Contested rolls past 100%

[Deleted_Account]

A: 100% vs B: 50% skill:
A wins 70.125% of the time. (this isn't 75%, because a roll of 96-100% on A's part still loses)

A: 102% vs B: 50% skill.
A wins 59.88% of the time.

Breaking 100% skill makes you worse at contested skills.

Thus, clearly the "halve both skills" system is junk.

Possible options:
Every 1% past 100% gives you a +1% to your success roll.
Equivilently, every 1% past 100% lowers the opponent's skill by 1%.

This makes extremely high skill ridiculously effective.

Change the contest rules:

Both players roll. If one "outranks" the other (on the scale of crit/success/fail/botch), the victor is clear.

If the result is a "tie" (ie, both botch, both fail, both success, or both crit), you reroll in a special way.

You use your roll as your new target number. This prevents having to roll ties forever. However, if your skill is over 100%, you get to keep the excess points to boost your new target number.

         Crit  Win  Lose  Botch
Crit    REDO    A     A     A
Win       B   REDO    A     A
Lose      B     B   REDO    A
Botch     B     B     B    REDO

On a REDO, use the last roll as your new target.

If your old target was over 100%, and your opponents old skill was over 100% but less than yours, add the difference between your skills to your new target.

If your old target was over 100%, and your opponent's wasn't, just add the points in excess of 100% to your new target.

Example:

Alice has 250% skill vs Bob with 150% skill.

Alice rolls 51(success), Bob rolls 34(success).
Both succeed (gasp). REROLL.

Alice's skill is 100% greater than Bob's.

Alice's new target number is 51+100 = 151.
Bob's new target number is 34. He doesn't get any bonus because his skill was under Alice's.

Alice rolls 35(success), Bob rolls 85(failure). Alice wins.

Example 2:
Alice and Bob both have 90% skill.

Alice rolls 25(success). Bob rolls 70(success). Both succeed, REROLL.

Alice's new target number is 25%, Bob's is 70%. Alice is in trouble.

Alice rolls 62% -- damn, a failure.
Bob rolls 100% -- a botch! Alice wins.

Rolls provided by http://www.irony.com/igroll.html

...

High skill takes a bunch of lucky rolls to erode away, or hitting them with a crit against a normal success.

 

[bluejay]

Uh-huh.

This has been discussed a lot here.

You can use my calculator (in my signature) to test for yourself and the halving mechanic can significantly change the odds.

 

[Deleted_Account]

Alternative solutions?

Searching for "100%" and "contested" didn't turn up much in the way of useful threads.

Gah. Searching for "100%" and "contest" gets me lots of hits. @_@

Serves me right for using the wrong tense!

 

[bluejay]

Yakk, I wish I had one.

I think the problem is that I want a solution that fulfills a few criteria: -

1. The odds don't radically change. What would be nice is if they levelled off slightly for bigger increases. This cannot happen in a linear system (i.e. one who wins by the most or subtract the same amount from both skills) because differences in skill of 100% prevent the low skill character from winning.

2. Characters of any skill levels can interact. Again this references point 1. A character with a skill of 500% doesn't automatically beat a character with a skill of 5%.

3. The maths is fairly rudimentary.

 

[bluejay]

Ok, firstly I think that halving cannot be the way to go.

Example:

2 guys, A and B.

A has 100% in athletics, B has 40% in athletics.

In a race, A has 86.9% chance of winning.

Now if we give A 101% (effectively halving down to 50%) then there is no skill that we can give B that gives A 86.9% or higher. Even giving B 1% against A's 50% still gives A a mere 62.1% chance of winning. Why, because if A rolls anything over 50 then B can still win by rolling lower.

For this reason I don't think we can allow the higher number to be halved.

Remember, at 100% A only fails on 96-100.

Hmm.. still thinking on this one. I have some ideas but they don't 'feel' that nice and might be awkward in play.

 

[Rurik]

I use subtract the amount of the higher skill over 100 from both skills.

For example 120 vs 80 becomes 100 vs 60. 150 vs 125 becomes 100 vs 75. It has worked very well for me.

 

[Deleriad]

I think the problem is that I want a solution that fulfills a few criteria: -

The problem being, of course, that if it existed we would already know it and as we don't know it, it doesn't exist. In fact, even if it did exist, I'm not sure we would all agree anyway.

The beauty and the problem of RQ is that if you tell someone that they have a 65% chance of doing something then it's obvious what it means. On the other hand, what does having a skill of 120% mean? And if two people are armwrestling and one is 65% at arm wrestling and the other is 50% what does that tell us about how often each one wins?

Something I saw a while ago that has stuck with me is using the tens die to indicate level of success. You would need to ditch the current critical rules then each time you make a skill test the tens die gives you a measure of success: the higher the tens die, the better the result. E.g. you have 65% in a skill, roll 35% so the tens die gives you 3 "success" points. If you fail, you get a negative number of success points equal to the difference between the tens die and the tens number of your skill. E.g. skill 65% roll 84%. Tens die is 8, skill is 6 therefore -2 success points.

In an opposed contest, the person with the most success points wins. If they both have the same, then lowest roll wins.

To deal with the other problems; if you have a skill over 100 then you add the excess "tens" to your die. E.g. skill 146% means you add 4 success points to each result. Roll 71 implies 7+4 = 11 success points.

To maintain the RQ ethos: 01 always beats any other roll. 00 always loses to any other roll.

Finally, to add some extra variability: rolling a double (e.g. 44) doubles the number of success points (including, if you fail, the number of negative success points). E.g. Roll 77: skill 80%, success - equals 14 success points. Skill 52%, fail, -3*2 = minus 6 success points.

The beauty of the system is that the success points give you a way of measuring degree of success which require none to minimal maths; I'm a big fan of any system that reads off the dice. For example, if I were to run it I would use 5 Success Points break points: e.g. 5SP equals a critical, 10 SP equals double critical which would turn a linear system into an exponential one: i.e. 5SP = double, 10SP=quadruple, 15SP = 8 times and so on.

I've never actually tried this and the thing is, the more problems you try to fix, the more you make and there's an issue of when the charm of RQ starts to disappear.

 

[bluejay]

I think the problem is that I want a solution that fulfills a few criteria: -

The problem being, of course, that if it existed we would already know it and as we don't know it, it doesn't exist. In fact, even if it did exist, I'm not sure we would all agree anyway.

Are you sure about this? How many people involved with the game or on this forum have degrees in Mathematics or Statistics?

 

[Deleted_Account]

Anyone like my REDO system?

Use the usual 4 levels of success (crit, hit, miss, botch). If you beat them this way, you win.

If you tie, reroll using your previous roll as your new skill level.

If you are both over 100%, the player with the excess points gets to add it to their skill level.

If only your old skill level was over 100%, you get to keep the points on top of 100% in your new skill.

So:

Alice @ 150% vs Bob @ 50%.

Alice rolls a 75%, Bob rolls a 45%.

Both succeed. Alice has 50% excess on top of 100%.

Alice's new target number: 75%(what she rolled) + 50% (excess) = 125%.

Bob's new target number: 45% (what he rolled).

Next roll. Bob rolls a 5% (damnit, almost a crit), Alice rolls a 15%.

Bob's target is now 5% (that sucks!).

Alice's target is now 15% + 25% (excess) = 40%.

...

This continues until someone gets a higher success than the other.

Mathematical analysis:
It shouldn't take very long. The excess of one player goes away almost instanty, and from then on he has about a 50% chance of succeeding on any one attempt.

The other player either still has 100%+, or quickly ends up with an effiectively random target number (ie, 50% success chance).

The game continues if they tie, and after at most a few rounds ties have less than a 50% chance of happening. Once that happens, the average contest length is 1 round.

In other words, it shouldn't usually take more than 2 to 4 rounds to finish a contest, regardless of the relative skills of the characters. Not ideal, I'll admit, but it won't last forever.

In comparison, if you waited for crits/failures, it would take an average of 7 rounds for two people with 95% skill to decide who wins.

 

[simonh]

Alternative solutions?

See the article "Skills over 100" on my site, linked in my sig, for my preffered approach. Only a slight lag in advancement over 100% thresholds, no maths of any kind and scalable to skills in the hundreds range.

 

[Deleted_Account]

Cute!

Might I suggest a slight tweak to get rid of that hiccup?

For skill XYZ%:

Base: +X
Roll 00: -1
Roll under XY: +1 (ie, roll under 1/10 of your skill)
Roll under YZ: +1 (ie, roll under the tens and ones of your skill)

...

In other words:
For every 100% you beat your skill by, upgrade your success grade by 1.
If you roll under skill/10, upgarde your success grade by 1.

So with 220% skill:
1 to 20%: under 1/10, beat skill by 200%, and a success. +4! Super-super-crit.
21% to 22%: under 1/10, beat skill by 100%, and a success. +3! Super-crit.
23% to 95%: beat skill by 100%, and a success. +2! Crit success.
96% to 99%: beat skill by 100%, and a failure. +1! Normal success.
00%: beat skill by 100%, and a botch. +0! Normal failure.

There is still the lag from 96% to 100% that doesn't do anything...

What do you do when two characters have the same threshold of success? (ie, two people just get normal successes).

 

[telsor]

Yes, the thread has been covered before, but anyway..


What about on an 'equal' result, both parties deduct their roll from their skill and try again.

So
A= 150% chance
B= 125% chance

A rolls 40, B rolls 75. Standoff!
Adjust skills, so
A= 110% ( 150-40 )
B= 50% ( 125-75 )

A rolls 90, B rolls 20. Standoff! Obviously a fierce contest, tension rises.
Adjust Skills, so
A= 20% ( 110-90 )
B= 30% ( 50-30 )

Etc ( expect no further adjustments take place as both are under 100 )


Yeah, it could take some time, but it's simple and would achieve the goal. ( no, I don't know the odds ).

 

[Utgardloki]

I think I like the subtract method. My flavor allows either player to subtract any amount that does not bring his own chance below 5%, and his opponent takes the same penalty.

This could possibly result in two skilled swordsmen "testing" each other out. If you know your opponent's score, you can calculate exactly how much to subtract from your own score to have the best chance of getting through his defenses. But since you normally don't know your opponent's score, you have to guess what is going to give you a decent chance of hitting without giving him an almost certain chance of parrying your blows.

Another wrinkle I have is that criticals trump successes. So this becomes another element of the calculation. (e.g. if your score is 758% and your opponent has 158%, you might not want to subtract and take a 75% of a critical. OTOH, if your score is 758% and your opponent is 158%, you can just take a 158% penalty and watch him weep.)

(Note: characters with skills as high as 758% were brought up in my thread on immortal characters. I don't expect to see very many of these types of characters brought into play in my games.....)

 

[weasel_fierce]

I use subtract the amount of the higher skill over 100 from both skills.

For example 120 vs 80 becomes 100 vs 60. 150 vs 125 becomes 100 vs 75. It has worked very well for me.

Im inbetween either using the Stormbringer solution (20% of skill is critical, crit beats regular), or using your suggestion.

 

[Magistus]

I use subtract the amount of the higher skill over 100 from both skills.

For example 120 vs 80 becomes 100 vs 60. 150 vs 125 becomes 100 vs 75. It has worked very well for me.

A friend pointed this out, what happens for 175 vs 75? That becomes 100 vs 0.

 

[Halfbat]

A friend pointed this out, what happens for 175 vs 75? That becomes 100 vs 0.

Or 95 vs 5, if the 5%/96+% rules are used. At 201%, 96 vs 5; 301%, 97 vs 5....

-------------------------
So, if I can get it right, even here the suggestions are still variants of:
1) Subtraction method (upper - lower) - possibly hiccups as the %ges don't match (is a "150" 75% better than "75" or 100% better?)
1.1) Voluntary Subtraction (either character takes a voluntary subtraction).

2) Staged success - makes use of the improvements beyond 100% to boost (say) criticals. This is similar to the combat system.
2.1) Staged success with a range of specials (similar to the old style impales) - what's the math on this like?

3) 100% boost - (aka the simonh system) each +100% boosts the degree of success by a factor (fumble to fail; fail to success; success to critical - can be combined with staged success)

4) Legendary Heroes - Includes halving but on failure the dice are rerolled as someone must win. What's the math like, bluejay? Sounds somewhat recursive to me.

Other suggestions appear to start getting complicated and don't match the "bluejay" criteria.

 

[gamesmeister]

Alternative solutions?

See the article "Skills over 100" on my site, linked in my sig, for my preffered approach. Only a slight lag in advancement over 100% thresholds, no maths of any kind and scalable to skills in the hundreds range.

This is a good system that still fits within the RQ ethos. I really like it.

 

[simonh]

I think I like the subtract method. My flavor allows either player to subtract any amount that does not bring his own chance below 5%, and his opponent takes the same penalty.

But it allows a moderately more skilled character to 'bury' his opponent's chance of success, drastically and IMHO unfairly stacking the odds in his favour. IMHO a more fair system would be something like a 2-for-1 tradeoff. For every 2% penalty I take, I can inflict a 1% penalty on an opponent.

 

[simonh]

Cute!

Might I suggest a slight tweak to get rid of that hiccup?

For skill XYZ%:

Base: +X
Roll 00: -1
Roll under XY: +1 (ie, roll under 1/10 of your skill)
Roll under YZ: +1 (ie, roll under the tens and ones of your skill)

Interesting statistically, but a pure blind bu**er to explain or figure out. I'm still not entirely certain I understand it correctly.

 

[bluejay]

4) Legendary Heroes - Includes halving but on failure the dice are rerolled as someone must win. What's the math like, bluejay? Sounds somewhat recursive to me.

Hmm, this is similar to an idea that I had which I sort of dismissed as awkward.

I haven't checked the maths here but it certainly feels vaguely right (i.e. I have no idea to be honest)...

Here's my system: -

Two characters make an opposed roll. If either character has a skill of over 100% then they are both halved until both have skills of 100% or less.

Both characters make their rolls. If one wins and the other fails then the result is clear.

If both succeed then highest wins as normal.

If both fail then we take the original skill values (i.e. before halving) to calculate if the roll was less than or equal to the unaltered skill. If one player rolls beneath this value but the other doesn't then again there is a clear victor. If both roll below this value (i.e. both had skills above 100) then highest roll wins again.

Finally, if both roll above their unaltered skill values lowest roll wins.


Here's the obligatory example.

A has 140% chance of success and B has 80%.

In an opposed roll, their skills are resolved as 70% vs 40%.

If A rolls 70 or less and B rolls over 40 then A wins.
If B rolls 40 or less and A rolls over 70 then B wins.

If A rolls 70 or less and B rolls 40 or less then highest roll wins.

Now, here's the new bit!

If B rolls above 40 then as long as A rolls below 140 he wins. Although he can't fail here you may wish to consider 96-00 or even just 00 as failure for A.


Second example, A 150% vs B 120%.

If A rolls above 75 and B rolls above 60 then highest roll still wins (as both A and B have original skill values above 100).

I haven't done the maths on this and I admit that it is complicated and quite awkward.

It is a potential solution...