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

Goto Comments

Now, let's take a look at the probability for standard attack rolls, using 2d6. (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

2D6 Result Probability of Success Probability of success with 1 reroll Probability of success with 2 rerolls
2+ 100%  100  100
3+ 97%  99.9991% 99.999973%
4+ 92%  99.9936% 99.999488%
5+ 83%  97  99.5
6+ 72%  92  98
7+ 58%  82  93
8+ 42%  66  80.5
9+ 28%  48  63
10+ 17%  31  43
11+ 8%  15  22
12+ 3% 6 9

Quintessential Zombie Spider-ManAssuming your average attack value is [10] and the average Defense Value is [17], you're going to need to roll a [7] or higher to hit your opponent. The odds are favorable under this situation (58%) that you're going to hit. Realistically though, I don't take much comfort in 58% (I've rolled [1-5] plenty of times with two die). If you look at it from the other side it's a little scarier -- i.e. there's a 42% chance your attack will miss!

Probability Control changes that dramatically, increasing the chance of rolling a [7] to a full 82%. With 2 re-rolls, that goes up to a whopping 93%!

Statistically, with one probability control, odds are good if you need to roll an [8] or higher (66% probability).

Statistically, with two probability controls, odds are good if you need to roll an [9] or higher (63% probability).

So, once again, it comes down to how lucky you're feeling. If you need an 11 or higher, even with just one Probability Control the chance is just 15% -- not very good. And remember, the dice hates you.

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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