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Message no. 1
From: Mon goose <landsquid@*******.COM>
Subject: Open test probability
Date: Mon, 12 Jan 1998 16:39:25 PST
Iv’e checked out the chart of TN success probabiltites on the Archive,
and I was wondering- has anybody made a chart for probabilties of
rolling a particular number in an OPEN Test? This is a much more
difficult calculation: I can’t even figure out the formula, although
there is one, since I figured out a fair portion of 2 colums by hand and
there was definately a pattern.

Ironically, with 2 dice or more, higher results are MORE probably,
within their "bracket" of 6. For exaple, with 2 dice, 5's happen 9/36,
4's 7/36 , 3's 5/36 , 2's 3/36 , and only 1's 1/36. This pattern
continues, less pronouncedly, for values above 6, with 11's being
maginally more probable than 7's. Its less pronounced because in most
cases you are only re-rolling 1 die when going over 6. This would hold
true even more strongly for greater numbers of dice.

WHY? Because you have to consider that your not only trying to roll as
high as a certain number, but that if you roll higher, the result is
actually that higher number. This might give a clue to using the normal
probablity chart to derive one for Open Tests.

Just as satisfactory, to me, would be a dice rolling program I could set
to do a open test many times that would record and report the results.

Is it important? Not really- just wondering. I was suprised none of
the dice rollers on Paolo’s page seem able to make open tests or report
the results of many automated rolls.

Help / pointers, anyone?


Mongoose / Technological progress is like an ax in the hands
of a psychotic - Einstein

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
Date: Tue, 3 Feb 1998 23:31:25 -0500
>Ivíe checked out the chart of TN success probabiltites on the
Archive,

>and I was wondering- has anybody made a chart for probabilties of

>rolling a particular number in an OPEN Test? This is a much more

>difficult calculation: I canít even figure out the formula, although

>there is one, since I figured out a fair portion of 2 colums by hand
and

>there was definately a pattern.

>

>Ironically, with 2 dice or more, higher results are MORE probably,

>within their "bracket" of 6. For exaple, with 2 dice, 5's happen
9/36,

>4's 7/36 , 3's 5/36 , 2's 3/36 , and only 1's 1/36. This pattern

>continues, less pronouncedly, for values above 6, with 11's being

>maginally more probable than 7's. Its less pronounced because in
most

>cases you are only re-rolling 1 die when going over 6. This would
hold

>true even more strongly for greater numbers of dice.

>

>WHY? Because you have to consider that your not only trying to roll
as

>high as a certain number, but that if you roll higher, the result is

>actually that higher number. This might give a clue to using the
normal

>probablity chart to derive one for Open Tests.

>

>Mongoose / Technological progress is like an ax in the hands

>of a psychotic - Einstein


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.


Notation:

P[1]=1/6 ; Thats the chance to roll a one with one die.

p[6]=0 ; There is zero chance to roll a six because you always

roll again and add to it.

P[7]=1/36


Example:

Assume you have only 1 die to role.

You want to know the chance of getting 8 or more.

Thats 1 minus the chance of rolling anything less than an 8.

The chance to roll less than an 8 is the total of the chances to roll
each

possible number less than 8.

31/36= 1/6 +1/6 +1/6 +1/6 +1/6 +0 +(1/6)*(1/6)


0.1389 or 5/36 = 1 -31/36 would then be the chance to roll atleast an
8.


Now to figure out the odds for rolling two dice getting atleast an
eight.

Thats one minus the odds of not rolling an 8 eight with both dice.

1 -[31/36][31/36]

for a case of three dice it's 1 -[31/36]^3 and so on for more dice.


Here is a table. I did not round the numbers just truncated them.


Number Minimum target

of Dice Number

2 3 4 5 6or7 8 9 10 11

1 5/6 4/6 3/6 2/6 5/36 4/36 3/36 2/36 1/36

<fontfamily><param>Geneva</param>2 0.972
0.888 0.75 0.555 0.258 0.2098 0.1597 0.1080 0.05478

3 0.995 0.9629 0.875 0.7037 0.3614 0.2976 0.2297 0.1575 0.08103

4 0.999 0.9876 0.9375 0.8024 0.4501 0.3757 0.2939 0.2043 0.10656

5 0.999 0.9958 0.9687 0.8683 0.5265 0.4450 0.3527 0.2485 0.13138

6 0.999 0.9986 0.9843 0.9122 0.5922 0.5067 0.4067 0.2903 0.15551

7 0.999 0.9995 0.9921 0.9414 0.6489 0.5615 0.4561 0.3297 0.17897

8 0.999 0.9998 0.9960 0.9609 0.6976 0.6102 0.50141 0.3669 0.20177




12or13 14 15 16 17

1 0.02314 0.01851 0.01388 0.00925 0.00462

2 0.04576 0.03669 0.02758 0.01843 0.00923

3 0.06784 0.05453 0.04109 0.02752 0.01382

4 0.08942 0.07204 0.05440 0.03652 0.01839

5 0.11050 0.08922 0.06754 0.04544 0.02293

6 0.13109 0.10609 0.08049 0.05428 0.02745

7 0.15120 0.12264 0.09326 0.06304 0.03196

8 0.17085 0.13889 0.10585 0.07171 0.03644


</fontfamily>

Further Reading

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