Kelly Criterion Bet Sizer#

Calculate mathematically optimal bet sizes based on your edge and bankroll.

When to Use#

Use this skill when the user asks about:

• How much to bet on a specific wager
• Kelly Criterion or optimal bet sizing
• Position sizing for a bet with known edge
• Fractional Kelly or conservative bet sizing
• Sizing multiple simultaneous bets
• Maximum bet limits or bankroll allocation

Odds Conversion Reference#

Before computing Kelly, convert all odds to decimal probability format:

FormatExampleTo Decimal OddsTo Implied ProbAmerican (+)+1501 + odds/100 = 2.50100/(odds+100)American (-)-2001 + 100/oddsDecimal2.50Already decimal1/decimalProbability40%1/probAlready prob

Operations#

1. Single Bet — Full Kelly#

Calculate the optimal Kelly stake for a single bet. User must provide: bankroll, odds (any format), and their estimated true probability.

bash

python3 -c "
import sys
bankroll = float(sys.argv[1])
odds_input = sys.argv[2]
true_prob = float(sys.argv[3])

# Convert odds to decimal
if odds_input.startswith('+'):
    decimal_odds = 1 + int(odds_input[1:]) / 100
elif odds_input.startswith('-'):
    decimal_odds = 1 + 100 / abs(int(odds_input[1:]))
else:
    decimal_odds = float(odds_input)

b = decimal_odds - 1  # net odds
p = true_prob
q = 1 - p

# Kelly fraction
kelly_f = (b * p - q) / b if b > 0 else 0
kelly_f = max(kelly_f, 0)  # never negative

implied_prob = 1 / decimal_odds
edge = true_prob - implied_prob

print(f'Odds: {odds_input} (decimal: {decimal_odds:.4f})')
print(f'Implied prob: {implied_prob:.2%} | Your estimate: {true_prob:.2%} | Edge: {edge:.2%}')
print(f'Kelly fraction: {kelly_f:.4f} ({kelly_f:.2%} of bankroll)')
print(f'Recommended stake: \${kelly_f * bankroll:.2f} of \${bankroll:.2f} bankroll')
if kelly_f <= 0:
    print('⚠️  No edge detected — Kelly says do not bet')
elif kelly_f > 0.10:
    print('⚠️  Kelly > 10% — consider fractional Kelly to reduce variance')
" BANKROLL ODDS TRUE_PROB

## About

Built by [AgentBets](https://agentbets.ai) — full tutorial at [agentbets.ai/guides/openclaw-kelly-sizer-skill/](https://agentbets.ai/guides/openclaw-kelly-sizer-skill/).

Part of the [OpenClaw Skills series](https://agentbets.ai/guides/#openclaw-skills) for the [Agent Betting Stack](https://agentbets.ai/guides/agent-betting-stack/).