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Research

Working papers.

What the platform actually sells is a pre-computed multi-dimensional map of the tournament world, a tool for placing individual players on it, and a decision layer on top. Three foundational papers describe those layers — ELCOMBO (the placement math), MUCHO (the map and the shrinkage rule), MOTA (the action-pricing decisions). Two method extensions cover daily scheduling and pooled-action settlement. The working papers circulate only inside active Stable-tier engagements and consulting sessions; this is the mathematical core of the platform. The public Substack covers the same ideas in informal prose, without the proofs.

How it actually works

It's a map, not a formula.

The platform corpus is segmented along (buy-in × speed × game type × field size × site) into thousands of buckets. Each bucket carries a population skill prior fit on the players who actually play that segment. Transfer functions between adjacent buckets bridge the segments — a year's worth of $5 turbo results meaningfully constrains your starting belief at $50 turbo without you having to play 5,000 hands at $50 turbo first.

Your individual results don't get evaluated in a vacuum. They get placed on the map. With 50 games in a bucket, your posterior is mostly the bucket prior — you haven't escaped the gravity well yet, and a 1st-place finish doesn't move the needle much. With 5,000 games, your posterior is mostly you — the per-player sufficient statistics dominate, and the bucket prior fades. That shrinkage is what makes the model verify a winner in a few hundred games where a naive ROI calculation would need a few thousand.

ELCOMBO is the math that places one player at one point. MUCHO is the atlas and the shrinkage rule that moves them across it as their data accumulates. MOTA is the decision layer — given a placed player and a tournament, output a Kelly-optimal sell fraction, fair markup, schedule weight, and certainty-equivalent growth rate. The fancy jargon below (Boltzmann, Lagrange, MaxEnt, Cramér–Rao) is the update rule. The product is the map.

Foundations

The three papers.

ELCOMBO is the math at one point. MUCHO is the map and the shrinkage rule that moves a player across it as their data accumulates. MOTA is the action-pricing layer that consumes a MUCHO posterior. Read in order; each builds on the previous.

  1. Generative model
    № 1

    ELCOMBO — The Placement Tool

    ELCOMBO (Entropy-Lagrange-Cramér Ordered Max-Boltzmann Outcomes): the math that places one player at one (bucket, sample) point on the map. A two-parameter maximum-entropy finish-distribution over the simplex of finish-position probabilities for a single tournament, conditioned on observable structure — field size, payout vector, rake. Mathematically a Gibbs/Boltzmann exponential family that drops out of Jaynes' constrained-MaxEnt program with Lagrange multipliers on two structural sufficient statistics. Joint sufficiency of the two parameters for the asymptotic ROI distribution is proved: additional player-level covariates do not asymptotically reduce estimator variance once the two are fixed. This sufficiency is what makes the rest of the stack work — it's why a player's parameters in one bucket carry over (with a transfer correction) to an adjacent bucket. Sample-complexity bounds (VC capacity + Cramér–Rao) give the floor on data needed to recover the parameters within KL precision ε. ELCOMBO is the update rule, not the product. The product is what MUCHO does with it.

    Working paper · in-session circulation

  2. Atlas + shrinkage
    № 2

    MUCHO — The Map of the Field

    MUCHO (Maximum Uncertainty Contextual Hypothesis Ordering): the pre-computed atlas that turns a SharkScope profile into a placement on the tournament-world map, plus the shrinkage rule that decides how much to trust your personal data versus the bucket prior. The platform corpus is segmented along (buy-in × speed × game type × field size × site) into thousands of buckets; each bucket carries a population ELCOMBO prior fit on the players who play it. Adjacent-bucket transfer functions move skill estimates between segments without losing data — 1,000 games at $5 turbo project a tighter starting posterior at $50 turbo than a cold start would. With few games in a bucket the posterior is mostly the population prior; as the per-player sufficient statistics accumulate, the prior fades and personal parameters take over. The Bayes-rule classifier (Neyman–Pearson log-likelihood ratio against the population prior) returns a posterior over archetypes, with confusion matrices, Shannon-entropy luck decomposition, and per-format breakdowns. The MUCHO acronym names the active-learning rule itself: the next-observation choice that maximally reduces expected posterior entropy. This is the actual product — the map and the shrinkage rule. The math under it is the cheap part to copy; the map is what isn't.

    Working paper · in-session circulation

  3. Decision layer
    № 3

    MOTA — Options Writing on Tournament Outcomes

    MOTA (Mean-Optimized Tournament Alpha): the decision layer that consumes a MUCHO-supplied posterior and outputs sell fractions, markups, schedule weights, and bankroll trajectories. Treats sold action as a covered call written on the player's own finish — the buyer pays a premium (markup × cost basis) and receives the corresponding share of the realised payout. Derives the certainty-equivalent-optimal sell fraction integrated over the posterior, Kelly's closed-form growth identity g = μ − ½σ² (Kelly 1956), the markup threshold above which selling increases compounded growth despite reducing arithmetic EV, and first-order correction terms when buyers are correlated through swap pools or repeat backing relationships. The numbers are decision-ready: this is what the MOTA tab in the platform shows you, and what the staking package builder pipes into the action market. Without MUCHO's posterior in front of it, MOTA collapses to standard Kelly with a guess at the inputs.

    Working paper · in-session circulation

Method extensions

On top of the foundations.

Two applications: dynamic programming for the daily schedule, and Shapley-value settlement for pooled action. Both consume MOTA outputs; neither is a new theory.

  • Method · Schedule

    Bellman Scheduling Across the Weekly Grind

    Dynamic-programming formulation of the multi-tournament scheduling problem: at each decision point, the player chooses which tournaments to register from the available slate to maximise expected log-bankroll over the planning horizon. Per-tournament value is supplied by MOTA; per-decision value is the Bellman-equation fixed point given the bankroll state, time budget, and screen-space constraint. Buy-in decay, time-of-day, and field-size modifiers enter as scalar offsets on the ELCOMBO parameters, so the relevant state collapses to bankroll and remaining slate without an explicit Markov state-space.

    Working paper · in-session circulation

  • Method · Stable

    Shapley Settlement in Pooled Action

    Accounting protocol for pooled-action environments under adversarial reporting, plus a closed-form Shapley-value settlement algorithm. Sensitive ledger entries (transfers, expenses, profit chops, loan issuance) require two distinct non-creator signatures and a source-truth attachment before posting to balances. Settlement of variable-markup, partial-bullet, multi-entry tournaments is computed via the Shapley value over the realised contribution graph, with closed-form simplifications for the common cases (uniform-markup full-bullets, single-bullet with re-entries). Implemented as the Stable-tier audit flow.

    Working paper · in-session circulation

Access

Working-paper circulation.

These are the mathematical core of the platform — the IP we spent years building. They circulate inside active engagements only:

  • · Stable-tier subscribers — full library, requestable on Discord, alongside whatever implementation questions come up while you're using the stack at scale.
  • · Consulting clients in session — papers relevant to the work we're actually doing together, shared as part of the engagement.

Each PDF includes the full derivation, the assumptions under which the stated result holds, and references to the implementing code. Mucho+MOTA tier subscribers get the platform but not the papers — the math underneath is what keeps the system worth subscribing to in the first place.

The public blog covers the same topics in informal prose without the proofs — a good place to start before becoming a Stable subscriber or scheduling a consulting engagement. Topic guides at muchomota.com/learn; full essays at muchomota.com/blog (mirrored on blog.muchomota.com for email subscribers).

See the Stable tier → Browse the writing Book a session