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HeroClix Probability and Statistics
The Le (12/10/2015)
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Related: Vegas Odds:
Blades / Claws / Fangs

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HeroClix Probability and Statistics
 Let's take a close look at how HeroClix probability works.

First for the uninitiated -- Probability Control is a power that lets you reroll your dice once. Of course, if you have two uses of Probability Control, you'll be able to reroll your dice twice.

First, we'll take a look at probability with just 1d6. This is a great chart to use if you're rolling a single die with something like Support, Regeneration, or Blades/Claws/Fangs. Remember that you can only use Probability Control on your rolls during your turn, so you typically can not reroll Super Senses or Impervious. (Note that some numbers are rounded)

Edit: [2] has been clarified to show unrounded values.

D6 Result Probability of Success Probability of success with 1 reroll Probability of success with 2 rerolls
1+ 100%  100 100
2+ 83%  97.11% 99.5087%
3+ 67%  90 97
4+ 50%  76 88
5+ 33% 56.5 71
6 17%  31 43

For those using Blades/Claws/Fangs, a common question is: "Should I use the printed damage, or roll for BCF?" It depends on your odds, and if you like to gamble. Statistically, if your base damage is [3], then you should use BCF since odds are good (67%) that it will result it will result in 3 or higher.

With a single use of Probability Control, statistically you should roll BCF if your base damage is 5 since you have a 56% chance of rolling [5] or higher. (Personally though, in this situation, I would only roll of my base damage was 4 or lower).

Right: Discounted HeroClix Singles

And even with 2 Probability Controls, rolling a [5] or higher has a whopping 71% chance.

Honestly though, if you're already doing [5] base damage, then BCF isn't even worth it it unless you're really trying to spite your opponent. And even more honestly, I've rolled a [1] more times than I care to admit (note there is a 17% chance to roll a specific number without Probability Control).

So do you use BCF or not? Statistics don't lie, but honestly it comes down to how lucky you feel. As a rule of thumb, always roll for BCF if your base damage is [2] since there's only a 17% chance it will show up as a [1].

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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