A statistical model that infers a player's tournament-poker skill from observed results by combining a population prior with personal history, returning a probability distribution rather than a point estimate.
A Bayesian skill model infers a player’s tournament-poker skill by combining two ingredients: a population prior (how the typical player at this stake/format/site performs) and the player’s own results (their realized cashes, ROI, and finish distribution). The output is not a single number but a posterior distribution over the player’s skill parameters — typically two: cash-frequency (CF) and heads-up (HU) edge.
Why it matters: with 200 tournaments played, raw ROI is too noisy to act on; the Bayesian posterior shrinks the personal estimate toward the population mean by an amount that depends on sample size and population variance. As more games accumulate, the prior fades and personal data dominates. This is empirical Bayes / partial pooling — provably more accurate than either pooled (population-only) or unpooled (personal-only) estimators when the underlying skill is heterogeneous across players.
In Mucho+MOTA, the Bayesian skill model produces the per-player belief cloud that downstream tools (Kelly stake sizing, schedule optimization, action pricing) read from. See also SALSA, archetypes, and shrinkage.
The bet-sizing formula that maximizes the long-run growth rate of a bankroll. In tournament poker it determines what fraction of bankroll to risk per buy-in given expected ROI, variance, and bankroll size.
In poker staking, the running balance a backed player owes their backer from past unprofitable sessions; future winnings cover this balance before any profit chop occurs.
A model that converts tournament chip stacks into expected dollar equity, used for final-table deal-making, bubble play, and any decision where chip EV diverges from $-EV.
Tournament formats where part of the buy-in is awarded for eliminating other players. Three common variants — Standard knockout, Progressive (PKO), and Mystery — have meaningfully different variance profiles.
A capital reserve a backed player posts so the backer can recover funds if the player abandons the arrangement mid-makeup. In Mucho+MOTA the bond is invisible to honest players — settlement happens automatically via oracle.
A staking package where multiple investors buy shares of a player's action across a defined slate of tournaments, with profit and makeup pooled at the slate level rather than per-tournament.
Mucho+MOTA's MaxEnt-based tournament simulator that produces an entire ROI distribution from two structural parameters (cash frequency and heads-up edge), the field size, the payout vector, and the rake.
The vector of prize amounts assigned to each finishing position in a tournament. The shape of this vector — top-heavy versus flat — dominates ROI variance more than skill at most stake levels.
In tournament poker, average net profit per dollar of buy-in invested. ROI is the headline skill metric but is dominated by variance over realistic sample sizes — confidence intervals, not point estimates, are what matter.
The dispersion of tournament outcomes around expected value. In tournament poker variance is heavy-tailed and dominates short-run results — most observed deviation from expected ROI is variance, not skill change.
The two Lagrange multipliers in Mucho+MOTA's MaxEnt tournament simulator that internally control the cash-frequency and heads-up sufficient statistics. Lambda is the dual representation of the (CF, HU) archetype parameters.