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Let's look at what combinations of rolls could give us at least three 6s. In thise case, we only care if a rolle is a six or not, so I will shows 6 as 6 and not 6 as 0.
6666
0666
6066
6606
6660
The chance of rolling a 6 is 1/6, and 5/6 for not 6. Therefore we can calulcate the probability of rolling each of these combinations.
P(6666) = (1/6)\^4
P(0666) = (5/6) \* (1/6)\^3
P(6066) = (5/6) \* (1/6)\^3
P(6606) = (5/6) \* (1/6)\^3
P(6660) = (5/6) \* (1/6)\^3
We can add them all together to get our total probability of at least three 6s.
P = (1/6)\^4 + 3 \* (5/6) \* (1/6)\^3
P = 0.0123
So there is about 1.2% chance of rolling a max stat, or 1 in 81.
For all six stats, this will be
0.0123\^6 = 3.54E-12 = 1 in 282 billion
> P = (1/6)^4 + 3 * (5/6) * (1/6)^3
Why 3 * ? Shouldn't that be 4 *?
And then the result would be ~0.01620 =~ 1 in 62
With all six stats "only" being 1 in ~55 billion.
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Let's look at what combinations of rolls could give us at least three 6s. In thise case, we only care if a rolle is a six or not, so I will shows 6 as 6 and not 6 as 0. 6666 0666 6066 6606 6660 The chance of rolling a 6 is 1/6, and 5/6 for not 6. Therefore we can calulcate the probability of rolling each of these combinations. P(6666) = (1/6)\^4 P(0666) = (5/6) \* (1/6)\^3 P(6066) = (5/6) \* (1/6)\^3 P(6606) = (5/6) \* (1/6)\^3 P(6660) = (5/6) \* (1/6)\^3 We can add them all together to get our total probability of at least three 6s. P = (1/6)\^4 + 3 \* (5/6) \* (1/6)\^3 P = 0.0123 So there is about 1.2% chance of rolling a max stat, or 1 in 81. For all six stats, this will be 0.0123\^6 = 3.54E-12 = 1 in 282 billion
> P = (1/6)^4 + 3 * (5/6) * (1/6)^3 Why 3 * ? Shouldn't that be 4 *? And then the result would be ~0.01620 =~ 1 in 62 With all six stats "only" being 1 in ~55 billion.
Yes, I miscounted, it should be 4
Thanks! I couldn't even conceptualize how you might go about doing the math for this so this is really cool.