Greetings Experts & Mathemagicians!

I was wondering if someone could help me express this in a *Theory Formula* VS * With concrete Values*

I am trying to express this, with a formula :

Variable Z : a value which represents 1 unit of a finite resource with a maximum amount existing (510 000)

All Z are currently in existence and none can ever be destroyed nor created anew.

1 unit of Z can only be in one of two locations, either in the initial genesis pool left untouched. Or has been successfully released from the genesis pool into a new pool which represents current <<circulating>> supply. Once a Z has been transferred, it can never go back to the genesis pool.

Variable X : a value representing the current supply of Finite Resource Z which is capped at 510 000, which is currently in Genesis Pool and has not been released.

Variable Y : a value representing the current Z in circulation which have been released from the Genesis Pool and currently reside in an <<available>> pool.

Variable W : The value representing the Z which were removed from the <<available>> pool because the resource was bought at a certain price determined by A.

Variable A : a certain trigger, like a wave or round of something with a total supply of 8, no decimals (1,2,3,4,5,6,7,8)

happens consecutively from 1 to 8 if a certain criteria is met.

Variable Ab : The released supply of the finite resource based on variable A (8 possibilities : Ab value changes based on value of A.

Everytime A happens, and it happens in order from 1 to 8 if certain criteria are met, then Variable

If A=1, then Ab = 2000 Z released from Genesis pool to Circulating supply.

If A=2, then Ab = 4000 <<idem>>

If A=3, then Ab = 8000

If A=4, then Ab = 16 000

If A=5, then Ab = 32 000

If A=6, then Ab = 64 000

If A=7, then Ab = 128 000

If A=8, then Ab = 256 000 (as A Reaches 8, then the genesis pool as been depleted and ALL supply is in circulation forever)

Variable K : The Resource*s Current Worth (Currency) which the value changes based on how many A happened. if A=1 then Y = 2. If A=2 then Y = (A=2)*2 and so forth.

If A=1, then K = 2

If A=2, then K = 4

If A=3, then K = 8

If A=4, then K = 16

If A=5, then K = 32

If A=6, then K = 64

If A=7, then K = 128

If A=8, then K = 256

J = The amount of K which was amassed during event A=1 through 8.

The Genesis Pool is created, A=1 happens automatically since the event exists.

For A=2 to be true then all the supply from the available pool Y, were transferred to pool W, because Ab was sold at K value.

The objective is to demonstrate that no matter how many times A (the trigger or wave) happens, that the new released supply Ab is equal to half of the current Y Circulating supply)

Any thoughts on how to express this or if some variables are useless ?

Is there a way to express it where all Waves (A) are included ?