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Re: (TFT) Crunching the numbers...

StanRydzewski writes:

> I found Dan Tulloh's suggestion about taking the
> highest three of X dice to be quite intriguing.
> The math is beyond me, too, so I wrote up a die-
> rolling program and cranked out 50,000 6d6, 5d6,
> and 4d6 rolls, taking the highest three results,
> and noting how many times each possible result
> came up.

The other way to do this is to have the computer
generate all of the possible rolls and count up
the sample space.

> < ... snip tables ... >
> A couple things of interest.  Note that the 
> Highest Three method produces a much "smoother"
> progression of difficulty for rolls vs. moderate
> stat levels (say, 12-14).  People with stats in 
> this range just have no business trying to make 
> 6d6 rolls under TFT's summation system, but they
> have a reasonable shot at it with the Highest 
> Three system.  Conversely, having a stat higher 
> than 15 is of less importance with the Highest 
> Three system, because a roll of 16+ is automatic
> failure whether you have a 15 or a 25 in the
> stat--and as you can see the chance of rolling 
> a 16+ becomes quite great when you're taking 
> the highest three of 4 or more dice.

I found that I rarely needed a DX stat higher 
than 20 as dex adjustments that happen in combat
can take you down to the 16 number quite often.

> There is one aspect of the Highest Three system 
> that troubles me, though, and that's critical 
> success/failure.  The TFT system maintains a 
> roughly 2% chance of critical success (a 3 or 
> 4, when rolling 3 dice), regardless of the number
> of dice being rolled.
>   But obviously when you're selecting the highest
> three of five or six dice, you're going to get a 
> lot of 17's and 18's, and not many 3's and 4's:
>                 6d6,     5d6     4d6   
> Crit Failure:    18%     12%     6%
> Crit Success:   0.01%   0.08%   0.42%
> These numbers are based on the same 50k rolls
> that I did for the first table.
> While one can argue that the chance of critical failure
> *should* be higher when you're trying a 5d6 roll, I'm 
> not sure that it should be six times higher.  And 
> critical success...well, it's one in ten-thousand with 
> a 6d6 roll.

Interesting insight, Stan!  Personally, I am of the 
opinion that you outline above - if you are attempting
something really difficult, the odds of critical failure
should be greater.  This methodology fits well with the
idea of the Expert Swordsman that was discussed earlier;
something that is difficult for the novice (have to add
a D6 or two) should be easier for the Expert (who gets 
to subtract a d6).

Stan's argument is one-sided though, I think the TFT 
system really falls apart when working with tasks of
relaxed difficulty.  Take away 1d6 and you are rolling
2d6, take away another and you are rolling only 1d6!

This system allows the GM to place a relative value on
the difficulty of a task which can then be affected by
the character's talents and abilities.

> One possible way around this would be to always roll 
> three red dice, regardless of how many dice are being
> used to make a roll.  That way you could always base 
> the occurrence of critical results on the red dice, 
> while using the highest three to determine success/
> failure.  Or is that gettting too complicated?

Using red dice to determine auto success/failure? hmmm...
I'll havta give that some thought!

> Interesting stuff...

Thanks!  (if that was a compliment)  :D

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