Tag Archives: Probability

How do you roll? #RPGaDay, Day 1

While I’ve always tried to respond to RPGaDay via Twitter (@thedicemechanic), I’ve never gone into any detail in a blog entry. This year, I’m going to try harder.

RPGaDay 2016

When it comes to dice-rolling, my preference is the real thing. There’s something about the feel of dice, the sound of them clattering across the table that tells me I’m playing a game. Apps are fine as an emergency, so you’re never without a convenient randomiser, but for play it has to be the real thing.

Virtual Dice

Funnily enough, my love for dice doesn’t extend to Virtual Tabletops. I’ve a bit of experience of both Fantasy Grounds and Virtual Tabletop Simulator, both of which have dice icons that have to be grabbed and thrown. I hate this. I much prefer roll20’s default, which quickly generates a number. Real dice I love, virtual dice just leave me cold.

Diceless

No thank you. Except sometimes. The idea of role-playing without a random element at all just doesn’t appeal. I have played Everway, Jonathan Tweet’s brilliantly clever game that incorporates three types of resolution mechanic in the one game: random (“fortune”, based on cards), story-based (“drama”, based on GM fiat) and deterministic (“karma”, highest stat wins). I have to say I loved that, but a lot of the appeal was in the sheer damn cleverness of the game.

super_arm_wrestlingI also think diceless philosophy should have a greater presence in traditional RPGs. In D&D, for example, a Str 18 Muscleman is significantly stronger than a Str 10 Norm: pretty much any test of strength should automatically by won by the former, rather than going to a Str vs Str roll where the weaker character wins 1 in 3 times (66/30, 4% tie)

But in general, I really love rolling dice!

Cards

Having said all of this, I am quite confident that I could be divorced from my love of dice by a card-based mechanic. I have always loved card-based elements within roleplaying games. Deadlands and TSR’s Marvel Super Heroic Adventure game both used cards within their resolution mechanics. WHFRP 3rd edition is almost entirely card-based, although as with D&D4e (as you’ll see from my most recent posts, currently very much in my thinking), it’s more about convenience of tracking powers than a bespoke card-based resolution mechanic.

However, when it comes to card play, there are a couple of examples that really stand out for me.

Everway cardsEverway’s vision deck is just a beautiful resolution mechanism that plays strongly against my deterministic, numerical nature. But I love it. The idea of drawing a card and then interpreting the result intuitively based on the image, it’s applicability to the situation or symbolism is just so wonderful in it’s profundity and utter uniqueness.

Torg drama deck

Torg’s Drama Deck does a great job of handing more control into the players’ hands. Different cards offer mechanical bonuses to actions, for engaging in subplots and for effective team work, which means success in tough encounters is truly as much down to player skill as character ability. In addition, the pacing mechanic built in to card play – with each player putting no more than 1 card per turn into their pool – means that players are incentivised to play the long game, building up their card resource round by round before triggering them at the last possible moment for a famous last-ditch victory. This was the first RPG mechanic that reflected the pacing seen in action movies, with the Indomitable Hero taking blow after blow, his gun knocked out of his reach, the villain at last getting his hands on that weapon just as the Hero’s out-stretched hand closes around a handy spanner and knocks his opponent out for the count.

What I really like about cards is how they appeal to my Gamist nature. I like the idea of player skill being able to influence success in RPGs. However, I’m not a big fan of games that induce analysis paralysis by including reams of tactical options, manoeuvres and quirky rules that incentivise rules-lawyerly play. Cards are a great compromise that allows for tactical game play without encouraging players to spend hours poring over rule books. They can also provide for “controlled randomness”, giving players’ the choice as to when they really want to succeed and when it might not matter so much.

So far, I’ve come across a number of card-based mechanics that add to an extra dimension to game play. However, I’ve yet to find the one that does everything I would want from a card-based system. When I do, it might finally be time to kiss those rolling randomisers goodbye…

 

 

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Advantage to the Max!

As I discussed previously, Advantage is the powerful yet simple super-mechanic that sits within D&D5, providing an easily managed impetus to drive the game in whatever direction the DM wants to go: if not its beating heart, then certainly a clean well regulated kidney or perfectly functioning non-cirrohtic liver. No, I don’t think that metaphor works particularly well either, but feel free to take it and use it yourself all the same, no need to thank me.

The simplicity of Advantage, for some, may also be its weakness. For those gamers who like a little crunch from time to time, the Advantage mechanics are a bit of a one-trick pony. If things are good, you get Advantage. If things are bad, you get Disadvantage. If things are, well, complicated, you get nothing. Simple, yes, but not especially nuanced. However, another of the great things about Advantage is it is actually extremely resilient to being messed around with. Here are a couple of suggestions as to how you can take Advantage to the max.

 

2D20 GOOD, 3D20 BETTER – DOUBLE ADVANTAGE

If you want to reflect a situation where the cards really are stacked in one character’s favour, one easy house-rule is to throw in an extra d20:

Double Advantage: roll 3d20 and take the highest result.

I’d suggest this can add value in your game in some very specific circumstances:

  • Stacked Deck – a character has Advantage from 3 or more sources. E.g. they’re attacking with Help from a colleague against a Blind opponent who has been Stunned.
  • Did I crit? – The die roll could have some bearing on the situation that isn’t just success or failure. E.g. in combat, you might want to know if a blow is a critical hit or not.
  • Failure is an option – the odds aren’t so stacked in that character’s favour that you just automatically give them the most favourable result possible.

When not to use Double Advantage? If there’s no time pressure and no consequences for failure, don’t roll at all. Ever. Just don’t waste everyone’s time. Don’t turn our beautiful game into a dumb exercise in dice rolling.

Don’t show me the odds
Double Advantage has a relatively modest impact on the probabilities:

  • The odds of rolling <4 are pretty small in both Advantage & Disadvantage
  • Advantage gives you an 80% of rolling 10 or better. Double Advantage makes it 91%, the equivalent of another +2 modifier
  • Advantage will get 15 or more 51% of the time. With Double Advantage its 66%
  • Advantage has 9.8% chance of a natural 20. Double Advantage increases this to 14.3%

Advantage Prob 1 You can also check out the non-cumulative probabilities here: http://anydice.com/program/4704

Complicating what is simple
Of course, if you’re interested in taking a simple rule like Advantage and turning up the crunch level, there’s probably another Advantage rule that you’ve already discarded. That’s the rule that says any situation that has both Advantageous and Disadvantageous factors is resolved with a straight d20. It’s a rule with zero impact on any probabilities, it’s just there to keep things clean, simple and tidy. If you can handle a bit of untidiness in your game, just go for it. Not that you need my permission!

 

EXCEEDING YOUR LIMITS – BOOST

As I’ve said before, Advantage increases your chance of success, it doesn’t make success possible where it otherwise wouldn’t be. If that doesn’t sit right with you, you follow the D20 system Modifiers Golden Rule: dish out +2 or -2 as you see fit. Having said, that’s not really D&D5’s style. The Bless spell, with a hint of Cortex system, points to a better, more interesting way:

Boost: a character who has a Boost rolls an addition d4 and adds the result to their total. If you already have a bonus die from some other effect, e.g. Bless, roll this in addition to the boost die and take the highest.

You should apply Boost where something both makes an action easier for a character and makes it possible to exceed their normal limits. E.g. when one character uses the Help action by distracting their mutual opponent to create an opening, instead of awarding Advantage it may make sense to award a Boost. Similarly with the Working Together rules outside of combat: if the party ties a rope around the portly Wizard and gives him a bit of a tug to help him leap the crevice, they’re not just helping him achieve his maximum potential, they’re trying to push him beyond his limits. Award a Boost. Hell, maybe award an Advantage AND a Boost!

To see how this looks, see updated graph below. In terms of probabilities, outside of values <4 or >20, a single boost just increases the score by 2.5, the mean score for a d4, for any given probability. E.g. instead of 50% chance of getting 11, you have a 50% chance of getting 13.5.

Advantage Prob 2

As for Advantage plus Boost. Well, that’s the best option of all for near guaranteed success. And you know what, if you want keep stacking it on, you go for it. Even rolling 5d20, the 22% chance for a critical means there’s still plenty of uncertainty to help keep things interesting.

 

CONCLUSION

In summary, if you want to crunchify the Advantage rules, there are three immediately obvious options:

  • Allowing for super Advantages of 3d20 or even more
  • Scrapping the rule that says any number of Advantage + any number of Disadvantage cancel each other out
  • Replicating the die-based bonus from spells like Bless for more general modifiers such as team work bonuses.

Although they all add complexity, none of these will do any harm to the fundamental probabilities built into the system. So if you like crunch and you miss the stacking modifiers of 3rd edition D&D, you can easily replicate that style of play in D&D5 without breaking the game.

Caveat: there is one class that disproportionately gains from the Double Advantage house rule. With an increased critical range, the Champion sub-class of Fighter would benefit more than any other class from multiple Advantage. E.g. a crit range of 19-20 is 8% more likely with Double Advantage, compared to just 5% more likely for a natural 20. Game breaking? Probably not.

 

So what do you think, loyal, intelligent and charming reader? Is this something you’d consider adding to your game, or mere statistical frippery?

Please feel free to leave your comments below or send your thoughts, considered or otherwise, via Twitter @thedicemechanic

Edited 24th September: added Conclusion & Caveat. Corrected a typo, graph titles and ended probability curves for d20 rolls at 20.