**Jun 27th 2018, 3:42:52**

Ruled by multies?

**Jul 1st 2018, 23:46:04**

**May 24th 2024, 18:22:37**

Originally posted by **osloos**:

Very interested in seeing the $80 analysis. Can anyone provide?

This is 13 years old at this point, but here you go (qz ended up picking x = 0.25):

Mathematical analysis:

The idea is to see how varying x affects the late set oil price floor, or alternatively when it is worth it for destockers and other countries to burn oil barrels for additional PM units.

The key thing to take away from this is that all of the formulas reduce to a proportional relationship between x and the price of oil at the break even point for buying oil.

Suppose that x is the number of PM units (a PM unit is an extra 3 troops, 2.5 jets, 2.5 turrets, and 1 tank) that a country gets for burning one barrel of oil. We'd expect x to be less than 1.0

0) TMBR reselling (sell oil to get extra reselling time)

So our TMBR has cash to spend. It can either spend pm_mod * 2025 to get 6.5 additional NW or it can buy

1/x oil barrels to get an additional PM unit.

Since it takes time to spend money on the pm, we get (1 + price_of_oil / x / (pm_mod * 2025)) units worth of reselling at a cost of price_of_oil / x

nw gained from not buying oil = (price_of_oil / x) * 6.5 / (pm_mod * 2025)

nw gained from buying oil = 6.5 * (1 + price_of_oil / (x * pm_mod * 2025)) - 0.6 * (2025 * pm_mod + price_of_oil / x) / (0.94 * public_turret_price)

If we set the above two equal and simplify we get:

6.5 * 0.94 * public_turret_price / 0.6 = price_of_oil / x + pm_mod * 2025

x = price_of_oil / (6.5 * 0.94 * public_turret_price / 0.6 - pm_mod * 2025)

From here we can vary the price of oil and easily see how it affects things. So if we wish for the equilibrium oil price to be $100:

if public_turret_price = $110, x > 15.58 for oil to be worth buying

if public_turret_price = $130, x > 0.476 for oil to be worth buying

if public_turret_price = $150, x > 0.24 for oil to be worth buying

if public_turret_price = $170, x > 0.162 for oil to be worth buying

if public_turret_price = $190, x > 0.12 for oil to be worth buying

1) TMBR destocking (extra time stocking)

2) no mb theo (extra time stocking)

We can combine the above two. Call the stocking income per acre s.

To get an additional turn of destocking time, we need (1 + s / (pm_mod * 2025)) turns worth of pm,

so we need s = (1 / x) * (1 + s / (pm_mod * 2025)) * price_of_oil for it to be worth it.

x = price_of_oil * (1 / s + 1 / (pm_mod * 2025))

For a rep casher going TMBR or a farmer going no mb theo, x is around 0.25 if price_of_oil = $100

3) demo public destocking

need

money - cost_of_oil / (private_dpnw) = cash / public_dpnw

if public dpnw is better than turrets and worse than jets:

x = price_of_oil / (-1225 * 245 / public_dpnw + 1225)

if price_of_oil = $100:

if public dpnw = $265, x > 1.08

if public dpnw = $280, x > 0.65

if public dpnw is worse than turrets:

x = price_of_oil / (-420116 / public_dpnw + 1654)

if price_of_oil = $100:

if public dpnw = $290, x > 0.48

if public dpnw = $300, x > 0.39

if public dpnw = $325, x > 0.276

if public dpnw = $350, x > 0.22

if public dpnw = $500, x > 0.12

4) Extra PM space during war

Not related to destocking or balancing, but included for completeness.

extra cost to buy q troops = price_of_oil * q / (3 * x)

for $100 oil:

if x = 0.1, extra cost = $333m

if x = 0.25, extra cost = $137m

if x = 0.5, extra cost = $66.6m

if x = 0.75, extra cost = $44.4m

if x = 1.0, extra cost = $33m

5) Max price selling at the end of the set

Let c measure market commission (0.94, 0.9, or 1.0)

One pm unit would be sold at the end of the set for pm_mod * 2025 * 3 * c assuming the market empties

So for buying oil to be worth it, we need pm_mod * 2025 * 3 * c - price_of_oil / x = pm_mod * 2025

x = price_of_oil / (pm_mod * 2025 * (3 * c - 1))

For $100 oil:

CI, x > 0.034 for oil to be worth buying

TMBR, x > 0.05 for oil to be worth buying

no mb theo, x > 0.037 for oil to be worth buying

demo, x > 0.033 for oil to be worth buying