Math Behind WAX.FUN

This page explain a math behind how pricing and curve progress works within WAX.FUN

Let's look into main parameters in our formulas

s - supply

r - user reserve, in WAXP tokens sent to WAX.FUN

r0 - initial reserve, amount in WAX calculated by taking initial

s_m - max_supply, theoretical max supply.

s(r) = s_m - s_m * r0 / (r + r0)

price(r) = (r + r0)^2 / ( s_m * r0 )

cap(r) = (r + r0)^2 / r0

To uniquely define a curve we have to specify (r0, s_m). For this we have following conditions:

s(r2) = N - amount of tokens to list, r2 - amount of WAX corresponding to N tokens to provide into WAX.FUN, so it reaches bonding curve progress 100%

Now,

cap(r0) = W0 - initial capitalisation (in WAX)

cap(r2) = W1 - final capitalisation (in WAX)

s_m = N / (1 - sqrt(W0/W1))

Example of calculations

Initial Market Cap is 1,500 USD at a time of token creation

Target Market Cap is 21,000 USD at a time of token creation

N in our case is 800M tokens

We can consider several cases for WAX price below:

wax_to_usd_1 = $ 0.05

wax_to_usd_2 = $ 0.12

wax_to_usd_3 = $ 0.3

W0 = 3250 / 0.05$ = 65 000

W1 = 50 000 / 0.05$ = 1 000 000

r0 = 65 000

r2 = sqrt( 65 000*1 000 000 ) - 65 000 = 189 951

s_m = N / (1 - sqrt(W0/W1)) = 1073754845, in practice our max supply is always 1 BLN tokens.

Let’s see how WAX price affects calculated values in the table below

As you can see WAXP token price doesn't affect whole math behind, it affects just amount of WAXP needed to reach 100% bonding.