Ecaflip's Luck Simulator
I believe there are two major problems with Ecaflip's Luck:
- The spell description is not very clear
- The mathematics are often misunderstood
This page will attempt to clear up both of these issues.
The Spell Description Is Not Very Clear
If you've used Ecaflip's Luck before, you may have noticed how it works. More likely, however, you tried it once, got hurt, didn't notice the exact numbers, re-read the description, remained confused, and gave up on the spell.
Here is what the spell description reads:
50% damage received x2, or else healed by x1 (2 turns)
At the time of this writing, the Dofus wiki makes things more confusing by formatting and coloring the description in the following way:
50% damage received x2,
or else healed by x1
(2 turns)
Here is, perhaps, a more useful description, of my own design:
When you receive damage, 50% of the time you will receive twice that damage; the other 50% of the time, instead of taking damage, you will be healed by an amount equal to the damage you were "supposed" to take.
The Mathematics Are Often Misunderstood
At first glance, it seems like this spell, on average, breaks even; that over time, you would, on average, take as much damage as you heal.
(Further, people have a tendancy to put much more emphasis on extreme cases than average cases than is reasonable - see list of cognitive biases @wikipedia for this and more - so when Ecaflip's Luck kills you, you're likely to hate the spell more than you really should.)
Based on this assumption, the common advice for Ecaflip's Luck is to only cast it when you're about to die, thereby giving you a 50% chance of surviving (you don't care about taking double damage when the next hit will kill you anyway).
However, Ecaflip's Luck actually leans in favor of the caster, which I will demonstrate in two ways:
First, with some basic math: consider the normal case, taking full damage. With Ecaflip's Luck, you will instead either take twice damage (full damage + full damage) or be healed instead of taking damage (full damage - full damage, + healing; or: full damage - full damage - full damage, where negative damage equals healing).
So half the time, damage is increased one fold, but the other half, it is decreased two fold - the odds are in your favor!
Second, if that's difficult to follow, or seems hard to believe, I have created an "Ecaflip's Luck Simulator":
Ecaflip's Luck Simulator
This simulation recreates the effects of Ecaflip's Luck (level 5, non-critical hit) on a character with 1000 HP out of a maximum of 1500HP, hitting that character with five 100HP attacks. It compares the results of the simulation when run on a character with and without Ecaflip's Luck.
(Imagine two identical characters being hit with an AoE attack which deals precisely 100HP per hit, except one character has Ecaflip's Luck; the other doesn't.)
10 such simulations are run. You can refresh this page to see the results of 10 new simulations.
Simulation 1
| Ecaflip's Luck? | HP Remaining | ||||
|---|---|---|---|---|---|
| Attack 1 | Attack 2 | Attack 3 | Attack 4 | Attack 5 | |
| No | 900 | 800 | 700 | 600 | 500 |
| Yes | 800 | 600 | 700 | 800 | 600 |
Simulation 2
| Ecaflip's Luck? | HP Remaining | ||||
|---|---|---|---|---|---|
| Attack 1 | Attack 2 | Attack 3 | Attack 4 | Attack 5 | |
| No | 900 | 800 | 700 | 600 | 500 |
| Yes | 1100 | 900 | 700 | 800 | 600 |
Simulation 3
| Ecaflip's Luck? | HP Remaining | ||||
|---|---|---|---|---|---|
| Attack 1 | Attack 2 | Attack 3 | Attack 4 | Attack 5 | |
| No | 900 | 800 | 700 | 600 | 500 |
| Yes | 800 | 900 | 700 | 800 | 900 |
Simulation 4
| Ecaflip's Luck? | HP Remaining | ||||
|---|---|---|---|---|---|
| Attack 1 | Attack 2 | Attack 3 | Attack 4 | Attack 5 | |
| No | 900 | 800 | 700 | 600 | 500 |
| Yes | 800 | 600 | 700 | 800 | 600 |
Simulation 5
| Ecaflip's Luck? | HP Remaining | ||||
|---|---|---|---|---|---|
| Attack 1 | Attack 2 | Attack 3 | Attack 4 | Attack 5 | |
| No | 900 | 800 | 700 | 600 | 500 |
| Yes | 800 | 900 | 1000 | 1100 | 900 |
Simulation 6
| Ecaflip's Luck? | HP Remaining | ||||
|---|---|---|---|---|---|
| Attack 1 | Attack 2 | Attack 3 | Attack 4 | Attack 5 | |
| No | 900 | 800 | 700 | 600 | 500 |
| Yes | 800 | 600 | 400 | 200 | 0 |
Simulation 7
| Ecaflip's Luck? | HP Remaining | ||||
|---|---|---|---|---|---|
| Attack 1 | Attack 2 | Attack 3 | Attack 4 | Attack 5 | |
| No | 900 | 800 | 700 | 600 | 500 |
| Yes | 800 | 600 | 700 | 500 | 300 |
Simulation 8
| Ecaflip's Luck? | HP Remaining | ||||
|---|---|---|---|---|---|
| Attack 1 | Attack 2 | Attack 3 | Attack 4 | Attack 5 | |
| No | 900 | 800 | 700 | 600 | 500 |
| Yes | 1100 | 900 | 1000 | 1100 | 900 |
Simulation 9
| Ecaflip's Luck? | HP Remaining | ||||
|---|---|---|---|---|---|
| Attack 1 | Attack 2 | Attack 3 | Attack 4 | Attack 5 | |
| No | 900 | 800 | 700 | 600 | 500 |
| Yes | 1100 | 900 | 700 | 500 | 600 |
Simulation 10
| Ecaflip's Luck? | HP Remaining | ||||
|---|---|---|---|---|---|
| Attack 1 | Attack 2 | Attack 3 | Attack 4 | Attack 5 | |
| No | 900 | 800 | 700 | 600 | 500 |
| Yes | 1100 | 900 | 700 | 800 | 600 |
Results
If Ecaflip's Luck breaks even, then, on average, the character under the effects of Ecaflip's Luck should end with about as many hit points as the character not under its effects.
Let's see what really happened...*
| HP Without Ecaflip's Luck | HP With Ecaflip's Luck | |
|---|---|---|
| 1 | 500 | 600 |
| 2 | 500 | 600 |
| 3 | 500 | 900 |
| 4 | 500 | 600 |
| 5 | 500 | 900 |
| 6 | 500 | 0 |
| 7 | 500 | 300 |
| 8 | 500 | 900 |
| 9 | 500 | 600 |
| 10 | 500 | 600 |
| Total | 5000 | 6000 |
| Average | 500 | 600 |
* Keep in mind that random numbers can sometimes do wildly-random things (they are, afterall, random), and 10 simulations is not a very good sample size. You may want to refresh the page a few times and compare the results, especially if Ecaflip's Luck seems completely terrible, or completely over-powered.