Thanks!
Dice odds calculator?
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Does anyone know how to calculate probability for multiple dice rolls?
For instance, two different rolls for an attacking sub, is it still 33% chance of a hit (still 4 out of 12 chances), 66% (two chances of 33%), or 44% (the original third plus a slightly chance of both hitting, for example).
My Google-Fu has led me to all kinds of not helpful pages (they want sum totals, like playing craps or something) and I haven’t done this kind of math in decades.
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Well, I happened to find it with a LOT more digging… so I thought I’d share.
Apparently its easier to do it based on missing. So…
Example is for, let’s say, submarines attacking…
Take your odds of one dice missing (2/3rd chance you WON’T get a 1 or a 2)
Then you take 2/3 to the Nth power, N being however many rolls you get, so…
Attacking with two subs gets you 2/3 to the 2nd power, or 5/9th chance you’ll miss OR, more helpful…
two attacking subs have a 44.4% chance of hitting once and an 11.1% chance of both hitting.If you got 3 rolls, its 2/3 times 2/3 times 2/3rd, or 8/27th chance of missing or…
a 70.4% chance of hitting once.Link to the solution in case I need it again https://math.stackexchange.com/questions/2087463/multiple-dice-rolling-probabilities?rq=1
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I think you have it right for finding at least one hit. That case is relatively simple because it’s the probability of not hitting zero times.
It gets a bit trickier if you want to know other values but generally looks like:
Prob(# of hits) * Prob(# of misses) * # of ways it can happen
Mathematically it looks like:
Where, w = probability of a hit
x = number of units hitting
y = probability of a miss
z = number of units missing= w^x * y^z * NCR(x+z , x)
In your example you’re finding the probability of zero hits which is nice because the first and last term equal 1 and can be ignored:
(2/6)^0 * (4/6)^3 * NCR(3,0)
= 1 * (64/216) * 1
= 29.6%So the probability of not hitting zero times is 70.4% like you said.
Let’s say you want to know the probability of getting 2 hits exactly:
(2/6)^2 * (4/6)^1 * NCR(3, 2)
= (4/36) * (4/6) * 3
= 22.22%If you’re unfamiliar with the NCR function, these are called “combinations”. The function exists on some calculators and you can do it in excel using =combin(x,y). With 3 subs there are 3 possible ways of getting 2 hits, sub A+B, sub B+C and sub A+C, hence 3 in my example.
If you plan on going very far down this rabbit hole you’re likely going to want an excel spreadsheet.
Hope that helps.
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It does, thank you!
The sub scenario is what kicked off this pursuit for me. Specifically, at the opening of Global 1940, What are the odds of two German subs getting a single hit on Britain’s cruiser.
I mean, its easy enough to figure out how many hits total you might get, on average, from a stack of infantry, but there are plenty of smaller strikes of trying to take down one or two units I was trying to figure out my odds for.
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