# Re: How Many Sevens Should You Expect in Six Throws of the Dice?

>Mark Rafn wrote:
>> Hardly. You're very likely to see many sets of 144 rolls that deviate a lot
>> from the expectation of 24 7s.

Timmyrocker <timmyrocker@xxxxxxx> wrote:
>um... not by much actually. i have been impressed over and over by 144
>rolls having almost exactly 24 sevens, rarely deviating from a range of
>22-26 sevens.

You haven't haven't counted precisely very often, or you've been surprisingly
lucky in terms of seeing such a small variance in number of 7s in 144 rolls.
You should see 22-26 about half the time. A little fudging and a little
selective memory can turn this into "rarely deviating", I suppose...

You should see 24, with a standard deviation somewhere around 4.5 (back of
envelope, maybe it's a bit less). This means 90% of the time, it'll be within
7.2 rolls, 99% within 11.25. Looked at another way, there is a 1% chance for a
set of 144 rolls to contain fewer than 13 or more than 35 7s.

A range of 22-26 is about half a standard deviation, and just under half the
time will a set of 144 rolls be in that range.

>You will see an occasional high deviation, but i clearly wouldn't
>characterize it as you did : "many sets of 144 rolls that deviate a
>lot".

Depends on your definition of "many", I guess. If someone is basing a theory
on the idea that in 144 rolls, one is guaranteed to have 22-26 7s, the fact
that over half the time they're wrong seems like a lot to me.

If you're saying that it's often between 13 and 36, I'd say there's not a lot
of deviation - only 1% or so of the time.
--
Mark Rafn dagon@xxxxxxxxx <http://www.dagon.net/>
.

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