_limit = discount_burn(INF) / cost_burn(INF) efficiency_limit = 24000 / 14895 efficiency_limit = 3.903708523096942
Theoretical efficiency limit is 3.9
It is reasonable to use CHI only when there is a significant gas price difference between minting and burning. Required price difference equals to the ratio of minting cost to gas savings cost obtained from burning. As with efficiency the required price difference approaches minimun when number of tokens approaches infinity.
gas_price_diff = cost_mint(INF) / (discount_burn(INF) - burn_cost(INF)) gas_price_diff = 36032 / (24000 - 6148) gas_price_diff = 2.018373291507954
Theoretical minimal price difference is 2.02
Discount percentage is the ratio between gas savings cost obtained from burning and actual transaction cost without CHI usage. To calculate discount limit we fist need to calculate the amount of tokens to burn. Maximal discount in Ethereum is 50% of spent gas. Then burn discount should be equal to 50% of transaction cost and burn cost.
txn_cost + burn_cost = 2 * burn_discount txn_cost + burn_cost = 2 * 3.903708523096942 * burn_cost txn_cost = 6.807417046193884 * burn_cost
With knowledge of required burn cost we can calculate theoretical discount limit.
discount = (burn_discount - burn_cost) / txn_cost discount = (3.903708523096942 * burn_cost - burn_cost) / (6.807417046193884 * burn_cost) discount = (3.903708523096942 - 1) / 6.807417046193884 discount = 0.4265507024753895
Theoretical CHI discount limit is 42.65%