Optimum Morph Level

If you're trying to maximize your lord stats you should worship a gain-boosting deity and automorph. This article is for those that are trying to morph as quickly as possible.

This is an attempt to calculate the optimum Morph level. Scroll down for the bottom line if you don't care for the math.

Assumptions:

• Fail probability is linear between 300 (20%) and 500 (50%) and linear again between 500 and 999 (100%).
• Expected fail levels is (1000 - level) / 10. I'm aware that this is slightly more than observed, but shoudn't be more than 10 levels or so.

Let

• S(x) be the expected levels you do if you first try morph at level x
• p(x) is probability of failing at level x
• f(x) is number of fail levels

Then:

S(x) = p(x) * x + (1 - p(x)) [f(x) + S(x + f(x))]

( Note that you do f(x) "half-xp" levels so effectively you only "lose" f(x) levels. )

We can just calculate the above for various x. For simplicity, assume S(some sufficiently high level) is fixed.

Running these numbers for S(500) = 0.5 * 500 + 0.5 * (50 + S(550)) + ... or roughly 550

• S(430) ~ 450 * 0.4 + (1 - f(450)) * [S(500) + 50] ~ 530
• S(370) = 370 * 0.3 * [S(430) + 60] * 0.7 ~ 530
• S(300) = 300 * 0.2 + [S(370) + 70] * 0.8 ~ 540

Bottom Line

Morph early and often.

• Optimum morph level is somewhere around 370. Could be 400. Could be 350.
• TNL/worship etc. don't matter.
• Difference between morphing at 300 and 400 and 500 is not more than 10-15 levels. So it isn't all that important when you morph.
• Expected levels you do at hero is roughly 550.