Rurik said:

atgxtg said:

Has anyone done any crunching with the "tens switching idea?" I was wondering if that would work out.

I did. Or tried. Basically how I came up with my formula was drew up a 10 by 10 grid and started plotting results. Once the pattern of wins and losses realative to the three variables I used (High Skill, Low Skill, Difference between High Skill and 100), The formula could be generated.

I was hoping someone would save me the work. Guess I'm half(ve) to look at it.

Without coming up with hard one big problem showed itself. Take the case of 101 vs 100, or even 110 vs 90. These get reduced to 50 vs 50 and 55 vs 45 respectively, only the higher skilled character gets a re-roll. Without hard numbers it is safe to say that the higher skilled character gets a BIG advantage even though the odds should be roughly even - kinda the opposite of the halving rule.

I don't think this is quite as big a problem as you might think. THis is probably the worse case scenario and probably the test case for this idea, since this is the one area when halfing works and the adjustment is going to be the thing messing the results up.

Even so, at 55/45 the benefit is limited by only be partially useful. THe benfit gets gbetter the greater the difference in advantage. With a 55, it makes rolls like 56, 65-69, 75-79, 85-89, 95+ only useful if the opponent fails (roughly half the time for a 11% "edge" that gets reduced again since the opponent could wind up rolling a better result that the switched result). Even the rolls under the skill are not always useful. If the opponent rolls a 40, and the advantaged character rolls a 73, he will still lose with a 37. The flipping is of no use whatsover when you roll doubles, so that elimitates 10 numbers right there.

My rough estimates are that switching is almost

*half *as good as a reroll. A reroll has a 50-50 chance of being better than the orignal die roll, so the math for that would be 1-skill^2 (as a percentage). If this is half as good then:

51/49 (worse test case)

1-(0.51^2) =73.99% for a reroll

If the flipping is worth half a reroll then:

73.99 can round off to 74%

74-51=23.

23/2 =11.5

So 50+11.5=61.5%

THat's probably about 9% higher than it probably should be, but that should be the system at it's worse, and a 9% margin of error for worse case isn't a bad as some options.

Rurik said:

The other problem is say 170 vs 150. Do both get to swap their dice? if so someone has to swap first (presumably the lower skilled character). In most cases this is just as bad as not being able to swap at all. And the math gets even more complicated. Maybe the Brain could handle it, but it is pretty complex from this stand point.

THis isn't as bad eother. For one thing they can both swap at the same time, since we can tell what a better roll is without needing to see the opponent's ability. For instance if we hlave 170 to 85, we know that a 76 is still better than a 67 without even looking at the other players roll.

Secondly, in most cases both swapping isn't just as bad as neither, since the range of numbers that a swap is helpful is directly tied to your skill score. For example, using the 170 vs 150 numbers from above, we can halve that to 85 vs 75. Now if the first character rolls a 67 and switches it to a 76 he is improving his roll. On the other hand if the second character rolls a 67, changing it to a 76 won't help becuase it would be above his skill.

A character who gets halved toa 98 can pretty much read his dice as he wishes, but someone halfed to 51 has barely half the options.