Brain Hurts! 4d6 with individual rerolls

[Jason]

I am pondering the idea whether I should use 4d6 with individual die rerolls for my homebrew system, meaning the players roll 4d6 and can reroll a number of individual dice up to their skill level (max 4). So far, so good. But I cannot for the life of me figure out, how to calculate the changed probabilities and distibutions of the possible results after rerolls.

I am looking for 5 distribution tables, one for no rerolls and one each for 1, 2, 3 and 4 rerolls. I have the distribution table for no rerolls (that one was simple) but struggle with calculating the odds with rerolls.

Can any of you shove me in the right direction? Of course, I would appreciate complete tables, but what I am mostly asking for atm, is just the proper math to do it on my own.

And do you have an opinon as to how viable such a dice mechanic would be?

Thanks in Advance,

Jason

[rasmuswagner]

I am pondering the idea whether I should use 4d6 with individual die rerolls for my homebrew system, meaning the players roll 4d6 and can reroll a number of individual dice up to their skill level (max 4). So far, so good. But I cannot for the life of me figure out, how to calculate the changed probabilities and distibutions of the possible results after rerolls.

I am looking for 5 distribution tables, one for no rerolls and one each for 1, 2, 3 and 4 rerolls. I have the distribution table for no rerolls (that one was simple) but struggle with calculating the odds with rerolls.

Can any of you shove me in the right direction? Of course, I would appreciate complete tables, but what I am mostly asking for atm, is just the proper math to do it on my own.

And do you have an opinon as to how viable such a dice mechanic would be?

Thanks in Advance,

Jason

So....you want a slow-as-fuck resolution system, in order to generate outcomes whose probability is completely opaque?

[angelfromanotherpin]

If a re-roll is worse, does the new result stand? If not, you're just doing a roll-and-keep system and can use the [highest x of x d6] function on anydice.com. If it does, using tables is very problematic because of the element of player judgement that shows up in the middle of the process.

[hyzmarca]

I am pondering the idea whether I should use 4d6 with individual die rerolls for my homebrew system, meaning the players roll 4d6 and can reroll a number of individual dice up to their skill level (max 4). So far, so good. But I cannot for the life of me figure out, how to calculate the changed probabilities and distibutions of the possible results after rerolls.

I am looking for 5 distribution tables, one for no rerolls and one each for 1, 2, 3 and 4 rerolls. I have the distribution table for no rerolls (that one was simple) but struggle with calculating the odds with rerolls.

You struggle for calculating the odds because there is a a variable that you're missing. What rules do the players use to determine when they reroll?

A player you rerolls anything below 4 is going to produce drastically different odds than one who only rerolls on a 1. And those are going to be drastically different from a player who rerolls anything less than 6 but only on a friday and only if one of the dice is a 2.


Basically, you need a different chart for every reroll rule a player might follow. And that's a mindbogglingly huge number of charts.

[deaddmwalking]

And missing one other thing as well... If the player succeeds then they won't roll any dice over again. So are the DCs static? Can a player sometimes succeed with a 6 and other times require an 18?

[momothefiddler]

Yeah, if you're not keeping the higher of the two, it's a mess and you shouldn't do it. If you are, the behavioral objections are irrelevant and the complex resolution objection is completely relevant.
Regardless, at that point it's highest 4 of 4+skill d6, and the distributions are pretty straightforward.
Edit: I don't know if you're familiar with anydice, but the "At Least" tab is probably what you want to look at, or at least worth a glance.

[PhoneLobster]

Should I drop by and point out that yet again when confronted with a pointlessly opaque and complex basic roll mechanic proposal it is yet again something someone is interested in... despite themselves having no idea what the fuck it does.

Every. Single. Time.

[deaddmwalking]

I think it's clear what the intent is - everyone rolls 4d6 so everyone is on the same RNG (4-24) which effectively has a 20 point range which works with many of the conceits of d20. Further, skilled people are 'better' than unskilled people thus allowing the rerolls. The fact that when to roll again is a player decision (which might be a good thing in some cases) is what makes this so complicated. And so how much better is someone with 3 rerolls versus 4? It's worth asking the question.

You might consider every rank adding +1 dice with each character keeping their best 4. So skill 4 characters would roll 8 dice while skill 0 characters would roll 4. That's much easier to quantify how much each skill rank is worth.

Playing with dice is fun and maybe you stumble into an interesting mechanic that helps a game.

[OgreBattle]

If it's only 4 dice ever being rolled perhaps a moving target number could work for you, easy to calculate odds, the reroll step is removed so saves some table time.

Untrained needs 6's (.66 hits)
trained 5+ (1.33 hits)
experts on 4+ (2.00 hits)
masters on a 3+ (2.66 hits)
ultra genius masters succeed on a 2+ (3.00 hits)

Then calculate their hits vs a threshold of success, or opposed roll.

Basically what warhammer tabletop does.

[Jason]

If a re-roll is worse, does the new result stand?

That's the plan, atm.

If it does, using tables is very problematic because of the element of player judgement that shows up in the middle of the process.

That's the problem I ran into. There may not even be a solution to my problem, but I wanted to ask others first, before I threw in the towel.

And missing one other thing as well... If the player succeeds then they won't roll any dice over again. So are the DCs static? Can a player sometimes succeed with a 6 and other times require an 18?

The target numbers would be task specific. I have not yet finalized the numbers but I currently use the following a s guidelline:

10 - Trivial
12 - Easy
14 - Normal
16 - Difficult
18 - Very difficult
20 - Next to impossible

This works reasonably well for a base distribution for 4d6 with limited die roll modifiers ranging from -4 to +4, but I wanted to know the impact rerolls would have on thise numbers. Whether I would need to increase them (or rather, by how much), if I dropped the base modifers instead.

So, my base system would view a task of average difficulty (TN 14) as a 55% success rate for an untained attempt. A professionally trained Charater (skill 2) would yield a 76% success rate on the same task and a grandmaster of the discipline (Skill 4) would yield a 90% success rate.

I am fairly happy with those numbers and would like to achieve the same or similar numbers with the reroll mechanic. I am, however, not certain, if it is even possible, as I fail to compare the actual odds.

Edit: I don't know if you're familiar with anydice, but the "At Least" tab is probably what you want to look at, or at least worth a glance.

Not familiar with it, yet. But I'll go and check it out. Thanks.

[momothefiddler]

If a re-roll is worse, does the new result stand?

That's the plan, atm.

Bluh. Okay, that's a mess.

Do you intend to have graduated levels of success or failure? That is, does failling by 10 have worse consequences than failing by 5?

Do you intend to make it clear what the DC is before the roll? Or at least to tell the player if they've succeeded or failed before they choose to reroll?

If failure is ungraduated and players learn of failure before reroll, you can break it into two options: either the player succeeded, in which case it doesn't matter, or the player failed and has rerolls left, in which case they're gonna reroll their lowest die, or the player failed and has no rerolls left, in which case they've failed. In this situation, the ability to ignore successes leaves your probabilities still fairly similar to keep highest 4.

If players are sitting there unsure if their current number is high enough, though, this pretty much becomes an exercise in psychology instead of probability. You could do worse than assuming dice are rerolled if they're less than the average on a d6 (3.5) - that is, 1s, 2s, and 3s are candidates for rerolls and 4s, 5s, and 6s aren't. That's still a vague approximation, though, and you're gonna end up heavily influencing your outcomes with things like how you word your descriptions of challenges and what words you use for failure and so on, and I really don't suggest it.

---

Edit:

So, my base system would view a task of average difficulty (TN 14) as a 55% success rate for an untained attempt. A professionally trained Charater (skill 2) would yield a 76% success rate on the same task and a grandmaster of the discipline (Skill 4) would yield a 90% success rate.

I am fairly happy with those numbers and would like to achieve the same or similar numbers with the reroll mechanic. I am, however, not certain, if it is even possible, as I fail to compare the actual odds.

The highest 4 of 4+Skill ends up being curved a little differently, but you can still compare them. Using the At Least tab on the anydice function I linked, you can see that for DC14, highest 4 of 4 gives you (obviously) the same 55%. Highest 4 of 6 gives you 88%, and highest 4 of 8 gives you 97%. You could also make your average difficulty DC 16, which leaves untrained at 34%, Skill 2 at 73%, and Skill 4 at 90%.

In general, your maximum result stays the same, but each point of skill means more on a keep highest vs a simple addition.

[Jason]

Should I drop by and point out that yet again when confronted with a pointlessly opaque and complex basic roll mechanic proposal it is yet again something someone is interested in... despite themselves having no idea what the fuck it does.

Not being interested in something that you don't yet understand is epistemological stagnation. Trying to force a system you don't understand is stupid, however. That's why I am trying to wrap my head around it, to see if it is worthwhile or if it is not.

Why am I even interested in it? Several reasons:

1. I dislike the basic skill+attribute modifier because the extremes of such systems are ridiculous. As an examples take shadowrun, where you can be "legendary" with a weapon (agility 1, skill 7), yet still be effectively less capable than a "Novice" elven street punk (agility 7, skill2).
While that is mechanically fine, it's thematically dissonant. I would like my ststem to be thematically harmonious.

2. While my argument from point 1 still stands I also want both physical aptitude and technical training to matter, just in different ways. You can be well trained in fencing, for excemple but if you are to weak, your sword will be too slow, putting you at a disadvantage. My current solution to that is to grant additional "utility actions" (those are not combat actions, but things like reload, aim, etc.) based on the skill level. I am not happy with that solution, so i am looking for different ways.

3. I am currently using only the skill value as a modifier, with an additional modifier, if the respective attribute is too low or too high (more than 2 points difference). That is a rather clunky mechanic, however, so I am looking for different solutions.

That's where the idea with individual rerolls came in. I don't want to just hand out additional dice, as that would basically mean a +3.5 modifier per die, effectively exploding my resolution range and a die reroll would allow for a more likely middle ground scenario, and not impact the extremes as much as a flat modifier. My possible resolutions would still range from 4 to 24 but a higher skill (and thus more possible rerolled dice) would shift the probabilities for higher results up a little notch. In the end, an effective shift by 2 would mean a shift by an entire difficulty category.

Bluh. Okay, that's a mess.

That's the vibe I'm getting so far.

Do you intend to have graduated levels of success or failure? That is, does failling by 10 have worse consequences than failing by 5?

Not gradually, no. I do have, however a critical success/failure mechanic (rolling 4 of the same kind). If the result is above the TN, it's a critical success, if not, it's a critical failure.

Do you intend to make it clear what the DC is before the roll? Or at least to tell the player if they've succeeded or failed before they choose to reroll?

Players would know the TN before they roll.

If failure is ungraduated and players learn of failure before reroll, you can break it into two options: either the player succeeded, in which case it doesn't matter, or the player failed and has rerolls left, in which case they're gonna reroll their lowest die, or the player failed and has no rerolls left, in which case they've failed. In this situation, the ability to ignore successes leaves your probabilities still fairly similar to keep highest 4.

The highest 4 of 4+Skill ends up being curved a little differently, but you can still compare them. Using the At Least tab on the anydice function I linked, you can see that for DC14, highest 4 of 4 gives you (obviously) the same 55%. Highest 4 of 6 gives you 88%, and highest 4 of 8 gives you 97%. You could also make your average difficulty DC 16, which leaves untrained at 34%, Skill 2 at 73%, and Skill 4 at 90%.

In general, your maximum result stays the same, but each point of skill means more on a keep highest vs a simple addition.

Sweet! Thanks.

If it's only 4 dice ever being rolled perhaps a moving target number could work for you, easy to calculate odds, the reroll step is removed so saves some table time.

Untrained needs 6's (.66 hits)
trained 5+ (1.33 hits)
experts on 4+ (2.00 hits)
masters on a 3+ (2.66 hits)
ultra genius masters succeed on a 2+ (3.00 hits)

Then calculate their hits vs a threshold of success, or opposed roll.

Basically what warhammer tabletop does.

I am currently using a similar system for my damage resolution mechanic (static number + variable amount of d6, every d6 equal to or lower than the attacker's skill = 1 damage extra).

[momothefiddler]

Okay, so we have a system where success is binary, failures turn into crit failures and successes turn into crit successes if all four dice are the same (0.08% of the time, or 1 in 1300 rolls EDIT: I lied, this is actually a whopping 0.46% of the time), and players know the DC before they roll.

(Sidenote, I'm used to TN being for individual success thresholds in SR-style dice pools and DC being for total required amount after adding everything - that might just be something I made up, though. Do other people here have any experience to add to that?)

Anyway, given that, I've obtained the results for skill 1-3 here. This is absurdly complex, computationally, and Anydice refuses to run it if I add in skill 4, because it takes too long. (And fwiw, if a computer refuses to do it, don't ask your players to).

I've included the highest x of 4+x, for comparison. You end up with this for rerolling:

	Skill 0	Skill 1	Skill 2	Skill 3
DC 10	90.28	96.57	98.79	99.57
DC 12	76.08	89.24	95.15	97.77
DC 14	55.63	74.96	85.92	92.02
DC 16	33.56	54.10	68.65	78.56
DC 18	15.90	31.31	44.78	55.75
DC 20	5.40	13.18	21.44	29.26

And this for keep highest 4:

	Skill 0	Skill 1	Skill 2	Skill 3
DC 10	90.28	96.69	98.93	99.66
DC 12	76.08	89.75	95.80	98.30
DC 14	55.63	76.23	87.86	93.92
DC 16	33.56	56.30	72.73	83.47
DC 18	15.90	33.91	50.76	64.58
DC 20	5.40	15.07	26.83	38.90

So I don't have numbers for you on Skill 4 for the rerolls, but I stand by my point that if they know the TN and success is binary, there's no reason to go with rerolls instead of highest 4 - and the similarity of the above tables supports that claim.

[Jason]

You are amazing! Thanks a lot!

[vezidoroga]

Momo, I think you may have made a mistake. The results for a skill 1 player should be identical between the "highest 4" and "reroll" procedures (assuming binary success and known DC). I have limited understanding of the Anydice syntax, but it looks like it's rerolling even after a success.

Jason, do you intend the individual dice rerolls to be taken sequentially or all at once? That is, does a skill four player have up to four chances to reroll the lowest die or does she have a single chance to reroll up to four dice? The former is equivalent to "keep highest four" (again, assuming known DC and binary success), the latter is more complicated but would give strictly lower chances of success.

If the latter is what you mean, I might be able to come up with something close to optimal behavior, but how your players would actually reroll would probably deviate from it, especially the non-mathy sort.

[erik]

I'm still baffled by what the virtue of this system is supposed to be.

It takes longer than most popular systems due to adding 4 dice and taking rerolls.

Outcomes are not intuitive, whereas other systems are easily predictable.

The curve poorly handles bonuses (a mere +2 can be +1% or +20%, and +10 or more wrecks the range) which limits granularity and meaningful choices.

Upsides are... ? ? ?

Now, this isn't the worst roll mechanic I've ever seen (that would be One Roll Engine, with Unknown Armies as runner up), but I sure don't see the point of it.

Just use 2d6+x vs TN or d20+x vs TN and you'll be better off.

[Mask_De_H]

The point is obviously to be a unique and special snowflake.

[momothefiddler]

Momo, I think you may have made a mistake. The results for a skill 1 player should be identical between the "highest 4" and "reroll" procedures (assuming binary success and known DC). I have limited understanding of the Anydice syntax, but it looks like it's rerolling even after a success.

You're right that it doesn't check for success before rerolling. I forgot to account for that. Also good point that that makes Skill 1 also identical between the two options. Your claim that those are equivalent, though... Hm.

Individual rerolls are equivalent to rolling them all and then choosing one to discard before seeing each die after five (so you get five, drop one, add one, drop one, etc). That's a stupid approach. Trying something else.

Let your current roll at any point be {A,B,C,D}, in ascending order. Either this sums to the DC or more, in which case you've succeeded, or it doesn't, in which case you reroll A in favor of A1. If A1>B, this step is identical to a stage of the keep highest sort. If A1<=B, it doesn't matter because either you've succeeded, you're rerolling it again anyway, or you're out of rerolls (in which case no four of your dice were high enough to work - you'd have failed anyway.)

Point is, you only ever reroll the lowest die and you only reroll it if you were already failing, so the reroll can't actually ever make things worse, even though it seems like they can.

So yeah. I apologize for missing that, Jason. vezidoroga is correct - at that point they are the same. Just go with keep highest.

---

It takes longer than most popular systems due to adding 4 dice and taking rerolls.

Agreed, which is why I've been lobbying for highest 4 - it's a single roll.

Outcomes are not intuitive, whereas other systems are easily predictable.

"You always end up between 4 and 24, but higher skill (more rerolls) gets you better at hitting those higher difficulties and makes you more consistent at hitting the lower ones." Sure, it's not "+1 skill is +5% chance of success", but we've seen over the years how easy that is to understand (it's obviously not, because people can't percentages). I don't know that I've ever played an IRL game with someone who could tell me the expected value of their 1d20+14 anyway, but as for general progression I feel this is plenty intuitive.

The curve poorly handles bonuses (a mere +2 can be +1% or +20%, and +10 or more wrecks the range) which limits granularity and meaningful choices.

Curved distributions do give differing value to bonuses at different points, and there's been plenty of discussion on this board about whether that's a good thing or if it sets your parents on fire. But anything with 3 or more dice is going to have that aspect. Also, +10 (in addition to being stated as impossible) doesn't wreck the range, which remains 4-24 regardless of your number of rerolls. Sure, at that point you're never gonna fail a DC14 task, but you're still never gonna succeed at a DC25 task, and that fits expectations just fine.

Upsides are... ? ? ?

Upsides are that it fills the stated desire of having a fixed range, which it does even if you somehow get 10 rerolls. There was also the stated desire that high attributes not obviate high skill, but that depends on how attributes interact with the resolution system, which is outside the scope of what we've learned so far.

Just use 2d6+x vs TN or d20+x vs TN and you'll be better off.

I don't want to just hand out additional dice, as that would basically mean a +3.5 modifier per die, effectively exploding my resolution range and a die reroll would allow for a more likely middle ground scenario, and not impact the extremes as much as a flat modifier.

[erik]

momo, I must've failed in my clarity. When I was talking about bonuses I was talking about static bonuses to outcome, not extra rerolls. If extra rerolls are the only possible currency then this system is a little bit terrible.

Those upside examples are ridiculous. A fixed range isn't an intrinsic good. It does make it so that there is no task so impossible that the most inept character cannot succeed via luck. A room full of monkeys are more likely to write a successor to Shakespeare's works than the greatest writer in the world.

Limiting maximum skill by maximum attribute is an ok solution but it sounds like Jason wants to over-complicate it.

Curved distributions do give varying values to different TN's and 2d6 is a pointier curve, but many more people are familiar with probable outcomes on 2d6 vs. (4+X)d6 keep 4 and can make informed decisions.

I don't know that I've ever played an IRL game with someone who could tell me the expected value of their 1d20+14 anyway

Really? Jesus. You must have a player pool of math illiterates to never have played with someone who understood d20. I hope it was a small sample pool.

Few people might not know the expected probability, but they should know the middle and the significance of a bonus. They don't have to know the expected value, but I bet almost all of them know that they have a 50% chance to succeed against something needing an 11 and each +1 bumps it 5%. Some people might be off by 5%, but still they are ball-parking it close. Likewise most people know that 7 is the middle of 2d6 and a 1/36 chance to get box cars or snake eyes respectively.

If I ask people what the average result of 8d6 keep best 4 is, I'm getting blank stares guaranteed.

Moving on to crits...
With keeping highest rolls you're pretty much never going to have critical failures and only rarely on successes (and only via 4x6's) since rerolls increase the chance of getting a 6. So that aborted crit mechanic is dead on arrival.

[hyzmarca]

Now, this isn't the worst roll mechanic I've ever seen (that would be One Roll Engine, with Unknown Armies as runner up), but I sure don't see the point of it.

That sounds like a challenge, to me. We can totally make a roll system that's much worse than ORE.

[erik]

Now, this isn't the worst roll mechanic I've ever seen (that would be One Roll Engine, with Unknown Armies as runner up), but I sure don't see the point of it.

That sounds like a challenge, to me. We can totally make a roll system that's much worse than ORE.

Just do your best to channel your inner Stolzecock.

Wow, my phone autocorrected Stolze into Stolzecock, something I've never typed before. It knows my heart.

[hyzmarca]

Now, this isn't the worst roll mechanic I've ever seen (that would be One Roll Engine, with Unknown Armies as runner up), but I sure don't see the point of it.

That sounds like a challenge, to me. We can totally make a roll system that's much worse than ORE.

Just do your best to channel your inner Stolzecock.

Wow, my phone autocorrected Stolze into Stolzecock, something I've never typed before. It knows my heart.

First of all, the system calls for 3d10s and a d20. Base TNs range from 3 to 65.5, depending on difficulty, before modifiers are applied.

The d10s should be different colors. I recommend red, green and black and will be using those colors for reference from this point on.

The d20 is a modifier and is not added to the roll. Instead, if the d20 produced an odd result that is greater than 5, you multiply the red d10 by that result, and divide the green d10 by it. If the result is even and greater than 5, you multiply the green d10 and divide the red d10. If the d20 is less than 5, you multiply the black d10 by twice that number and divide the other two dice by half of it.

Then you add toss results together.

You do not round anything. You never round. If you get a fractional result, then use fractions. TNs can be fractions.

Now, TN modifiers can range from .48 to 1.98 and stack multiplicity.

[erik]

That's more complicated but I don't know if it is worse than ORE. You don't have a method for rewarding system mastery in there by offering a spectrum of superior and inferior dice selections while including sidebar text chastising system mastery by saying that you know your system is a broken mess and it is the fault of players if they find it is broken.

A computer could resolve your system without problems but ORE would remain a pile of shit no matter the processor.

[momothefiddler]

momo, I must've failed in my clarity. When I was talking about bonuses I was talking about static bonuses to outcome, not extra rerolls. If extra rerolls are the only possible currency then this system is a little bit terrible.

Okay. Unless I've missed something, those aren't discussed at all here, so I guess that's why I was confused.

Those upside examples are ridiculous. A fixed range isn't an intrinsic good. It does make it so that there is no task so impossible that the most inept character cannot succeed via luck. A room full of monkeys are more likely to write a successor to Shakespeare's works than the greatest writer in the world.

Mmm... that's all true.

I don't know that I've ever played an IRL game with someone who could tell me the expected value of their 1d20+14 anyway

Really? Jesus. You must have a player pool of math illiterates to never have played with someone who understood d20. I hope it was a small sample pool.

I mean, most of it was with people who like the nWoD dice system. I.E. yes. I don't play RL games anymore because nobody I know RL is worth playing with. Makes me sad.

Few people might not know the expected probability, but they should know the middle and the significance of a bonus. They don't have to know the expected value, but I bet almost all of them know that they have a 50% chance to succeed against something needing an 11 and each +1 bumps it 5%. Some people might be off by 5%, but still they are ball-parking it close. Likewise most people know that 7 is the middle of 2d6 and a 1/36 chance to get box cars or snake eyes respectively.

If I ask people what the average result of 8d6 keep best 4 is, I'm getting blank stares guaranteed.

I'm really surprised you live in a world where box cars and snake eyes are an obvious 1/36. That's really implausible to me. Which isn't to say I disbelieve you so much as wow our experiences are very different. That said, is there a reason those values have to be known offhand? Are you against charts in books beyond them being inelegant?
I suppose you're used to people who would know all that on a d20 or 2d6 without charts, so I guess keep in mind that I'm not, but still?

[momothefiddler]

That's more complicated but I don't know if it is worse than ORE. You don't have a method for rewarding system mastery in there by offering a spectrum of superior and inferior dice selections while including sidebar text chastising system mastery by saying that you know your system is a broken mess and it is the fault of players if they find it is broken.

A computer could resolve your system without problems but ORE would remain a pile of shit no matter the processor.

I looked up ORE and wow.

Okay here we go:
Aspects go from 1-5, Capabilities go from 1-4. You choose how many dice you roll, between 1 and your corresponding Aspect, but the first die you roll is a d12, the second a d10, the third a d8, the fourth a d6, and the fifth a d4, and only your lowest result counts. Thus, Aspects express your potential, because with Keenness 5 you have the ability to roll up to 5 dice but at Keenness 1 you have to roll a single d12. For each point of your corresponding Capability, you get to either add 1 to your result or ignore one die when considering your lowest. This means that Capability is a measure of your efficacy within your level of potential, but also shows your ability to "Push The Envelope", which is the term for when you go all-in and roll a single 1d12 in order to add your whole Capability rating to the result. Big risk, big reward, since that's the only way to get a 16 - a megasuccess.

If you succeed by more than one point, you get additional degrees of success - these come at 2, 4, 5, and 7 - which benefit you in some way determined by the MC.

Any dice that match are Locked In and cannot be ignored with a Capability rating, BUT, in return, for every such Locked In set you gain an additional effective Capability rating, which can be used as normal. (Note that I said one per set, not one per pair - don't try to munchkin more than one Capability rating out of a triple 9!)

Once per Cycle you may elect to Put It All On The Line, which lets you roll a d20 in addition to any other dice, at the expense of applying no Capability rank at all. Be sure to save this for very important situations, since you can't do it very often!