## Monday, June 5, 2017

D&D 5th Edition has this featured new mechanic called "Advantage and Disadvantage" and I don't like it. In fact, this alone is pretty much capable of making me look not much further into 5E. In case you're living in a cave: "Advantage" lets you roll twice and take the better d20 in a variety of circumstances; "Disadvantage" makes you roll twice and take the worse d20. (To me this brings to mind the mechanic for the "Luck" superpower in FASERIP Marvel Super Heroes).

But I did wonder as to the exact probability distribution. There a couple of sites that have done this in the past, but for some reason they made it look like some big complicated analysis was involved. Hint: It's close to the most basic thing you can do with probability; if this was surprising for you, spend an afternoon reading the start of a chapter on probability. For disadvantage it's P^2 and for advantage it's 1-(1-P)^2, where P is the base probability of success (because of the complement rule for "not", and the multiplying rule for "and"). The results:

The obvious thing is that the mechanic is nonlinear. It gives a near-negligible change at the far ends, equivalent to a +1 bonus on a d20; or up to a +5 bonus in the middle for targets of 10-12 (symmetric penalties for disadvantage). This essential nonlinearity makes it hard for a DM to gauge its effect in a particular situation, because it scales up and then down depending on the original success target. Probability analyses are made more complicated in the design stage. In the middle, +5 is a rather huge level of bonus (arguably too large) by D&D standards.

In fact, this unpredictable up-and-down scaling is exactly why early RPG designers wanted to get away from rolling two dice (e.g., 2d6) and start using d20's, with their linear probability distribution, in the first place. To quote Jon Peterson in Playing at the World (section 3.2.2.1):
Gygax surely knew, as we can ascertain from the previous section, that the probability distribution for pairs of dice favors sums in the middle disproportionately; thus, the accuracy dice for Chainmail are far more likely to roll a 7 than a 12. The resulting bell curve creates all sorts of anomalies when you aim to roll over a given number; for example, a modifier that adds or subtracts 1 from the sum of throws can skew the results by different percentages depending on what the dice yield. Designers can scale the requirements to hit a target accordingly, but the subtle differences in likelihood may not be apparent to the players themselves. Unfortunately, with only six-sided dice as implements of chance, the options available to designers are limited... Modifiers to the roll of a d20, as opposed to the bell curve of 2d6, have a much more predictable result on the probabilities associated with event resolution.

1. Do you know the "Troll dice roller and probability calculator"?

It can help when dealing with complex probability math.

http://topps.diku.dk/torbenm/troll.msp

1. Also... I like to think of this kind of mechanic as a way to rise the entropy. This means that if you was uncertain if you would but gained Advantage then it is likely that you will succeed. But if you gained Advantage but was unlikely that you would succeed then it still be unlikely that you will succeed.

2. I've got a link to Torben's Troll Dice roller in the right sidebar. I've communicated with him in the past on his academic article on the system.

Your second comment is equally true about traditional D&D bonuses, and they're also easier to gauge mentally and more subject to refinement in the design process.

2. I think I understand your point about the probability, but I am not sure I get why it is a bad thing.
My understanding of the goal of the mechanic was "how do we make it more likely for the thief to succeed at thief things, without it being impossible for the non-thief to succeed. And the mechanic seems to do that.
Caveat, I have not run 5e since the playtest, so I have no direct experience with it in action.

1. It's a blunt instrument and you can't refine it, mentally manage it, or account for multiple such effects.

3. This is precisely why I've always disliked the advantage/disadvantage mechanic. It effectively becomes a fluctuating modifier for any given task.

If you were reasonably likely to succeed you're extremely likely to succeed when you have advantage. Which makes complete and utter sense. The reverse is true when you have disadvantage.

At either end of the difficulty spectrum - whether something is extremely easy or difficult - it doesn't confer as much of bias in success or failure. It's straight-forward really.

However I also see another way to interpret it (per the above chart); in the event that you need a 20 to succeed at something, it does make you twice as likely to do so. Going from a flat 5% chance to do so to 10%. However in the event that you have disadvantage - it's pretty clear your chance of getting a 20 is low - but not 0%. So I'd say there's a fundamental flaw with the above chart with respect to understanding the probabilities involved, which might be the source of some confusion or dissatisfaction with the mechanic.

1. The probability percentages are rounded to the nearest integer. The exact probability of rolling a 20 with disadvantage is (as noted) (0.05)^2 = 0.0025 = 0.25%.

5. So, if you don't like non-linearity, my rule of thumb is just to replace advantage/disadvantage with +4/-4 on the d20 roll, but, critically, to keep the more important rule of advantage and disadvantage:

They don't stack, and if you have both, they cancel entirely.

To me, that's the element that really speeds up play. A lot of modifiers that make sense in context but add up to a Baroque system get swallowed by a convenient rule that doesn't let the numbers swing too far out of alignment.

(and the silver rule of advantage/disadvantage is that if it really, really looks to the referee like it should stack, either just give away the result by fiat or only check to see if a critical or fumble result occurs)

1. I feel like the traditional idiom of D&D is for a ±2 or ±4 for "stuff". If someone wanted to be really rough and use a stock ±4 okay but it starts to not look like the rationale for a d20-based system has been lost. (+4 on d20 is pretty close to +1 on d6)

On the other hand, I don't see any good reason to lose stacking from multiple effects except that the advantage/disadvantage makes that impossible to gauge for most people. That's a huge change to the stock D&D system.

2. Sure, keeping in mind that the coarse granularity is only for things that aren't the one or two things most in focus (for 5e attacks, it's the basic Ability Mod + Proficiency, cover, and effectively AC - so three things).

On the other hand, the upside of coarse granularity is that you can easily switch those to +1 on 1d6 when you want to switch scales.

All that said, I mostly use advantage/disadvantage mechanics in my more gonzo games, where I really like the fact that it gives more natural ones and twenties and hence more critical and fumble results.

6. I think the key is that it is not an intuitive test of probability. Im fine with *summing* multiple dice because clustering around the mean is intuitive but when rolling twice for a single action it is not clear what a single roll means - it seems like two 'attacks' but it is not at all that.

7. The trouble is that +1 on a d20 doesn't actually have a consistent effect (only the appearance of it). +1 can double your chance of success, or have almost no effect at all. In contrast to your analysis I'd say the advantage of linear rolls is clarity of the chance of success, and the issue with advantage/disadvantage is that it throws away that clarity. I selected my open dice system in precisely so that +1 always reduced your chance of failure by a fixed proportion. There's no perfect solution (obviously) but I think it works best if you have clear goals in mind and stick to them. It seems most common for games to choose their dice mechanics based purely upon aesthetics, and in this case I think they've stuck "cool" onto "clarity" and possibly ended up with neither.

1. No, +1 on d20 is definitely a consistent effect of increasing probability by 5 percentage points. What you're talking about is a second-order effect, really a percent change in percentage points. Link.

2. I disagree! As a mathematician this sort of thing is why I strongly dislike percentages. If I increase something by 50% and then increase it by another 50%, I have not increased it by 100%, I've increased it by 125%. Adding percentages doesn't really make any sense (though, bizzarely, that's what people do). Most people if you said "add 10% to the price and then take 10% off the price" would think you were back where you started, whereas you've multiplied by 1.1 and then by 0.9.

You agree that a change of needing 10+ on a D20 compared to needing 11+ on a D20 is an almost negligible change, whereas going from needing 1+ to needing 2+ turns auto success into possible failure, and going from 20+ to needing 21+ turns unlikely success into an impossibility? So they're clearly having an extremely different effect on the probability.

3. You seem to be talking about something different than what Delta is talking about. He's talking about percentages, you're talking about quantities.

4. We're both discussing percentages. The question is whether "predictable result on the probabilities" (i.e. +1 increases the probability by 0.05) which is self-evidently predictable and comprehensible is in fact a "consistent effect on the probabilities".

An easier way of expressing it is that if I could get an absolute +5% chance of winning at roulette then that has a small improvement on me putting all my money on red, but a *huge* improvement if I put all my money on #13. So I'm saying that +5% at roulette does not have a "consistent effect". As a gambler I would most definitely be complaining it wasn't fair! Whereas Delta is saying that as the probability is consistently increased by an absolute +5% that it must therefore be considered a consistent effect.

It's a semantic argument about the meaning of the words - probably better suited to a pint down the pub than over the internet!

5. LWSHURTZ - perhaps you meant Delta's talking about probabilities whereas I'm talking about proportions.

It's also worth mentioning that in probability for two mutually exclusive events the chance of either occurring is the *sum* of the probabilities, so with probabilities you do often add percentages - which would be extremely rare when discussing proportions.

6. That is what I meant, thank you. However, I can't really parse what you mean when you say that a +5% chance of winning on roulette has different relative effect depending on whether you place your bet on red or #13. I mean, I get what you're driving at - your overall chance of winning on red is higher, so the +5% makes a smaller difference compared to the base rate than when you bet on #13... but that comparison, while true, is also irrelevant. So what if it does? The fact is, the change in probability is exactly the same for each one. Why would I care about the probability-relative-to-unmodified-chance? I think that's a fallacious move, tied to the assumption that the option with the smaller chance has a bigger payoff - true in the case of routlette, so the +5% has a greater expected value, but that's contingent on the circumstances. 5% is 5% is 5%.

7. But I'll happily take you up on the pint! Discussing semantics with friends is exactly my idea of a fine way to pass an evening!

8. The point is you would care because suddenly the game is entirely changed. Normally putting a bet on anything always gives you an average return of 36/37. Giving yourself +5% turns that into an average return of 2.77 for #13, but 1.073 for red. That is the effects on the people playing the game and having no idea whatsoever about the underlying probabilities are exceedingly obviously extremely different. It is *exactly* the same in other circumstances I described. The difference between 0% chance of dying and 5% chance of dying is huge, 50 to 55% and noone would really notice.

In other words, if the only way in which you feel the impact is the same is by looking at the underlying numbers, then the impact isn't equivalent. Why would you care that the absolute change in probabilities is the same?

9. Sorry, I just find this response baffling in the extreme. Your argument seems to rest on the idea that I wouldn't care about a 5% change in my chance of dying in one case and I would in another, but since I care about both equally, because they are the *same change in my chance of dying*, that's just flat-out false. I mean, I want to make sure I'm understanding you here - I don't want to give you short shrift - but is your argument essentially a psychological one? That the 5% is somehow "different" from one case to the other because people care about them differently?

10. No. For that particular part of the argument consider if I'm climbing something I know to be perfectly safe and I notice my rope is frayed meaning there's a 5% chance of me dying - then I will stop and won't carry on. A perfectly safe bet has just become dangerous. If I'm climbing Everest solo and I notice that the rope is frayed and the chance of me dying has gone up from 50% to 55% then I would carry on regardless as a highly risky activity has become slightly more risky.

It might sound like it's a psychological effect, but it isn't. Imagine climbing Everest solo with a 1% chance of dying per rope pitch, and there are sufficient pitches that there's a 50% chance I'll die. Consider increasing my chances of death by 5%. If I mean chance of death is *1.05 then it doesn't matter if that's +5% per pitch or +5% for the climb - it's the same. If I mean add 5% to the chance of death then is that +5% per rope pitch (which would make death on the climb almost a certainty) or +5% for the whole climb? Adding fixed percentages doesn't really make sense as a modification to chances.

The same is true of the average damage done in a D&D combat. If you need an 11 to hit, then +1 means you do 10% more damage every round. If you need a 20 to hit then +1 means you do 50% more damage on average each round. So the +1 has a very different effect. This is, of course, where I first noticed the effect in D&D - bless normally had little effect but in one combat I noticed it had a huge impact on the outcome.

11. Look, I don't want to sound insulting, but nothing you're saying here makes sense.

The first paragraph is a description of a psychological effect - you specifically couch the difference in terms of whether you would care about the adjustment or not. Then you say it's NOT a psychological effect!

The only part that isn't about psychology is the bit about relative rates of return, but as I noted above, you have yet to provide a reason to care about that - at least, not one that doesn't boil down to a dubious psychological assessment.

Look. Imagine there's a contest, the payoff of which is $100. In Case A, I have a 0% chance of winning that can be modified by +5% to 5% by use of a technique I know. Expected payout rises$5, from $0. In Case B, I have a 50% chance of winning, with the same modifier potentially in play. Expected payout STILL ONLY RISES$5 (from $50)! Now, your whole position seems to be based on the idea that I would care less about the extra$5 on the expected payout in the second case, but you stubbornly refuse to say WHY. You just assert it as a fact, when it's nothing of the sort, except maybe for you, and in any case, it's a PSYCHOLOGICAL ASSESSMENT. There's no objective change to the payouts, just a subjective (and idiosyncratic) assessment of the relative worth of the payouts in Cases A and B.

And even if everyone thought the way you did, it doesn't say a damn thing about the percentages, because the change in chances ARE the same, whether people care more or less about them or not. That is, even if everyone cared less about the change in expected payout in Case B, you've provided no reason to think that's RATIONAL. Maybe - MAYBE - you could get something going with declining marginal utility, but I doubt it.

12. I don't know why people get so upset discussing these sort of things, but you obviously have. I'm sorry you don't agree with my argument. I think we should stop the argument here as it's not fair on Delta's blog which is a a friendly place.

13. I'm not upset, just baffled. And I would appreciate it if you'd clear this up, if I am indeed misunderstanding your argument. You keep insisting it's not a psychological argument, but you keep coming back to whether people would "care" or not, which I find confusing in the extreme. I understand that the 5% increment represents a greater change in chance proportionally when you start with a lower chance, but what hasn't been established is why that matters. Can you explain that without reference to psychology or some hypothetical actor's mental states? If not, then I think we have our evidence that it is, in fact, a psychological argument.

14. Kind of busy this week (final exams, etc.) so I didn't have time to read all this. Did you guys read the Math Forum link above? I notice you're not using the proper term "percentage points" to clear up the ambiguity. 2nd Link.

15. I've explained it more clearly (and without any reference to psychology) on my blog today http://explorebeneathandbeyond.blogspot.com/2017/06/fairness-of-dice-modifiers.html.

Thanks for pointing out the useful term "percentage points" which is helpful for clarity, but I don't think that's been the point of disagreement here.

16. Joe, thanks for the link and the work that went into that post. Not entirely sure I can subscribe to the definition of "fair" being proposed there. But I left a slightly longer comment on your blog. (And thank you for using "percentage points" that made it much easier for me to parse :-)

8. I like the advantage / disadvantage rule, precisely because it provide a significant bonus in the middle without ruling out failure on the low end, or guaranteeing success on the high end. It is also a simple mechanic.

The only problem I have with it is, know when to use it and when to use a simple +x.

1. It's a blunt instrument and you can't refine it, mentally manage it, or account for multiple such effects.

9. I do not like the fact that using the advantage/disadvantage system means losing the ability to stack multiple effects, or the fact that no more granular change than approx 20% (in the range that 5E usually uses) is available. That said, because most target numbers in 5E are gonna be somewhere between 6 and 14 (or so it's been explained to me - I'm no expert), the scale of the effect is roughly predictable. Probably not worth it, still, but there you are.

1. While you may not personally like the decision, it was indeed a deliberate decision by the designers to eliminate bonus stacking and only concentrate on substantial bonuses or penalties - though it's an incomplete process, and a few sacred cows like +X weapons were retained.

2. Oh, I'm aware it was a deliberate decision, I just think it was a very foolish one.

3. I agree with this. As a marker that when they said "5E will be compatible with any earlier version of D&D", they weren't really serious, it's what made me put the book down.

4. I mean, that was a thing they said that sounded nice at the time, but being compatible with every earlier version of D&D can't be done. I blame the marketing guys for making that promise, but I don't blame the designers for being unable to do the impossible.

10. yeah, advantage/disadvantage is one of the many things that led me to decide that 5e wasn't a good fit for me and my table.

11. I disagree. Ad/Disadvantage is a good mechanic because it's *fun* to use! But that said... remember your post from 2011, Normalising Resolutions, a linear increase in accuracy does not correspond to a linear increase in success. And what is a +2 really supposed to do?

Clearly it means that 10% more of all rolls are successes, but the way it affects your successes is nonlinear: your probability of success increases by 1+2/n, which could be anywhere from x3 to x1.11. It helps a low skilled person succeed much more than it helps a high skilled person succeed. Conversely, it reduces the probability of failure by a greater degree for a high skilled person than a low skilled person. Is this what is meant to happen?

With Advantage, you get two chances at success, so your probability of failure roughly halves across the board. Well that seems quite reasonable! Although, if you take the probability of success, it does something nonlinear.

A +2 may make the probabilities easier to guess, but does it give the correct probabilities? Advantage is a very easy and popular mechanic to implement, so it seems to deserve at least some analysis as to what it really does.

I think what this indicates is that we need to put a greater amount of thought into what a change in someone's probability of success actually means, and what do we really want to achieve by giving someone a bonus (and I think you're just the person to comment on this subject!).

1. It's not just about "fun".

Adding +10% percentage points is the more basic operation. Looking at the second-order effect of proportion of successes may score rhetorical points in some circles, but not here. Link.

2. I've posted on this today on my blog fairness of dice modifiers, and I was very surprised to find out how different the effects of advantage and disadvantage are.

Hopefully you'll see I'm not attempting to score rhetorical points, but feel free to disagree with my analysis.

3. Apologies for any glibness with regards to fun there! I do agree that it is easier to calculate the effect of adding +2 than applying Dis/Ad, and that it is easier to stack modifiers.

But setting mathematical complexity aside, my point was: are you sure that +/-2 actually gives the desired outcome? If a factor negatively influences all combatants, should the same -2 be handed out to all? If two archers of different skills are shooting at targets, will the wind that appears affect them both equally, or will the less experienced archer suffer more?

It seems that the main reason you reject the Dis/Ad mechanic is down to the ease of use, not because it's been shown to be an inferior model of reality - similar to how you rejected the alternative system in Normalising Resolutions.

I don't know if it's a better model for reality or not, that is something I'd be interested in exploring.

4. Well, that's fairly put, thanks for that. I must admit that I've been on a simplicity kick in mechanics (= faster pacing in-game) for some time now. Even if an effect is discovered to be "really" nonlinear, I'm happy to mash into a linear-regression modifier for purposes of gameplay and call it close enough.

12. I don't think you can discuss Advantage/Disadvantage Dice fairly without also discussing Bounded Accuracy at the same time. In the context (and constraints) of Bounded Accuracy, the dice mechanic is a fairly elegant solution ( ... increasing/decreasing odds while keeping the randomizer within a 1-to-20 range).
(Doubtless there are forums elsewhere online where diverging opinions get expressed on the subject of Bounded Accuracy --- "the foundational design philosophy behind the core of 5th Edition D&D.")

Taken out of context (e.g., house-ruled into an edition that cannot tolerate the "bounded-accuracy-ness" of advantage/disadvantage dice), then, yeah, be careful.

1. That's an interesting link and thank you for sharing it. I think that does a fairly good job of contextualizing why 5E mechanics/stats look so weird to me. In some sense it looks like an over-reaction by Mearls et. al. to problems in the 3E system (and/or maybe 4E?). That is: They've gotten progressively more volatile over time about re-upsetting the D&D applecart in every edition.

This business of bounding, not giving class to-hit bonuses, etc., just doesn't look like classic D&D. You're right that all that irritated me on reading 5E, and then advantage/disadvantage was the final straw that made me put it down. Thank you for synthesizing that for me.

13. Strangely, 5e "feels" more like 1e and 2e for me then 3e and 4e ever did. I ran the Caves of Chaos in 5e, and it rocked! It is the most fun I've had since I was a kid playing in Junior High School...that is the feeling it brought back, even with new rules such as Advantage. As a DM, I found Advantage fast and fun.

14. I have always had my doubts about the mechanic as well. I agree that it changes the traditional D&D model of how modifiers work. I also agree that its impact is "less clear" if by "clear" we mean "the new percentage chance is trivial to see" as it were.

However, I also feel that it very much simplifies things at the table. In the AD&D2 game I was playing for several years, we spent plenty of hours trying to figure out just how many crazy modifiers apply to certain situations. One could complain that the DM should have just made a call to keep things going, but I am not sure if that's really any better than just applying a coarser mechanic.

In the end, I'd much rather have the DM make the call whether a certain set of circumstances is "positive" or "negative" overall than to keep totalling up +/-2 modifiers from six different tables and 3 spell descriptions. (Yes, I know, maybe we shouldn't have tried to play AD&D2 but that wasn't my call.)

Sure, after the "all these things together make you more/less likely to succeed" call the DM could just as well say "+4" or "-4" or whatever number instead of rolling with advantage or disadvantage.

I guess my main point is that I don't like long tables of modifiers because either we have to pour over them in game or someone has to know them by heart. And compared to that, I'd take the mechanic any day of the week because it turns the DM's call into something actionable without further debate or pondering.

I guess I am becoming less concerned with the exact numbers these days and more concerned with just keeping things moving. If in the process we end up with slightly mysterious percentages (that nobody really has to compute if we're results-oriented) then so be it.

All that said, I have not actually ever used the mechanic in practice. I have also not added it to my house rules document, but the way I run B/X not many situational modifiers come up anyway. And of course I might very well just be wrong about it all. :-)

1. Sure, I couldn't agree more on the pacing and lack-of-table-lookups. My philosophy for some years now has been that the game must be runnable from memory by the DM. Cutting down tables and spell descriptions to memorizable chunks have been my primary projects.

I do just think that being able to add either +2, +4, or +6 in different situations is a level of granularity and clarity that I don't want to expunge. The effective +5 from advantage in the middle of the progression is just way too generous mechanically.

2. Thanks for saying this, because that triggered something "strange" in my brain. :-) I am about to give an exam in my programming course. Let's say some students get extra time on that, an "advantage" as it were. How much does that help?

For really good students it makes almost no difference: They finish early anyway, have most answers correct, and just twiddle their thumbs during the extra time.

The really bad students also don't gain much. They didn't know what to do in the first place, so more time will have them doubt, and doubt again, and doubt again, their answers. The lucky ones will actually find some issues and fix them, but probably not most. (In fact, the extra time might even result in a lower score.)

The students in the middle though, the ones that need maybe 2.5 starts where a good one needs 1, they'll actually benefit. They can do a few things wrong the first time around but use the extra time to fix at least some of those.

Maybe this whole mechanic is actually inspired by taking exams? :-)

3. Well, for my students extra time makes almost no difference for anybody, so maybe my perspective is just slightly different. (Which was evidenced again this semester after another instructor persuaded me to cut the programming final by half.)

15. Intuition is a poor substitute for actual analysis, so I apologize in advance for wasting anyone's time with my border-line innumerate thoughts here.

It seems to me that the point of advantage/disadvantage is to provide specifically this effect, wherein a character is given a high probability of success at the sort of task she would normally have a 50% chance of pulling off, but that tasks exceeding the character's natural ability remain unattainable or unlikely.

It seems like there's a strange marriage in D&D between linear chances of success and limited opportunities to improve the odds during a given challenge (at least, at most tables). This results in trying for 20% odds over and over being a pretty reasonable approach to a problem. 50% odds are sometimes perceived as damn good, at least to the intuition (+0 to hit, vs opponent with 10 AC, for example).

Under conditions where it's not uncommon to miss four attacks for every one that hits, advantage is a pretty good, well, advantage. Under conditions where you hit four times out of five, it's less so.

Putting aside the individual satisfaction that it provides to a player who gets frustrated at missing constantly because he hasn't quite got a handle on his poor bonus to hit being better spent on the mooks than the boss, my question is why would anyone want this? Or more precisely, why would anyone want to trade the ability to do something awesome and epic for a better chance to do something average and unworthy of note? Whatever the statistics might show about being better off over the long run, there is a subjective value to scoring a 20 at a crucial moment and turning the tide of a tough battle that gets lost or seriously obscured by the exchange.

I guess there was some focus testing done somewhere that showed player frustration at missing average rolls outweighed player elation at scoring difficult ones. I dunno.

Anyway, great post. Speaking as an innumerate clod who nevertheless loves fiddling with systems, insights into the math like these are super valuable resources.

1. This is a good perspective and thanks for that observation.

Personally my guess is that it's just lazy game design and probably not as well thought out or analyzed as any of us would hope.

16. Didn't care for advantage/disadvantage when it was introduced, as set modifiers are more predictable and easier to fine tune, plus you can just use the ±2 rule if you want simplicity

Oddly enough, though, this post has actually gotten me to ease up on my stance and I now find the concept somewhat intriguing. I kinda like how situational factors would affect actors of varying skill levels differently (which is true in some sense of set modifiers, but not in the same way)

The one thing I don't like is the lack of accumulative fortune. If we dropped that, wouldn't we see diminishing returns in the effective modifiers?

Say your target number's 11. Advantage would effectively give you +5, double advantage grants +7.5, triple is +8.75, etc. The effective modifier's naturally bounded (I think, anyway. I'm pretty rusty on probability, so it's quite possible I screwed that up). The one downside is too many dice if things get out of hand

Personally, I've fallen in love with a more adjudication-heavy "holistic" approach rather than traditional stacking