Traverse Fantasy

Following Lich Van Winkle's post about dee-five-six , I wanted to post about a realization I had that I'm sure others know but thought would be nice to record: 2D6+X where we take the sum PbtA-style approximates (X+1)D6 where we take the highest roll. Below is a table of result brackets: Result Sum of 2D6+X Highest of (X+1)D6 < …6 1–3 = 7–9 4–5 > 10… 6 Below is a table of results with increasing X ∊ [0, 3] for 2D6+X: 2D6+X < = > 2D6 41.7% 41.7% 16.7% 2D6+1 27.8% 44.4% 27.8% 2D6+2 16.7% 41.7% 41.7% 2D6+3 8.33% 33.3% 58.3% Below is a table of results with increasing X ∊ [0, 3] for (X+1)D6: (X+1)D6 < = > 1D6 50.0% 33.3% 16.7% 2D6 25.0% 44.4% 30.6% 3D6 12.5% 45.4% 42.1% 4D6 6.26% 41.9% 51.8% I think this is where we get the BitD and Trophy variations on the original PbtA roll, and I prefer that version because the results feel less obscure? Or just on the basis ...

Thank y'all so much for y'all's interest in the last one! Will respond when I can, just preparing for a (nice) busy week and weekend :) in any case, yep... they're back ! Been using them. Just slightly different. Bracket Hearts Power Aptitude Defense Speed Grunt 2 1 +1 11 3 Elite 4 2 +2 12 4 Champ 8 3 +4 14 5 Boss 16 4 +8 18 6 Minion* 1 1 +0 10 2 To translate each of the columns: Hearts: How much damage they can take. Power: How much damage they can deal per turn, possibly split into multiple attacks or spent on special effects. Aptitude: Attack bonus, or more generally for D20 checks if applicable. Defense: Roll against for D20 checks to attack. Speed: Initiative score to beat . Then, you can quickly build encounters by spending heart budgets on opponents (hold off on minions): Difficulty Heart Budget Easy 1/PC Medium 2/PC Hard 3/PC Deadly 4/PC Having used this to plan sessions an...

We got 100 responses ! This makes it very convenient for us, so let's work with it. Bitch. Results & Analysis Below are the five basic tiers or grades of results: Grade 50C 67C 80C 90C Terrible 1–3 1–3 1 1 Poor 4–8 5–8 5–7 — Okay 9–13 10–12 10–12 11–12 Good 14–17 15–16 15–16 — Excellent 18–20 19–20 20 20 On the table above, each ' xx C' column represents confidence of xx % over a certain interval. This means the 50C column indicates ranges with which at least 50% of people are confident; since the union of all ranges is from 1 to 20, this column covers all possible results of D20 and could be used as a table if you were nasty. The 67C column has gaps at the inflection points. The following values are missing, meaning that they have less than 67% agreement: 4, 9, 13, 14, 17, 18. Some of these values just barely fall short of the cut-off; however, 4 and 9 are very relatively contentious with less than 60% agreement. The 8...

There is a weird gap between armor proficiency and everything else. Armor proficiency just means you get to use the armor without getting disadvantaged on whatever saving throws. Everywhere else, it means you add your proficiency bonus. Let's first imagine a world where dexterity did not improve your armor class: what if your proficiency bonus did, instead? We can use a formula similar to the spell save DC, which is pretty common in other contexts: AC = 8 + Armor + Proficiency The trick is that, at early levels, 8 plus your proficiency is really 10. This means that this is a tricky way of saying your spell save DC is 10 plus whatever modifier, but you also get additional modifiers from advancing your character. This same thing applies to our hypothetical AC formula: if you wear a type of armor with which you have proficiency, your base is technically 10 but increases as you advance. This means a wizard's AC, having proficiency with no armor type, increases from 10 to 14 as they...

Need to write something to stay in the habit. Story's going well, just trying to avoid burnout. There are three separate "problems" I have: making attack and damage rolls separate per se is tedious; attack bonuses are tedious to track separately and can also be confusing, e.g., about whether you also add them to damage rolls; and the set of classic armor class values {10, 12, 14, 16} represents very low probabilities if you assume a typical modifier of 0. How about you use your damage roll as your attack bonus? Meaning:   D20 + D(Weapon) ≥ AC We would get probabilities as follows (notice that each die step adds ~5%): Damage AC 10 AC 12 AC 14 AC 16 d4 68% 58% 48% 38% d6 73% 63% 53% 43% d8 78% 68% 58% 48% d10 82% 73% 63% 53% d12 85% 77% 68% 58% Speeds things up in terms of hitting more often and also treating attack and damage rolls as a singular operation rather than two discrete steps of a procedure (even if you opt to r...

I suggested shifting goalposts more in favor of players, and a second idea: removing hearts altogether in favor of burdens, fictional effects which disadvantage the character by subtracting their value from rolls. Did that work out? Nope. Simulations Let's assume the original scale and its melee effects for a second: 20+: Triumph 11–19: Compromise 1–9: Failure 0-: Catastrophe For a sequence of attempted melee results, the outcomes for different aspect bonuses are as follows:  Aspect Bonus Total Turns Hits Dealt Burdens +0 6.4 2.6 5.4 +1 7.6 3.2 6.3 +2 8.7 3.9 7.2 +3 9.9 4.7 8.2 +4 11.3 5.9 9.2 +5 12.7 6.9 10.2 This means that a character can take from 5 to 10 "hits" (in the form of burden) while dealing on average 2 hits plus their aspect bonus. Their aspect bonus soaks up the effect of the burden accumulated until it exceeds the bonus, at which point it will basically always take 5 burdens to down the character. This al...

Did forbidden 5e math too. The whole game is fake! Shout-out to Paul Hughes' business card monster manual , and Reddit user Asinus for their calculations on average DPR per character tier . Basically, I figured out that the game really is balanced around monsters taking around 4 hits or 7 attacks to defeat if their CR equals the party's level. In other words, a medium encounter should take about 2-3 rounds to resolve. This is because monsters' hit points and armor class increases at more or less the same rate as player-characters' damage-per-round and attack bonus, respectively. We can extrapolate that deadly encounters have double the duration. The damage that a medium encounter deals per round also tends to be 20% of the player-party's total hit points, although it tends to be distributed between multi-attacks and legendary actions for more powerful monsters. An ancient white dragon (CR 20) attacks up to 6 times per turn, each dealing an average of 15 hit points;...

Wasn't happy with my last conversion because CR is not a pure measure of longevity like HD. It accounts for AC as well. Since then, though, I've come up with an actual measure for OD&D that counts both HD and AC! So we can do some mad science now. I mapped CR values to virtual HD values (virtual HP / 3.5), and found a really tight function for CR ≥ 1 and VHD ≥ 3. CR = 0.5 × VHD – 0.5 VHD = 2 × CR + 1 Let's put this funky function to the test. Below is a table converting monsters from 5e to OD&D and vice versa. Keep in mind that dragons of different ages do not truly have different HD values; instead, they have different hit points per HD. This turns out so that a red dragon with "10 HD" can have the equivalent of from 3 to 17 HD (which is really from 9.5 to 56.6 VHD with an AC of 2; ibid. ). For the purposes of this, I'm interpreting a wyrmling as a "very young" dragon and an ancient dragon as an "old" but not "very old...

Had a thought: speed rates in Fifth Edition pretend to be in five-feet increments, but they're really in increments of 1 sq. This means that a speed of 30 feet is really one of 6 sq. What if we used this as an initiative bonus instead of dexterity or intelligence? I'm eager to throw out the vestiges of the original D&D war game , but before then I had the thought of a simple armor table (which already exists in FMC Basic , but which I was also ready to re-employ for my 5e heartbreaker because it's easy to keep track of): Armor Type DC SP None 10 6 Leather 12 5 Chain 14 4 Plate 16 3 This means that an unarmored character moves 6 sq. (double in FMC Basic ), whereas a character in plate is half as fast. But what if you also want individual initiative while not wanting to introduce ability bonuses? Why not use one's speed, so there's a trade-off between being better protected or being quicker to move? That sounded intuitive, but ...

While simulating an idea I had for speed-based initiative , I realized that the results had implications for bonuses on d20 rolls in general. When two characters roll off, how good is a relative +1? Column A is where the more capable character breaks ties, and column B is where ties are broken with more rolls. Bonus Results A Results B Relative +0 50% vs 50% 50% vs 50% 100% +1 57% vs 43% 55% vs 45% 125% +2 61% vs 39% 59% vs 41% 150% +3 66% vs 34% 64% vs 36% 200% Those are really intuitive odds, actually! A character whose ability bonus is 3 pips greater than another is doubly capable. This contextualizes ability scores and modifiers in 5e proper: a character with an ability score of 16 is twice as capable as a character with a score of 10 in the same ability. Compare this to B/X where you need a score of 18 to get that +3 bonus. Then I simulated for a group of characters with bonuses ranging from [+0, +3]. Bonus Results A Results B ...

I had a suspicion the other day that HD 1 figures are more like HD 2 figures than HD ½ figures in terms of longevity since it will usually take at least 2 hits to defeat both (since HD 1, half the time, will have more hit points than damage dealt by a single attack). Simulated this and it turned out to be more-or-less true! Hit Dice Turns to Defeat Hits to Defeat Relative to HD ½ Relative to HD 1 ½d 2.37 1.16 100% 74% 1d–1 2.75 1.37 118% 87% 1d 3.22 1.58 136% 100% 1d+1 3.71 1.85 159% 117% 2d 5.01 2.51 216% 159% 4d 8.91 4.47 385% 283% 6d 12.9 6.49 559% 411% 8d 16.9 8.47 730% 537% 10d 20.9 10.4 897% 659% 12d 25.0 12.5 1078% 793% This effect is due to the Packing Problem, the effect of which Delta's D&D Hotspot also discusses on sweeping attacks : figures with less hit points "waste" overflow damage, whereas figures with more hit points soak the full force of the attack. This means tha...

The rat post was fun ! For my next trick, I will reveal the secret "challenge rating" system inside OD&D . Virtual Hit Points First, let me explain in greater detail some ground I covered in the last post. Hit dice are not the final word on monster longevity because they do not account for the likelihood that they will get hit by an attack. This means we can get a more accurate picture by calculating a figure's "virtual hit points": how much longer they last in combat as a result of their armor class. I did this years ago , but have a more accurate function now because of a simulation I ran. The results are as accurate for 4 hit points as they are for 35 hit points. AC Avg. HP Adj. 9 [10] 100% 8 [11] 111% 7 [12] 125% 6 [13] 142% 5 [14] 168% 4 [15] 198% 3 [16] 251% 2 [17] 334% As an example, an unarmored character with 10 hit points doesn't get anything extra, but if they were wearing plate armor it would be as i...

How many hit points does a giant rat have? My friend Gus L. posted this fun illustration the other day , proposing that the open-endedness of OD&D implies the possibility of giant rats with 8 hit dice. He takes page 20 of Monsters & Treasure as evidence for this, that giant rats have at least 2 hit dice and hypothetically up to 20 (not just 8!): This category includes giant ants and prehistoric monsters. Armor Class can be anything from 8 to 2. Hit Dice should range from 2 to anywhere near 20, let us say, for a Tyrannasaurus Rex. Also included in this group are the optionally usable “Martian” animals such as Apts, Banths, Thoats, etc. If the referee is not personally familiar with the various monsters included in this category the participants of the campaign can be polled to decide all characteristics. Damage caused by hits should range between 2-4 dice (2-24 points). My initial thought was I disagree because a “giant rat” might not qualify as a large animal even if it’s...

W.F. Smith at Prismatic Wasteland challenged bloggers to invent and name a new resolution mechanic for a TTRPG to commemorate the new year. In my typical fashion, I'm going to flip the challenge under the guise of participating in the challenge, and then transition to tangentially related that I was really wanting to talk about. 50-50 Resolution If a character does something whose outcome is uncertain or contested, flip a proverbial coin. If the outcome is more likely than not, it might as well succeed. If it is more likely to fail, it might as well fail. Stakes and outcomes are open to negotiation, in-character or not. That’s all there is to it! I've really liked this approach because I've felt lately that universal resolution procedures like the archetypal d20 system are hard to justify in their formal rigidity, and also tend to block interesting developments in play. They just don't make sense to me, and make less sense the more I think about them. What's ...

Have posted math similar to this, but now it's (1) specifically in the context of Odd-like rulesets and (2) comparable to stats that would be generated using 3d6. Suppose three saves: {X, Y, Z}. Set each to 10, and roll 3d6: +2 X, –2 Y –2 X, +2 Y +2 Y, –2 Z –2 Y, +2 Z +2 Z, –2 X –2 Z, +2 X The outcomes: Random but bound. Range from 4 to 16, like 4d4 but not annoying. Always add up to 30 and average to 10. Always even numbers, every 2 pips being 10%. Very rarely a boring, default array of [10, 10, 10]. If I were doing a game with four ability scores, I would set the character's "main stat" equal to 16 and randomize the remaining three using the above process. That's because I think games that rely heavily on both classes and stats can be kind of annoying, where if you get a mid main stat that kinda sucks.

Someone shared with me Chaos Reigns , a hack of OD&D combat. It’s not to my own taste (check it out still!), but it got me thinking about something I wish it had done: consolidate attack and damage rolls. Since everything is d6, why not! My thought was: roll 2d6 ≤ AC , and the damage is the highest of the two dice. For example, if a target has an AC of 7 and you roll a 2 + 5, then you hit and deal 5 damage. This is how the numbers break down, for AC values from 8 to 3. ‘DPA’ stands for damage-per-attack, and ‘DPH’ stands for damage-per-hit. Armor Class To-Hit DPA DPH 8 72% 3.5 4.3 7 58% 2.9 4.0 6 41% 1.9 3.4 5 28% 1.2 2.9 4 17% 0.6 2.2 3 8% 0.2 1.7 Given that table, I think values from 7 to 4 are the best range, and they could easily correspond to the typical four armor types (none, leather, chain, plate); alternatively, treat 7 to 5 as light/medium/heavy and subtract 1 for a shield. I like the numbers better than the Kubular meth...

Occasionally, I check Reddit to see if I missed anything interested in this sphere of things. Not usually, but today—yeah! Reddit user Kubular reported a misunderstanding of typical D&D combat from one of their friends, and took it as a possible new direction for one-roll combat. Here’s the link , and here’s the important bit: I rolled a 16 to hit and they had an AC of 13. I rolled a 5 for damage, but she was still looking at the 16 and was like “wait, why is it 5? Shouldn’t it be 3?” I was confused for a moment, but then I realized (a) she hadn’t seen my damage roll, and (b) I hadn’t explained how combat works and this was her first exposure to any RPG. So she saw the 16, understood armor class as representative of her armor, then just assumed that you would subtract the AC from the attack roll to get damage. Math Comparison That’s interesting! How does it compare to other methods? Let’s take for example: Original: Attempt an attack as per Chainmail , and take 1d6 damage ...

You're a regular 1d figure. How many tries does it take to defeat another figure like you? Maybe 1 if you can land a hit, or 2 if you account for your chance to do that. Nope, 3.0 tries, on the dot. Then it takes 2.6 tries if you have 1d–1 hit die, and 2.3 tries if you have ½d hit die. That's pretty bad. And that's just for a 50% chance to hit. Upping this by 20% gives 2.2, 1.9, and 1.7. Not helping. Think about it this way, too: to find the chance of one-shotting a figure, multiply the attacker's to-hit chance by the chance they will deplete the target's hit points. For a 1d figure at a 50% to-hit, that's a 25% chance. Add +2.5% per extra 5% to-hit. Not good. This is why I've said before that fighters need some sort of cleave or sweep or multi-attack to be "useful", as well as an increase in damage over time, but as they stand the numbers by themselves are quite bad, and bonuses to damage can be hard to scale without getting out of hand . Here...

Kaique pointed out in the comments of my last (actual) post, " 5e Campaign Structure ", that there is actually some variation in level duration between the beginning and end of a character's progression: namely, that levels in the second tier last for more adventuring days than levels in the other tiers. On one hand I wanted to bring attention to this in itself, but also I found another interesting effect. It seems like, if you round normally (instead of up or down), the total number of adventuring days it takes to level up is 31. This means that a campaign set at the default time tick, so to speak, takes 31 in-world days if you're hauling ass. This increases to 43 days if you round up, although that might not necessarily be reflective of actual play since 5e does not put any restrictions on leveling or gaining experience (e.g., a character could technically level-up midday and continue to gain experience even if they don't gain the benefits of that level until a...

There's one of two ways this will go: either I'm a crackpot, or I'm a captain obvious. Been thinking of two posts: Dwiz on long rests , and Inevitable Gumbo on experience . Dwiz points out that the function of long rests in 5e is not at all to simulate the effects of sleep than it is to pace the game, by way of the consumption and restoration of resources (esp.: hit points and spell slots). He finds that the "gritty realism" variant is better at this than the typical 8-hour rest rule, since it's more likely that the party will deal with approximately 7 encounters between long rests. Gumbo looks at the encounter experience chart for general challenge experience. Not only can you use the guidelines for encounter difficulty to gauge the experience earned from completing a challenge, but you can use that same method to determine experience in hindsight of an encounter. You could combine this understanding with a simplified pip system for tracking experience, unde...