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 Post subject: Smoothing the Probability Curves for TN>10
PostPosted: Sun Jul 10, 2011 8:01 am 
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Wow, it's been quiet around here lately.

I just wanted to share an idea. The basic dice roll mechanism in TROS appears to work fine up to a TN of 10, after which, most people are aware that there is a "kink" in the probability curve....P(TN=10) actually equals P(TN=11)....and after that there is a rather more gentle probability descent as TN rises.

Here is a graph of probability curves for a single success against TN's from 5 up to 16, using 1-20 dice. The lowest curve is for 1 die, and the highest curve is for 20 dice.

http://www.mediafire.com/?f6a7de46le658ij

It seems many players have done away with TN's higher than 10 by adopting the optional rules in TFoB and Companion. However the original sorcery rules still leave the possibility of higher TN's wide open, and as I continue to tinker with them I wondered about an alternative: a modification that "smoothed" the curves and enabled TN's greater than 10 to work predictably.

I entertained a few alternatives that dealt with high TN's, but then I eventually realised that high TN's were not so much the problem - it was TN10 itself. For whatever mathematical reason, the probability drop between TN9 and TN10 is disproportionately large compared to the curve leading up to it. Then there is no probability drop at all between TN10 and TN11.

So one proposed solution is to treat TN10 as a special case. If rolling dice against a TN of 10, half of the dice (rounding down) would be rolled against a TN of 9 instead. (This would need to be done as two separate rolls: you don't get to roll all your dice, and then choose which ones succeed versus a TN of 9.)

As awkward as this might sound, here is the smoothing effect it has on the probability curves:

http://www.mediafire.com/?bnb29hebn74bvce

I'm not claiming this to be a perfect solution, but for a relatively small fix it does appear to create a smoother and more predictable series of curves. (Compare with the former curves if you don't see what I mean.) The curves still flatten off at TN's higher than 11, but that doesn't seem so bad - it gives the player hope of succeeding against any TN, however small their dice pool.

A much harsher solution would be to treat all TN's above 10 as if they step up by 2. For example, for a TN of 11 one must actually roll 12's, a TN of 12 needs 14's, TN13 needs 16's, etc. (The potential confusion here is obvious - if the "target number is 11, why do I need to roll a 12 again?...) However this gives the following smoother if much less forgiving probability curves:

http://www.mediafire.com/?cpr6c9ppp6puwvu

Finally, I had the idea of treating each unit of TN value above 10 as a dice penalty: so a TN11 means rolling 1 less dice against TN10; a TN12 means rolling 2 less dice against TN10, etc. The penalty dice are still considered to have been rolled, but are treated as automatic fails. I sort of like the set of probability curves that result, because the influence of the number of dice on the probability is accentuated....encouraging the player to risk that one extra die. However, a side effect is that a gap of 10 or more units between the number of dice rolled and the TN means success is impossible. And the curves still have a serious "kink":

http://www.mediafire.com/?jch638jg2hoeapx

Besides avoiding TN's above 10 altogether, does anybody else have a fix?

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 Post subject: Re: Smoothing the Probability Curves for TN>10
PostPosted: Mon Jul 11, 2011 10:35 pm 
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Cogs42 wrote:
Wow, it's been quiet around here lately.


You're not wrong there!

Cogs42 wrote:
I just wanted to share an idea. The basic dice roll mechanism in TROS appears to work fine up to a TN of 10, after which, most people are aware that there is a "kink" in the probability curve....P(TN=10) actually equals P(TN=11)....and after that there is a rather more gentle probability descent as TN rises.

...

So one proposed solution is to treat TN10 as a special case. If rolling dice against a TN of 10, half of the dice (rounding down) would be rolled against a TN of 9 instead. (This would need to be done as two separate rolls: you don't get to roll all your dice, and then choose which ones succeed versus a TN of 9.)


For myself, I simply don't set the TN at 11. So, pragmatically speaking, there's TN 9, TN 10, and TN12 as three consecutive TNs.

However, that said I like your idea because it provides an extra TN. Personally I don't think it is too clunky -- the rule only applies in a very specific situation and as the referee sets the TN the referee can also remind the player to split the roll.

Good thinking!

Regards,

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 Post subject: Re: Smoothing the Probability Curves for TN>10
PostPosted: Mon Sep 12, 2011 11:19 pm 
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Joined: Thu Aug 19, 2010 1:19 am
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I must say I really like your proposed solutions for TN = 10. It elegantly smooths the probability drop, while retaining good enouph probabilities for higher numbers. Good post.


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