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HeroClix Probability and Statistics
The Le (12/10/2015)
 Page:  1  2  3 

Related: Vegas Odds:
Blades / Claws / Fangs

Goto Comments

Some characters, like Doctor Strange and Felix Faust, have a special ability that uses a 20 sided die. But as you'll see, even with Probability Control, your odds aren't very good to get a specific result.

Related: Pow! Felix Faust

Let's take a look at Probability of the d20. (Note that some numbers are rounded)

Edit: [3] and [4] clarified to show unrounded values. Edit: Special thanks to R3411Y for pointing out a 1/100 of a rounding error

D20 Result Probability of Success Probability of success with 1 reroll Probability of success with 2 reroll
20 (or less) 100%  100 100
19 95%  99.9975% 99.999875%
18 90%  99.9900% 99.999000%
17 85%  98 99.7
16 80%  96 99
15 75%  94 98.4
14 70%  91 97.3
13 65%  88 95.7
12 60%  84 93.6
11 65%  80 91
10 50%  75 87.5
9 45%  70 83.4
8 40%  64 78.4
7 35%  58 72.5
6 30%  51 65.7
5 25%  44 58
4 20%  36 49
3 15%  28 38.6
2 10%  19 27
1 exactly 5%  10 14.3


Remember, if you want a specific result, there is just a 5% chance that it will appear -- and a 10% chance it will appear with Probability Control. That's awfully small.

As such, this is where things get interesting, as Felix Faust has been a concern to many players.

Awesome Clix: TK MastersThere are 2 desired results from Felix Faust's d20 roll. The first is the RED JAR of CALYTHOS and the second is PROJECT THAUMATION.

Red Jar of Calythos is worded as
"Give Felix Faust a free action. Until your next turn, action tokens are not removed from opposing characters. Felix Faust must roll his d20 on his next turn.".

For Project Thaumation, it's worded as "Give Felix Faust a free action. Until your next turn, opposing characters may only be given free actions. Felix Faust must roll his d20 on his next turn."


In reality, there, there is a third problem with Faust's d20 roll - he can get the "ANY" result, allowing him to freely choose either of the above. So, under this scenario there are really 3 possible die rolls you want -- but that probability is just 15%.

We cover Felix's problem in more detail over at Pow! Felix Faust

With Probability Control, it only goes up to 28%! And with two Probabilities, it's just 38.6%! Does this kind of probability warrant banning Felix Faust? You be the judge.

Note that this particular set of rules doesn't matter much anymore. Wizkids recently changed Probability Control with this official errata: "Probability Control may only be used on rolls that utilize d6s."


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Your Comments:
Did I have a house rule without knowing it? I thought that you can only reroll a specific roll one time, regardless of how many characters were available for that turn.

Scenario 1: Scarlet Witch attacks Cyclops within line of sight of Destiny. If Scarlet witch misses, misses again with Prob, I take it Destiny can give her one more chance?

Scenario 2: Scarlet Witch has Probability Control on her dial as well as a special power that allows her to re-roll a missed attack. Can she re-roll the missed attack and then use Probability Control to try once more?

Posted by: Kragnorak on 1/12/2016 3:47:48 PM
@Youll never know
But ironically add 70% to any leadership roll in turn 1 when you only have three characters!

Posted by: MantisWarrior on 12/12/2015 2:18:11 PM
@MantisWarrior: Double those odds, and throw in a negative 10% chance if it is a Super Senses, Shape Change, Leadership, etc. roll.

Posted by: You'll never know... on 12/12/2015 10:07:09 AM
Great guide. Though the math is wrong. You have forgotten the human factor. I'm sure there is a rule along the lines of " reduce all chances by 10% for being MantisWarrior" :)
Reduce by a further 5% if there is a prize involved.
Reduce by a further 15% if Thor has missed his last 5 attacks and so it would be funnier for your opponent to see him miss on a roll of 4+ for a SIXTH TIME!
Or was that just last night's game? ;)

Posted by: MantisWarrior on 12/10/2015 10:38:44 PM
The odds of success when rolling 2 die is the opposite of the odds of failure. So when rolling 2 die, getting a 4+ has a 92% chance of success and 8% chance of failure.

With Probability control, you have the option of rolling a second time, so the chance of failure is .08 x .08 = .0064, or .64%... therefore the chance of rolling 4+ with one re-roll is actually 99.36%.

With 2 probability controls, the odds of failure is .08 x .08 x .08, or .0512% chance -- therefore, with 2 re-rolls, the chance of rolling a 4 or higher is 99.9488%.

Be advised that this is the probability that you will get a result of 4+ on one of the three attempts -- this is NOT the probability of getting 4+ on each attempt. If needed to get 4+ three times in a roll, that's a different formula.

Posted by: The Le on 12/10/2015 7:08:59 PM
From the perspective of a mathematics teacher that taught probability I would advise all readers of the article to disregard the math presented here. Its very misleading...wait I take that back its flat out wrong.

In other words...disregard all columns past the first. Simple example rolling 3 or better consecutively 97/100 multiplied by itself (97/100) yields 94%. Odds are multiplied by their fraction equivalents to measure odds when considering sample sets of 2 rolls, 3 rolls etc. you can NEVER get your desired roll 100% of the time (unless your goal is to roll a 2 or higher, or a 12 or less).

I have rolled a three (or less) twice in a row. I have also rolled 4 (or less) three times in a row.

Common sense dictates the simplicity of how this is just plain inaccurate. For more information please contact your high school math teacher.

So simple recap. Ignore this math.

Posted by: Math teacher: on 12/10/2015 6:10:00 PM
Wow! Very helpful, than you so much. This is definitely very helpful.

Posted by: Sandy Hawk on 12/10/2015 3:10:15 PM
Thanks for this, a very helpful reference!

Posted by: Matt on 12/10/2015 10:44:35 AM
@R3411Y: Some numbers are rounded. So a 99.6% probability would be rounded up to 100%. I'll get the exact number and update it later so you can see the exact probability.

Posted by: The Le on 12/10/2015 9:19:19 AM
Also on the D20. Having 1 as result is silly since there is an "any" choice on the die giving the minimum roll result 2 chance of hitting.

And the odds of wanting all 20 results is slim since 1 side is blank and would have no result.

Posted by: R3411Y on 12/10/2015 9:09:07 AM
How can you have a 100 percent chance at a 3 or a 4 with extra rerolls... there is always the chance of rolling a critical miss twice.

You should look into probability in the reworld.

Posted by: R3411Y on 12/10/2015 9:04:11 AM