Помощь в реализации формулы

pm = P_m = P_2 + (1 - P_2) / (n - 2) * (m - 2)  // задано
pm = p1 * q ^ (m - 1)  // геометрическая прогрессия
1 = p1 + ... + pm = (p1 * q ^ m - p1) / (q - 1)  // сумма m членов прогрессии

pm / q ^ (m - 1) = p1
1 = p1 * (q ^ m - 1) / (q - 1)

pm / q ^ (m - 1) = p1
p1 = (q - 1) / (q ^ m - 1)

pm / q ^ (m - 1) = (q - 1) / (q ^ m - 1)
p1 = pm / q ^ (m - 1)

pm * q ^ m - pm = (q - 1) * q ^ (m - 1)
p1 = pm / q ^ (m - 1)

pm * q ^ m - pm = q ^ m - q ^ (m - 1)
p1 = pm / q ^ (m - 1)

pm = pm * q ^ m - q ^ m + q ^ (m - 1)
p1 = pm / q ^ (m - 1)

pm = q ^ m * (pm - 1) + q ^ (m - 1)
p1 = pm / q ^ (m - 1)

q ^ m * (pm - 1) + q ^ (m - 1) - pm = 0
p1 = pm / q ^ (m - 1)

Решения для P_2 = 0.5 и n = 8

Предмет уровня 1

• P_1 = 1

Предмет уровня 2

• P_2 = 0.5
• q = 1

Предмет уровня 3

• P_3 = 0.58
• q = 2.075

раскрыть

Предмет уровня 4

• P_4 = 0.67
• q = 2.92

раскрыть

Предмет уровня 5

• P_5 = 0.75
• q = 4

раскрыть

Предмет уровня 6

• P_6 = 0.83
• q = 6

раскрыть

Предмет уровня 7

• P_7 = 0.97
• q = 12

раскрыть

Предмет уровня 8

• P_8 = 1

globals
    constant hashtable Hash = InitHashtable()
endglobals

library ItemAbility initializer init
globals
    constant hashtable Hash = InitHashtable()
endglobals

struct AbilityLevelChances
    static constant integer MaxItemLevel = 10

    private static key ParentKey

    readonly boolean edged
    readonly integer itemid
    readonly integer itemlevel
    readonly integer abilid
    readonly integer pm
    readonly real q
    
    static method create takes integer itemid, integer itemlevel, integer abilid, integer pm, real q returns thistype
        local thistype this = allocate()

        set .itemid = itemid
        set .itemlevel = itemlevel
        set .abilid = abilid
        if itemlevel == 1 or itemlevel == MaxItemLevel then
            set edged = true
            set .pm = 100
            set .q = 1.
        else
            set edged = false
            set .pm = pm
            set .q = q
        endif

        call SaveInteger(Hash, ParentKey, itemid, this)

        return this
    endmethod

    method onDestroy takes nothing returns nothing
        call RemoveSavedInteger(Hash, ParentKey, itemid)
    endmethod

    static method fromItemId takes integer id returns thistype
        return LoadInteger(Hash, ParentKey, id)
    endmethod

    method getChance takes integer abillevel returns real
        if abillevel > itemlevel or (abillevel < itemlevel and edged) then
            return 0.
        elseif abillevel == itemlevel then
            if edged then
                return 1.
            endif
            return pm
        endif

        return pm * Pow(q, abillevel - itemlevel)
    endmethod

    method getRandomLevel takes nothing returns integer
        local real rv
        local real max
        local real min
        local real p
        local integer level = itemlevel
        if edged then
            return level
        endif
        
        set rv = GetRandomReal(0, 100)
        set p = pm
        set max = 100.
        loop
            set min = max - p
            exitwhen level == 1 or (min < rv and rv <= max)
            set level = level - 1
            set p = p / q
            set max = min
        endloop
        return level
    endmethod
endstruct

private function init takes nothing returns nothing
    call AbilityLevelChances.create( /*
        */ 'I000', /*  item ID
        */ 5,      /*  item level
        */ 'A000', /*  ability ID
        */ 75,     /*  P_5
        */ 4.      /*  q
        */ )
endfunction

endlibrary