Kelly Criterion Calculator mechanism

Model scope

NEEDS_REVIEW because the exact ambiguity is that “odds” is not specified as net payoff odds versus gross decimal odds, and the half-Kelly calculation is named as an output but not defined. The educational-only disclaimer is appropriate, but the interface should explicitly label negative Kelly values and state whether practical recommendations are clamped to zero and/or capped.

• The formula f*=(bp-q)/b is standard only when b is net odds, meaning net profit per unit staked; it is incorrect if b is supplied as gross decimal odds without subtracting 1.
• The claimed half-Kelly output has no explicit formula; it should be defined as f_half=f*/2, with the treatment of negative values specified.
• The formula assumes a binary win/loss outcome, mutually exclusive outcomes, no fees or limits, and a constant bankroll basis; these constraints are not stated.

Units and conventions

• win probability p must be a decimal from 0 to 1, not a percentage such as 55 unless converted to 0.55.
• q is the loss probability and must equal 1-p.
• b must be positive net payoff odds, dimensionless: a $1 stake that wins $1.50 has b=1.50.
• If gross decimal odds D are supplied, convert using b=D-1 before applying the formula.
• The Kelly fraction is a fraction of current bankroll; multiply by 100 for the percentage output.
• Half-Kelly is assumed to mean f*/2, subject to confirmation.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "win_probability": 0.55,
    "net_odds_b": 1.5
  },
  "expected_outputs": {
    "kelly_fraction_percent": 25,
    "half_kelly_percent": 12.5
  },
  "working": "q=1-p=1-0.55=0.45\nbp=1.5×0.55=0.825\nbp-q=0.825-0.45=0.375\nf*=0.375/1.5=0.25\nKelly percentage=0.25×100=25%\nHalf-Kelly=0.25/2=0.125=12.5%"
}

Failure boundary

• Division by zero occurs when b=0; require b>0.
• Require 0≤p≤1; probabilities outside this range are invalid.
• A negative Kelly fraction indicates a negative edge, but the spec does not say whether to display it, clamp the recommended stake to 0%, or interpret it as taking the opposing side.
• The formula can recommend more than 100% of bankroll when the modeled edge is large; leverage, maximum allocation, and shorting constraints are unspecified.
• Estimation error in p and b can materially change the result, so the output should not be presented as a reliable individualized investment or betting recommendation.
• Fees, commissions, spreads, taxes, slippage, ties, partial losses, and correlated positions are not represented.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json