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Message no. 1
From: Mon goose <landsquid@*******.COM>
Subject: Re: Open test probability (badly expalained math, barely OnT)
Date: Wed, 4 Feb 1998 10:40:35 PST
>> I was wondering- has anybody made a chart for probabilties of
>>rolling a particular number in an OPEN Test?

>The trick to this is to realise all your interested in is
>the probability of the getting at least one total greater than or
>equal to the desired number.
<snip formula and calculations>

Thanks for all the hard work, but what you gave me is the probability of
getting at least one result of at least a particular number (X) in a
regular test with N dice. Thats a CLOSED test, IE one that has a TN.
In an open test, you want that probabilty, MINUS the chance of getting
anything higer, because a higher result isn't just an extra succes- its
the open test result!
Using your formula, minus the probality for the next number(x+1), would
work (I think).

I wanted the EXACT probabilty that ONLY X would be rolled on the highest
die- nothing higher.

My answer actually turns oput to be rather simple: Figure out the
portion of results in 6 that have X or less on a single die, And base
calculations off that. You want to find the "volume" of the thin slice
of a 6 unit "N space" that all the results with x ocupy, as a portion of
the space occupied by all results (6 to the n power results, with
subdivions of results for x's over 6).

I basically did the OPPOSITE of what I could do with your formula- I
calculated the probilty for all the results x or lower, and then
subtracted all the results x-1 or lower. An obvious solution if you
draw pictures for n=2 and n=3, with all the x's mapped down to fit from
1 to 6.


ANYWHO.... I graphed it out with a Mathamtica type progarm, and figured
the chances of extreme results were low enough, and moderate results
high enough, that I based my intitative system off open tests. The
actual numbers are not that intersting, except for the slight skewing
towards 9, 10, and 11 for 3 to 6 dice (those 3 results can 7-9% of
rolls).

The fromula given is nice for knowing the chance of an open test
EXEEDING a certain number, BTW, whichI realized afterwords was all I
really cared about (making sure some joker with 6 dice can't
consistantly roll 22's). DOH- I knew how to do that! Still, the
pictures were kinda pretty.

Mongoose / "Jack the soundbarier. Bring the noise!" -Cyberhound

get sucked into -The Vortex- Chicago's shadowland BBS
http://www.concentric.net/~evamarie/srmain.htm


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Message no. 2
From: westln@***.EDU
Subject: Re: Open test probability (badly expalained math, barely OnT)
Date: Wed, 4 Feb 1998 20:40:19 -0500
>>> I was wondering- has anybody made a chart for probabilties of
>>>rolling a particular number in an OPEN Test?
>
>>The trick to this is to realise all your interested in is
>>the probability of the getting at least one total greater than or
>>equal to the desired number.
><snip formula and calculations>
>
>Thanks for all the hard work, but what you gave me is the probability of
>getting at least one result of at least a particular number (X) in a
>regular test with N dice. Thats a CLOSED test, IE one that has a TN.
>In an open test, you want that probabilty, MINUS the chance of getting
>anything higer, because a higher result isn't just an extra succes- its
>the open test result!
>Using your formula, minus the probality for the next number(x+1), would
>work (I think).

Sorry my mind was else where when I got to the end. But you guessed
correctly. Just subtract the the probability from the next column to get
probability of rolling exactly X.

>
>I wanted the EXACT probabilty that ONLY X would be rolled on the highest
>die- nothing higher.
>
>My answer actually turns oput to be rather simple: Figure out the
>portion of results in 6 that have X or less on a single die, And base
>calculations off that. You want to find the "volume" of the thin slice
>of a 6 unit "N space" that all the results with x ocupy, as a portion of
>the space occupied by all results (6 to the n power results, with
>subdivions of results for x's over 6).
>
>I basically did the OPPOSITE of what I could do with your formula- I
>calculated the probilty for all the results x or lower, and then
>subtracted all the results x-1 or lower. An obvious solution if you
>draw pictures for n=2 and n=3, with all the x's mapped down to fit from
>1 to 6.
>
>
>ANYWHO.... I graphed it out with a Mathamtica type progarm, and figured
>the chances of extreme results were low enough, and moderate results
>high enough, that I based my intitative system off open tests. The
>actual numbers are not that intersting, except for the slight skewing
>towards 9, 10, and 11 for 3 to 6 dice (those 3 results can 7-9% of
>rolls).
>
>The fromula given is nice for knowing the chance of an open test
>EXEEDING a certain number, BTW, whichI realized afterwords was all I
>really cared about (making sure some joker with 6 dice can't
>consistantly roll 22's). DOH- I knew how to do that! Still, the
>pictures were kinda pretty.
>
>Mongoose / "Jack the soundbarier. Bring the noise!" -Cyberhound
>
>get sucked into -The Vortex- Chicago's shadowland BBS
> http://www.concentric.net/~evamarie/srmain.htm
>
>
>______________________________________________________
>Get Your Private, Free Email at http://www.hotmail.com
Message no. 3
From: "Ojaste,James [NCR]" <James.Ojaste@**.GC.CA>
Subject: Re: Open test probability (badly expalained math, barely OnT)
Date: Fri, 6 Feb 1998 15:52:32 -0500
Mon goose[SMTP:landsquid@*******.COM] wrote:
> The fromula given is nice for knowing the chance of an open test
> EXEEDING a certain number, BTW, whichI realized afterwords was all I
> really cared about (making sure some joker with 6 dice can't
> consistantly roll 22's). DOH- I knew how to do that! Still, the
> pictures were kinda pretty.

If that's all you're interested in, there's a much easier way to
think about it. Since open-ending is a 1/6 chance, you need 6 dice
to be able to expect 1 die to open-end. The average roll is 3.5,
therefore with 6 dice, you can expect one 9.5. With 36 dice, you can
expect one 15.5. With 216 dice, you can expect one 21.5.

So, if you keep the initiative dice beneath 36, you won't get 22s
easily...

James Ojaste

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