How does PKO variance compare to freezeout variance?

PKO tournaments reduce variance by approximately 60% compared to equivalent freezeouts. The frequent bounty payouts create a more consistent income stream, reducing the standard deviation of results over a sample of tournaments.

What is the power-law bounty capture model?

The standard proportional model assumes your share of future bounties equals your share of chips. Our power-law model (capture_share = chip_share^alpha) corrects that at short-handed tables. With alpha = 1.47 at 3-handed play, a 70/20/10 stack split maps to roughly 82/13/5 of future bounties instead of 70/20/10.

How many buy-ins do I need for PKO tournaments?

At a 5% risk of ruin, PKO tournaments require roughly 40-60% fewer buy-ins than equivalent freezeouts. A player with 30% ROI in a 1,000-player field needs approximately 41 buy-ins for PKOs vs 100 for freezeouts. Mystery bounty tournaments require significantly more due to envelope variance.

Why do mystery bounty tournaments have higher variance than freezeouts?

Mystery bounty variance comes from the envelope distribution. In the WSOP $1K Mystery Millions, the coefficient of variation is 8.55, meaning envelope outcomes range from $1,000 to $1,000,000. This randomness adds substantial variance on top of the standard tournament variance, requiring 4-5x more buy-ins than freezeouts.

PKO Variance Calculator

Variance and bankroll requirements across freezeout, PKO, and mystery bounty formats.

Tournament Parameters

Players

Places Paid

Buy-in ($)

Rake (%)

Your ROI (%)

Bounty Allocation (%)

Mystery Bounty Preset

Sample Size (tournaments)

Running 10,000 Monte Carlo simulations for each format...

Format Comparison

All three formats are modeled at the same expected value, so the only variable is how much your results swing. PKO tightens the swings; mystery bounty widens them.

PKO standard deviation Smoother than freezeout, so fewer buy-ins to survive a downswing	--
Mystery bounty standard deviation Wilder than freezeout, so more buy-ins to survive a downswing	--

Metric	Freezeout	PKO	Mystery Bounty

Expected value is held equal across formats by design, so standard deviation is the only moving part. The bankroll row is the practical takeaway: same profit, but PKO needs the fewest buy-ins to ride out a bad run and mystery bounty needs the most. Skewness and kurtosis for each format are in the methodology below.

Bankroll Requirements

How many buy-ins you need at each risk-of-ruin level, broken down by format. The 5% RoR row (highlighted) is the standard recommendation for serious tournament players.

Risk of Ruin	Freezeout (BI)	PKO (BI)	Mystery Bounty (BI)

Mystery Bounty Envelope Distribution

Statistical properties of the selected envelope preset. The coefficient of variation (CV) is the key number: higher CV means more variance from the bounty phase.

Mean envelope value	--
Coefficient of variation	--
Skewness	--

Statistic	Value

How This Calculator Works

Data Source

Alpha values fitted from 50,000 simplified tournament simulations per table size (2-9 players). Envelope distributions from published WSOP 2024 structures.

Calculation Method

The calculator runs three parallel Monte Carlo simulations (10,000 runs each) for freezeout, PKO, and mystery bounty formats with identical tournament parameters. PKO payouts use PrimeDope's power-law bounty capture model (chip_share^alpha instead of the proportional chip_share assumption). Mystery bounty payouts model envelope draws based on the selected preset distribution.

Update Cadence

Engine updated when new envelope distributions are published (typically after each WSOP series). Alpha values are stable across formats and do not change.

Distribution Shape by Format

Skewness measures how lopsided results lean toward rare big scores; kurtosis measures how often extreme outliers show up. Both climb as the bounty component grows, which is why the same standard deviation feels different across formats.

Metric	Freezeout	PKO	Mystery Bounty

Limitations

Simplified bounty capture model does not account for table dynamics, position, or stack-specific elimination probabilities
Mystery bounty envelope draws are modeled as independent; in reality, the pool changes as envelopes are claimed
ROI is applied uniformly across all finishing positions (real-world edge is concentrated in ITM finishes)