ICM
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.
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 $-EV.
ICM (Independent Chip Model) converts tournament chip stacks into expected dollar equity by computing each player’s probability of finishing in each remaining payout position, then summing payout × probability. The model assumes chip-stack proportionality: the probability a player finishes first equals their share of total chips, second is computed conditional on not finishing first, and so on.
ICM matters because chip EV ≠ dollar EV in tournaments. Doubling your stack does not double your equity — payouts are concave, so chips become worth progressively less per chip as you accumulate them. This makes folding marginally +cEV hands +$EV near the bubble, and makes chip-chop final-table deals worse than ICM-chop for short stacks.
ICM is a simplification: it ignores blinds, skill differentials, and position. More accurate models (Future Game Simulation, Malmuth-Harville) refine these but the core insight — the concavity of equity in chips — is robust.
In Mucho+MOTA, ICM math is embedded in the closed-form deal calculator and in the Schedule planner’s late-stage EV adjustments. See the deal-making essay and brinkmanship as default.
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.
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.