Luck
Some rolls in the game are Lucky or Unlucky.
Lucky rolls will be made twice, and the higher value is chosen. Diamond flasksDiamond FlaskLasts 6.00 Seconds
Consumes 20 of 40 Charges on use
100% increased Global Critical Strike ChanceRequires Level 27Right click to drink. Can only hold charges while in belt. Refills as you kill monsters. makes the critical strike chance lucky for a duration.
Unlucky
If a damage roll is unlucky, the damage calculation will be rolled twice and the lower value will be chosen. Rolls to critical strike chance/evasion/dodge/block are unchanged and only happen once.[1]
Effectiveness
On percentage rolls, such as critical chance, Lucky/unlucky rolls will be up to a 100% more/less modifier, changing linearly towards 0% as critical chance increases. On damage rolls, the average damage from the roll will be at up to 33% more or less, when the minimum damage is close to zero, but will have a much weaker effect when the minimum damage is closer to the maximum.
Calculations
More specifically, the lucky critical strike chance can be calculated from the following formula:
LuckyCritChance = 2*DefaultCritChance - DefaultCritChance^2
For example, the lucky critical strike chance for an default critical strike chance of 40% could be calculated as follows:
LuckyCritChance = 2*40% - 40%*40% = 80% - 1600%% = 80% - 16% = 64%
It should be noted that these calculations neglect the effect of accuracy on critical strikes.
Derivation of lucky rolls |
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This is a problem that can be solved with conditional probability. Let A be the default critical strike chance on the first roll, then the chance to NOT crit on the first roll is: B = 1 - A If the roll failed the die will be cast a second time with the same probabilities. The chance to crit on the second roll is: C = B * A The total probability to get a lucky critical strike is the sum of A and C. LuckyCritChance = A + C = A + B * A = A + (1 - A) * A = 2*A - A^2 |
References
- ↑ Mark_GGG (May 13, 2013 4:01 AM). "p/c new ring lori's lantern". Path of Exile Forum. Retrieved September 22, 2013.