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.
The Kelly criterion is the bet-sizing formula that maximizes the expected logarithm of wealth — equivalently, the long-run geometric growth rate of a bankroll. For a binary bet with probability p of winning a payoff of b-to-1, the Kelly fraction is f* = (bp − q) / b, where q = 1 − p.
For tournament poker the formula generalizes to a multi-outcome distribution (many possible finishes, a payout vector, sometimes bounties). The Kelly stake is no longer closed-form for arbitrary payouts but is computed by maximizing E[log(W + payoff)] over the sale percentage s ∈ [0, 1]. For a single-payout tournament the optimum is closed-form.
Practical note: most pros use fractional Kelly (0.25× to 0.5× full Kelly) because full Kelly is the volatility ceiling — it maximizes growth but produces drawdowns that are emotionally and operationally untenable. The “20 buy-ins” heuristic is a crude proxy for fractional Kelly that under-fits high-ROI players and over-fits low-ROI ones.
In Mucho+MOTA, the Kelly engine reads from the player’s Bayesian skill model posterior and returns per-event sell percentages and growth rates. See the full Kelly essay and the Kelly primer.
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.
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.