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*To*: tft@brainiac.com*Subject*: (TFT) Crunching the numbers...*From*: StanRydzewski <srydzews@ix.netcom.com>*Date*: Mon, 17 Jul 2000 20:00:06 -0400*Reply-to*: tft@brainiac.com*Sender*: tft-owner@brainiac.com

(Apologies in advance to people using proportional fonts. If you cut and paste this message into Notepad (or some such) the columns should actually line up.) 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. From there it was easy to get the approximate percentages of each result, and then the chance of rolling any given number or less, which is basically the chance of success. Here's what I came up with, along with the (actual, not approximate) percentages that exist with a normal 3d6 roll: Chance of success, taking the highest three dice, if required number for success (adjDX or whatever) is between 3 and 18: 6d6 5d6 4d6 3d6 3 0.06 0.28 1.12 4.63 4 0.06 0.28 1.12 4.63 5 0.06 0.28 1.12 4.63 6 0.20 0.80 2.67 9.26 7 0.61 2.01 5.55 16.20 8 1.54 4.20 10.14 25.92 9 3.45 8.05 17.06 37.49 10 6.95 14.07 26.48 49.99 11 12.81 22.66 38.06 62.49 12 21.72 33.95 51.00 74.06 13 33.78 47.58 64.41 83.78 14 48.86 62.32 77.04 90.72 15 65.68 76.64 87.09 95.35 16 65.68 76.64 87.09 95.35 17 65.68 76.64 87.09 95.35 18 65.68 76.64 87.09 95.35 Compare this with a similar success chart for 4+ die rolls given TFT's usual method: Chance of success, summation method 6d6 5d6 4d6 3d6 3: 6.08 5.87 5.40 0.46 4: 6.08 5.87 5.40 1.85 5: 6.08 5.87 5.40 4.63* 6: 6.08 5.87 5.40 9.26 7: 6.08 5.87 5.40 16.20 8: 6.08 5.87 5.40* 25.92 9: 6.08 5.87 9.72 37.49 10: 6.08 5.87 15.89 49.99 11: 6.08 5.87* 23.91 62.49 12: 6.08 9.79 33.56 74.06 13: 6.08 15.19 44.36 83.78 14: 6.08* 22.13 55.63 90.72 15: 9.65 30.50 66.43 95.35 16: 14.47 39.95 76.08 95.35 17: 20.59 49.98 84.10 95.35 18: 27.94 60.01 90.27 95.35 *Threshold of automatic success (ITL, p.38) Obviously rolls much higher than 18 are possible when summing 4+ dice, but those figures aren't needed for comparison with the Highest Three method.) 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. It seems like the original TFT method is designed with mega-level stats in mind, while the Highest Three system works better for people with "normal" stats...say, 18 or less. Under Highest Three it doesn't really matter if your DX is 16 or 25, your chance of making a 6d6 DX roll is the same. Under the original summation system that 25 DX will help at making such rolls. Of course, how many campaigns really have people with 25 DX? It seems to me that it might be better to suit the mechanics to the level of play that is more prevalent, where people have moderate stats, and that's exactly what the Highest Three system does. 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. 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? Interesting stuff... ===== Post to the entire list by writing to tft@brainiac.com. Unsubscribe by mailing to majordomo@brainiac.com with the message body "unsubscribe tft"

**Follow-Ups**:**Re: (TFT) Crunching the numbers...***From:*dwtulloh@zianet.com

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