SALSA
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.
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.
SALSA is the maximum-entropy tournament simulator at the core of Mucho+MOTA. Given five inputs — cash frequency (CF), heads-up edge (HU), field size, the payout vector, and the rake — SALSA returns the full distribution of finish positions for one player in one tournament. Composed across many tournaments, this becomes the player’s ROI distribution.
The construction is from Jaynes’ principle of maximum entropy: among all finish distributions consistent with the two structural sufficient statistics (CF, HU), pick the one that maximizes Shannon entropy. The result is an exponential family — a Boltzmann/Gibbs distribution — solvable in closed form via Lagrange multipliers. This is what the ELCOMBO paper formalizes.
Why two parameters? Because for the asymptotic ROI distribution, those two are jointly sufficient — additional player-level covariates do not asymptotically reduce the variance of the ROI estimator once CF and HU are fixed. This is why every Mucho+MOTA archetype lives on a 2D plane.
SALSA is the simulator; MUCHO is the atlas of population priors that places a player on the (CF, HU) plane; MOTA is the action-pricing decision layer that converts the simulated distribution into a Kelly-optimal sale percentage. See the SALSA wiki lesson.
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.
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.
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.