Skip to content
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). The MOTA whitepaper is public; ELCOMBO and MUCHO circulate inside active Stable-tier engagements and consulting sessions, where the implementation context makes them worth the read. Daily scheduling and pooled-action settlement aren't separate papers — once MOTA gives you a growth rate per hour and a sale price per cell, ranking tournaments and settling pools is mechanical. The public Substack covers the same ideas in informal prose.

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 and outputs a growth rate per hour. Read in order; each builds on the previous. Everything else the platform does — schedule selection, stable settlement — is a one-line consequence of these three.

  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 — Investment Engineering on Tournament Outcomes

    MOTA (Mean Optimised Tournament Alpha): a three-stage framework for engineering and pricing investment in a single tournament. Stage I supplies the player-specific ROI / win-probability belief — the input the engine runs on and the source of any garbage-in-garbage-out risk; estimation methods are deliberately out of scope. Stage II is investment engineering: solve for the sale percentage s* ∈ [0, 1] that maximises expected log-wealth, treating sold action as a synthetic asset whose risk/return profile the player actively shapes via markup. For a single-payout tournament the optimum is closed-form; multi-payout structures fall out of numerical optimisation over the same objective. Stage III is opportunity selection — comparing optimised assets across tournaments via time-normalised growth, EGR_mota / T_avg. The framework is provably weakly dominant over pure-Kelly play because it optimises over a strictly larger choice set, and converges to pure Kelly when bankroll grows large relative to buy-in or when true ROI substantially exceeds the market markup. The MOTA tab implements Stage II directly; the staking package builder pipes Stage III into the action market. The 5-page whitepaper (Dahlke 2023) gives the closed-form derivation and a worked example at $15K bankroll, 30% ROI, markup 1.2 — the W_ce-optimal sale is s ≈ 66.7%.

    Download whitepaper (PDF) · 5pp · Nov 2023 · 124KB →
Citation

Cite the MOTA whitepaper

If you reference MOTA in academic or operator-facing work, the following citations are canonical. ELCOMBO and MUCHO citations will be added once those papers exit working-paper circulation.

APA

Dahlke, F. (2023). MOTA — Investment Engineering on Tournament Outcomes. Mota GmbH. https://muchomota.com/papers/mota-whitepaper.pdf

BibTeX

@techreport{dahlke2023mota,
  author      = {Dahlke, Felix},
  title       = {{MOTA --- Investment Engineering on Tournament Outcomes}},
  institution = {Mota GmbH},
  year        = {2023},
  month       = {November},
  type        = {Whitepaper},
  url         = {https://muchomota.com/papers/mota-whitepaper.pdf}
}
Worked examples

The papers, on actual numbers.

Real screenshots from the live app, captured against the same code path subscribers run. One scenario per entry, from input to rendered grid. The proofs are gated; the outputs aren't.

All worked examples →
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