Optimum Morph Level - Revision history

3nki: /* Empirical Method */

2021-11-22T20:53:19Z

Empirical Method

2021-11-18T17:43:13Z

Bottom Line

2020-07-30T02:52:55Z

2018-01-11T21:10:00Z

2012-12-22T17:21:06Z

added empirical test

2012-07-22T20:56:13Z

2012-04-18T19:48:44Z

Typos

2012-04-18T19:33:25Z

Added categories

2012-04-18T16:43:06Z

typo/clarification

2012-04-18T16:30:25Z

clarification

@@ Line 41: / Line 41: @@
 </pre>
-On average, players morphed at level 522. Chance to morph at this level is 53% and is a safe place to start trying.
+On average, players morphed at level 522. Chance to morph at this level is 52.2% and is a safe place to start trying.
 Is this number the ''optimal morph level''? I wouldn't go into it since I'm not a mathematician, but it does correlate with the number presented in the earlier paragraph.

@@ Line 49: / Line 49: @@
 Morph early and often.
-* Optimum morph level is somewhere around 370-400.  If you're risk averse, wait until 520-560 [this minimizes the likelihood of getting perpetually unlucky -- the lower probability morph attempts have a lot more variance].
+* Optimum morph level is somewhere around 370-400 (389 should be 33.35% chance of success).  If you're risk averse, wait until 520-560 [this minimizes the likelihood of getting perpetually unlucky -- the lower probability morph attempts have a lot more variance].
 * TNL/worship etc. don't matter.
 * Difference between morphing at 300 and 400 and 500 is not more than 10-20 levels. So it isn't all that important when you morph, as long as you do it early.

@@ Line 6: / Line 6: @@
 * Success probability is linear between 300 (20%) and 500 (50%) and linear again between 500 and 999 (100%).
-<blockquote>• Note that, if true, this would theoretically mean levels between 300 & 500 are worth 1.5% additional chance of success per level, whereas levels after 500 each add only 1% chance of success.</blockquote>
+<blockquote>• Note that, if true, this would theoretically mean levels between 300 & 500 are worth .15% additional chance of success per level, whereas levels after 500 each add only .1% chance of success.</blockquote>
 * Expected fail levels is (1000 - level) / 10. I'm aware that this is slightly more than observed, but shouldn't be more than 10 levels or so.

← Older revision		Revision as of 21:10, 11 January 2018
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	* Success probability is linear between 300 (20%) and 500 (50%) and linear again between 500 and 999 (100%).		* Success probability is linear between 300 (20%) and 500 (50%) and linear again between 500 and 999 (100%).
		+	<blockquote>• Note that, if true, this would theoretically mean levels between 300 & 500 are worth 1.5% additional chance of success per level, whereas levels after 500 each add only 1% chance of success.</blockquote>
	* Expected fail levels is (1000 - level) / 10. I'm aware that this is slightly more than observed, but shouldn't be more than 10 levels or so.		* Expected fail levels is (1000 - level) / 10. I'm aware that this is slightly more than observed, but shouldn't be more than 10 levels or so.

@@ Line 25: / Line 25: @@
 * S(370) = 370 * 0.3 * [S(430) + 60] * 0.7 ~ 520
 * S(300) = 300 * 0.2 + [S(370) + 70] * 0.8 ~ 530
 == Bottom Line ==

@@ Line 22: / Line 22: @@
 We can just calculate the above for various x. For simplicity, assume S(some sufficiently high level) is known. Below, I use S(500) to be roughly 550 (since you expect to take 2 attempts to morph, so 50 lost levels).
-* S(430) ~ 450 * 0.4 + (1 - 0.4) * [S(480) + 50] ~ 530 [Since success probability at 430 is roughly 0.4)]
+* S(430) ~ 430 * 0.4 + (1 - 0.4) * [S(480) + 50] ~ 520 [Since success probability at 430 is roughly 0.4)]
-* S(370) = 370 * 0.3 * [S(430) + 60] * 0.7 ~ 530
+* S(370) = 370 * 0.3 * [S(430) + 60] * 0.7 ~ 520
-* S(300) = 300 * 0.2 + [S(370) + 70] * 0.8 ~ 540
+* S(300) = 300 * 0.2 + [S(370) + 70] * 0.8 ~ 530
 == Bottom Line ==
@@ Line 30: / Line 30: @@
 Morph early and often.
-* Optimum morph level is somewhere around 370. Could be 400. Could be 350.
+* Optimum morph level is somewhere around 370-430. Could be 400 or even 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, as long as you do it early.
+* Difference between morphing at 300 and 400 and 500 is not more than 10-20 levels. So it isn't all that important when you morph, as long as you do it early.
-* Expected levels you do at hero is roughly 550.
+* Expected levels you do at hero is roughly 520-550.
 [[Category: Gameplay]]
 [[Category: Hero]]
 [[Category: Lord]]

← Older revision		Revision as of 19:33, 18 April 2012
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	* 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, as long as you do it early.		* 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, as long as you do it early.
	* Expected levels you do at hero is roughly 550.		* Expected levels you do at hero is roughly 550.
		+
		+	[[Category: Gameplay]]
		+	[[Category: Hero]]
		+	[[Category: Lord]]

@@ Line 6: / Line 6: @@
 * Success 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.
+* Expected fail levels is (1000 - level) / 10. I'm aware that this is slightly more than observed, but shouldn'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
+* p(x) is probability of success at level x
 * f(x) is number of fail levels
@@ Line 20: / Line 20: @@
 ( 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.
+We can just calculate the above for various x. For simplicity, assume S(some sufficiently high level) is known. Below, I use S(500) to be roughly 550 (since you expect to take 2 attempts to morph, so 50 lost levels).
-Running these numbers for S(500) = 0.5 * 500 + 0.5 * (50 + S(550)) + ... or roughly 550
+* S(430) ~ 450 * 0.4 + (1 - 0.4) * [S(480) + 50] ~ 530 [Since success probability at 430 is roughly 0.4)]
 * S(370) = 370 * 0.3 * [S(430) + 60] * 0.7 ~ 530
 * S(300) = 300 * 0.2 + [S(370) + 70] * 0.8 ~ 540