A YouTube series rolls real dice to run elimination tournaments among same-CR D&D monsters. The same tournament is exactly solvable as an absorbing Markov chain — because the videos’ combat has no real decisions in it. Expected payoff, per the Master of Magic precedent: a good approximation plus the ability to diagnose why a monster over- or under-performs.
Links: BattleValue (the metric this would give a ground-truth oracle for), Risk — The Attrition Constant (the method’s completed sibling — the same absorbing-chain treatment carried all the way through on a much smaller game, including the state-space collapse this page will need; it also demonstrates the multi-oracle verification pattern, and its Lanchester-linear result is a live warning for the BV validation planned here), D&D Spell Damage Model (prior D&D math work), Master of Magic — Economic Analysis (the closest precedent — same complication classes), Caster of Magic — Spell Counter-Graph (the dominance-graph instrument to reuse), The Dominance-Frontier Lens, Yahtzee — 259 Trillion → 405 Million (where the EV-vs-win-objective distinction was worked out), BattleTech Simulator (the sibling project — same BV-validation motivation, but a state space that forces Monte Carlo; this one is its tractable proving ground), Monopoly (existing vault Markov-chain machinery), HeroClix (the prior art, revived — the HeroClix study this page cites as precedent is now its own project; source recon 2026-07-29 found both the dial data and the official rules fetchable and joinable, so the Hercules confound can finally be attacked with range and per-click powers in the model)
Chris’s critique of the source videos is that the combat is unfaithful — flyers don’t exploit mobility, spells are cast essentially whenever available, so melee brawlers are favored. That critique is correct, and it is also precisely what makes exact solution possible:
“Cast when available” is a fixed policy, and a fixed policy collapses a Markov decision process into a plain Markov chain.
If these monsters made genuine tactical choices, this would be a two-player stochastic game — and we’d be back to approximation. Because they don’t, the whole fight is a memoryless walk over a finite state space with an exact answer. The fidelity limitation and the tractability are the same fact. Don’t apologize for the simplification; exploit it, then measure what it costs (see Deliverable 2).
This is not an untried method for Chris. He built the same thing for HeroClix (1st ed.): Markov chains over combat, producing exact results, used to rank figures by value against cost. Nothing about this existed in the vault before 2026-07-20 — it is recorded here because it changes the project’s design, not as a war story.
Correction (2026-07-30). This page originally described the ranking as “BV/cost”, which implied wins divided by own cost. Chris clarified that the actual metric sorted units by cost and scored each by the point value of the opponents it defeated — so a 40-point figure killing 70-point figures ranks high, while a cheap figure that only beats other cheap figures does not. That distinction matters: value-per-own-cost is biased toward cheap units (measured Spearman −0.35 against cost, because a bounded numerator over a small denominator inflates), whereas the cost-weighted numerator is near-neutral (+0.19). Re-implemented in the
heroclixrepo and validated: it agrees with an independently-derived cost-curve residual at Spearman +0.858. The original method did not have the flaw the earlier wording suggested — see HeroClix.
What HeroClix adds that D&D doesn’t have — the dial. Every HP step has a different stat line, so figures gain and lose abilities as they take damage. This is the perfect Markov feature and a terrible closed-form-metric feature: a chain already carries HP in its state, so “stats are a function of remaining HP” is free — transition probabilities simply read off the current position. Any single-number metric has to average over the dial and lose the structure.
The Hulk case — damage granularity skips states. Hulk starts near base-human stats and gets stronger as he loses HP, making him a glass cannon. Chris’s finding: a multi-damage figure can push him past the meatier positions on his dial. Generalized, that’s a real principle — with position-dependent stats, one big hit ≠ several small hits summing to the same total, because large hits skip favourable states entirely. D&D has thinner but real versions of this: bloodied/half-HP phase changes, mythic traits, regeneration thresholds. Wherever a threshold exists, damage granularity is a strategic variable, not a rounding detail.
Chris’s headline HeroClix result: Hercules topped BV/cost — but only because he was a cheap, strong melee fighter, and range plus non-combat abilities were too hard to model. The metric crowned the figure that best fit the model’s blind spot.
That is the same melee bias predicted for D&D, now observed independently in a completed project. It stops being a guess and becomes a strong prior. It also exposes a confound in Deliverable 1:
If the exact model and BattleValue share a blind spot, their agreement is weak evidence. Both under-credit range and mobility. So “BV predicts the Markov win rates well” may only mean “two melee-biased instruments agree with each other” — not that BV is sound.
Design consequence: the mobility-on run (Deliverable 2) is not a bonus deliverable, it is the control that makes Deliverable 1 meaningful. BV must be scored against the kiting-enabled matrix, not just the stand-and-trade one. Without that control, this project would reproduce the Hercules artifact in a new game and mistake it for a validation.
(HP_A, HP_B, whose turn, resource/condition flags).Correction (worth stating plainly, because the first draft of this page got it wrong): scripted kiting does not break the Markov model. A dragon that breathes, withdraws, and returns on recharge is following a fixed policy — so it’s still a plain chain, just a different one. Model it as “the melee attacker connects only on the rounds the dragon chooses to close.” The recharge bit is already in the state. This matters a lot for feasibility: it means Deliverable 2 (mobility off vs on) is cheap, not a separate engine. Only adaptive choice is expensive.
The MoM analysis already enumerates this exact family of problems, which is why that page is the precedent rather than a loose analogy:
| MoM complication | D&D counterpart |
|---|---|
| Resistance; units effectively immune to half the spell list | Damage-type resistance / immunity, magic weapon immunity, legendary resistance |
| Special abilities (First Strike, Armor Piercing, Life Steal, Poison…) | Multiattack, riders, on-hit saves, grapple/restrain, regeneration |
| Ranged attacks get free damage before melee (first-strike multiplier) | Opening round + flight/reach — the axis the videos flatten |
| Multi-figure units (Lanchester applies differently) | Not applicable in 1v1, but returns if this ever goes to group fights |
| To-hit modifiers scaling effective attack | Attack bonus vs AC, advantage/disadvantage |
Chris’s expectation, calibrated to MoM: “at best I am expecting similar things to what we had with MoM — a good approximation, and the ability to dive into why performance was either too good or too poor.” That diagnostic capability is the actual product. An exact model that says “the roper wins 71% and here is the state-space reason” beats a dice tournament that says “the roper won.”
Chris: “the hard part might be sourcing and rules.” Agreed, and it splits in two:
1. Sourcing. Encoding hundreds of stat blocks correctly is the whole cost. Convert, don’t hand-enter — the 5e SRD is openly licensed and machine-readable dumps exist. Verify licensing and completeness before committing; a hand-typed monster table is an unverified artifact, a parsed one is cross-checkable against its source.
2. The rules/policy spec — this is the experimental protocol, not an implementation detail. Because “on the fly” decisions have to be frozen into a written policy, the policy IS the model. It has to be explicit and defensible up front (Chris: “enough rules to make sure it is done somewhat fairly”), because every ranking the project produces is conditional on it. Minimum decisions to pin down: spell/resource ordering, when to use a recharge ability, target-vs-condition priorities, whether to break grapples, opening-round assumptions.
Validate BattleValue against ground truth. BV = √(Attack × HP) is a lifelong vault project asserting a unit compresses to one number. An exact pairwise win matrix is the oracle that claim has never been tested against. Where BV predicts well and where it fails is a real result either way — and the MoM page’s complications list predicts where it should fail.
⚠ This deliverable already has a sibling: BattleTech Simulator (status: planning) — “Monte Carlo combat simulator to derive empirical BattleValue.” Same motivation, different method, and the difference is the whole point:
| BattleTech | D&D 1v1 | |
|---|---|---|
| State | 8+ locations × armor/structure, damage transfer, crits, heat | two HP pools + a few flags |
| Tractability | state space forces Monte Carlo | small enough for an exact answer |
So these are not competing projects — D&D is the tractable proving ground for the BV-validation methodology that BattleTech can only approximate. Doing D&D first means the BattleTech sim inherits a method already checked against exact truth. If only one gets built, build this one first.
The channel gained traction by starting at CR 1 and working up the chain, and it carries the previous tier’s champion up into the next tier as a guest entrant. Two consequences:
Mirror image / duplicate-creating monsters — Chris flagged a fight where you roll to hit, then
roll again to see whether you struck a duplicate (no HP loss; the image is consumed). This is the
ideal illustration of the project’s thesis: miserable to hand-roll, trivial as a matrix. It’s
one extra state dimension of size ≤4 (images_remaining), and a hit becomes a probabilistic branch
— image destroyed or real damage. Still perfectly memoryless.
Dragons underperform — a real dragon breathes, flies off, and returns on recharge; the videos’ model forces it to stand and trade, best-attack-available each round. Chris’s read is that this is why dragons do worse than they should. Per the correction above, this is directly testable and cheap: run the same matchup with kiting scripted on, and the delta is the measured cost of the abstraction. Prediction to check: the model should underrate monsters systematically in proportion to how much of their damage sits behind a recharge timer.
Chris: “I bet with the low HP of CR1, this will be a high variance mess.” Agreed — and it inverts into the strongest case for the method. Low HP ⇒ short fights ⇒ swingy outcomes ⇒ Monte Carlo (and literal dice) need enormous samples to separate a 52% matchup from a 48% one. The exact chain returns those numbers with no sampling noise at all. The method is most valuable exactly where the dice are least informative.
The sharp implication: if CR-1 matchups really are near-coinflips, then the source tournament’s CR-1 bracket results are mostly luck — a single-elimination bracket over near-even matchups measures seeding and variance more than monster quality. That’s a checkable claim about the videos, and it rhymes with the seeding-artifact point from Yahtzee and the non-transitivity hunt in Deliverable 3.
projects/ pointer once a repo exists; research page for now.