# Idea to replace halving mechanic

The benchmark I use to test against is this method:

1)Reduce the highest skill characters skill to 100.

2)Reduce the lower skill by the same percentage the higher skill was reduced by to get it to 100.

or: LowSkill/(HighSkill/100).

So a 150 vs 60 would become 100 vs 40. 300 vs 180 would be 100 vs 60. Most importantly, 101 vs 40 becomes 100 vs 39.

To me this is fair, and never reduces the odds. But it requires a calculator, and so is not a workable rule in my book.

While the extreme cases with my halving mods still hurt, when you move into ranges like 120 vs 80 the numbers are very close to the formula above.

It really comes down to giving up mathematical precision for playability.

bluejay said:
Ah, I hadn't seen that we were supposed to always round down. I'll amend my calculator accordingly!

Done!

I realized that while playing with odds. Meant to tell you.

So a 201 vs 160 should reduce to 100 vs 80. The break ponts are 101, 202, 404, etc.

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

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.

Flipping digits is not so easy to graph. It added 3 more variables, Losses that can be converted to wins, Ties that can be converted to wins, and losses that can be converted to ties (forcing a re-roll rather than losing), though just awarding ties to the higher skill elimantes two of those.

For a math purpose you don't just have A and B. you have A10 and A1 (tens and single) and B10 and B1, and the math starts getting really complex, and I am no spreadsheet wiz.

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.

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.

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.

regarding characetrs with 101% skil versus an opponent with 40%:

Rurik said:
By the book: 60.15
My Method: 76.15 Not perfect, but a lot better. This is the most extreme case (actually 101 vs 10 is more extreme).

Yes, but opponents with 10% skill are pretty rare, while town guards, trolkin, etc with skills in the 40-60% range are pretty common. No wonder Ruruik Runespear was taken out by a Trollkin, perhaps he way playing under MRQ rules!

Note that although this is the extreme case statisticaly, every single player character that gets to 150% will have to slog painfully through a long period where their character will drop drasticaly in effectiveness. This is a big deal, not a minor statistical anomaly. We will all be affected by it, for a significant period in our character's careers, and if you do get a character to over 200%, you'll go through it all over again for dozens of game sessions.

IMHO it's just not acceptable. Even your improvement to the system saddles every characetr that goes over 100% n their best skills - i.e. all player characetr one would hope, to a sudden drop in ability of up to 20% or so against fairly typical opponents.

Simon Hibbs

One possible solution to that would be to allow any character to willfully "hold back" part of their skill percentage, so that if your skill is 120%, you could hold it back to 99% for safety.

This even has a game-world-level explanation. You could bust out the fancy moves in combat (rolling with over 100%), or you could fight conservatively (holding back to 99%).

You'd be doing this for a long time during your character's career, but it would at least only freeze your advancement, as opposed to actually pulling it back. And it would still help you when you're forced to halve your skill by someone else.

Nephilim said:
You'd be doing this for a long time during your character's career, but it would at least only freeze your advancement, as opposed to actually pulling it back. And it would still help you when you're forced to halve your skill by someone else.

Or alternatively, we could use a game mechanic that isn't hopelessly broken.

Simon Hibbs

simonh said:
Or alternatively, we could use a game mechanic that isn't hopelessly broken.

Heh. Well, yes, obviously. That's why we're both trying to come up with alternate mechanics for this rule, right?

simonh said:
Nephilim said:
You'd be doing this for a long time during your character's career, but it would at least only freeze your advancement, as opposed to actually pulling it back. And it would still help you when you're forced to halve your skill by someone else.

Or alternatively, we could use a game mechanic that isn't hopelessly broken.

Simon Hibbs

We had one. THat is one reason why I can't understand the change. RQ3 with a "low roll wins if the success levels are the same" would be usuable for everything in MRQ and would solve all this.

I can accept change, but why change for something worse and more complicated?

Rurik said:
A very thoughtful post soltakss.

I noted the following.

soltakss said:
Resolution Rules:
Lowest Wins - on the same success level, the lowest roll wins
Highest Wins - on the same success level, the lowest roll wins

Highest Wins - on the same success level, the highest roll wins
it was a copy and paste without editing error.

I'm going to be amending my program to take into account various means of resolving success and will put them in a spreadsheet, when I have the time.

atgxtg said:
We had one. THat is one reason why I can't understand the change. RQ3 with a "low roll wins if the success levels are the same" would be usuable for everything in MRQ and would solve all this.

Actualy, the fact that currently in MRQ the lowest roll wins when both characters fail is the main cause of the statistical anomalies, because characters with lower skills are more likely to roll low fails.

Simon Hibbs

That's why I'm interpreting:
Whoever rolled the lowest in their skill test wins the opposed test.
to mean whoever gets closest to their own success target percentage.

OK, I've added a few more skill combinations and put them in an easy-to-view spreadsheet.

http://www.soltakss.com/rqm01.xls

Basically, you have a list of skill pairs and the results as percentages for each rules combination.

What is interesting, and unexpected, is that Highest Roll and Makes by the Most produce the same result. I need to check the individial die rolls to confirm this.

Anyway, when I get the time I'll add the other methods instead of halving and see what they come up with.

soltakss said:
OK, I've added a few more skill combinations and put them in an easy-to-view spreadsheet.

http://www.soltakss.com/rqm01.xls

Basically, you have a list of skill pairs and the results as percentages for each rules combination.

What is interesting, and unexpected, is that Highest Roll and Makes by the Most produce the same result. I need to check the individial die rolls to confirm this.

Anyway, when I get the time I'll add the other methods instead of halving and see what they come up with.

Nice! Thanks.

You are right about highest wins/makes by most. Actually, all three methods highest wins, makes by most, and closest to roll should give the same results - there are three variables that matter, the range below the low skill, the range between skills, and the range above the high skill. All variation in odds occurs because of difference between skill levels (everything above the high skill and below the low skill is 50/50). The three methods mentioned just move the successes and failures to different rolls, but all give the same number.

To me roll high is the easiest - the other two are more math intensive.

Also, seeing what happens at break points (100 vs 60 and then 101 vs 60) would show how good the methods are at handling the bump.

simonh said:
atgxtg said:
We had one. THat is one reason why I can't understand the change. RQ3 with a "low roll wins if the success levels are the same" would be usuable for everything in MRQ and would solve all this.

Actualy, the fact that currently in MRQ the lowest roll wins when both characters fail is the main cause of the statistical anomalies, because characters with lower skills are more likely to roll low fails.

Simon Hibbs

Yes, but that is a problem due to the way the other rolling rules work.

In RQ3 it would have been fine, as the higher skills granted a improved chance of getting a critical or special success. In addtion since there was no halving, a character who has over 100% only had a 5% chance of failing the roll, greatly resding the problemof low roll wins on a failure.

I know I wouldn't be uspet about a 97 failure beating a 98 failure. If a guy has 153% and rolls a 98, that;s the breaks.

soltakss said:
OK, I've added a few more skill combinations and put them in an easy-to-view spreadsheet.

That's interesting, and very useful but it doesn't show up the biggest anomalies. The largest fluctuations in odds occur for characters with skills in the low hundreds. I'd love to see this table with a row added for player 1 with 110% skill versus an opponent with 80% skill.

This would be very informative as this is the kind of situation that is handled most badly by the current rules. Any replacement rules need to be checked to make sure they fix the problem here, more than anywhere else.

Simon Hibbs

Couldn't agree more - it's the low hundreds (and probably low 200's) which really upset things, not the mid-100's. A 110-130 vs 30-50 would be more instructive, judging by the numbers.

But what this is showing is that halving, with the breaks hi/low, is the problem...

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