⚠️ UNAUDITED: Use at own risk

How Kelly4X Works

Understanding the Kelly Criterion, cascading pools, and auto-LP conversion flywheel.

The Kelly Criterion

The Kelly Criterion is a mathematical formula for optimal bet sizing developed by John Kelly in 1956. It determines how much to risk based on your edge and the odds offered.

Kelly Formula

f* = (bp - q) / b
  • f* = fraction of bankroll to bet
  • b = net odds (payout - 1)
  • p = probability of winning
  • q = probability of losing (1 - p)

Example: Coin Flip

For a fair coin flip (50% chance) with 2x payout and 1% house edge:

  • Probability of winning (p) = 49% (after house edge)
  • Payout multiplier = 2x
  • Net odds (b) = 2 - 1 = 1
  • Kelly fraction = (1 × 0.49 - 0.51) / 1 = -2%

Wait, negative? That’s correct! Kelly says the player shouldn’t bet because the house has an edge. But the house should risk 2% of their bankroll per bet.

Four Risk Tiers

Kelly4X offers four risk multipliers for liquidity providers:

1x Kelly (Conservative)

  • Risk: Ultra-safe
  • APY: 8-12%
  • Max Drawdown: 20-30%
  • Best for: Risk-averse LPs

2x Kelly (Balanced)

  • Risk: Moderate
  • APY: 14-20%
  • Max Drawdown: 40-50%
  • Best for: Balanced portfolios

4x Kelly (Aggressive)

  • Risk: High
  • APY: 22-35%
  • Max Drawdown: 60-70%
  • Best for: High risk/reward

8x Kelly (Degen)

  • Risk: Extreme
  • APY: 40-60%+
  • Max Drawdown: 80-90%
  • Best for: Maximum chaos

Cascading Pool System

The key innovation of Kelly4X is cascading pools. When a player places a large bet, it automatically cascades across risk tiers, with each pool only risking what their Kelly multiplier allows.

Example: $1,000 Bet

Player bets $1,000 on 2x coin flip (1% house edge):

  • 8x Kelly pool: Risks 8% × pool balance$320
  • 4x Kelly pool: Risks 4% × pool balance$160
  • 2x Kelly pool: Risks 2% × pool balance$80
  • 1x Kelly pool: Risks 1% × pool balance$40
  • Total capacity:$600

If the player wins, each pool loses proportionally. If they lose, each pool gains proportionally. This ensures fair risk distribution and allows the protocol to accept large bets.

Auto-LP Conversion Flywheel

The game-changer: winners automatically receive LP tokens instead of direct payouts (optional).

The Flywheel

  1. 1. Player bets → Places bet with tokens
  2. 2. Player wins → Receives LP tokens automatically
  3. 3. LP earns yield → Earns from house edge on all bets
  4. 4. Bet with LP → Can bet directly with LP tokens
  5. 5. Repeat forever → Never needs to withdraw

Key Benefits

  • Infinite retention: Players never need to withdraw
  • Liquidity bootstrap: Every winner becomes an LP
  • “House money” effect: Reduces pain of losing
  • Capital efficiency: Money stays in ecosystem, compounds infinitely

Betting Flow

Step-by-step process for placing and settling a bet:

  1. 1. Place Bet: Player calls placeBet() with tokens and bet params
  2. 2. Lock Liquidity: Contract calculates pool contributions and locks amounts
  3. 3. TEE Generates Random: Off-chain TEE creates provably fair random number
  4. 4. Settle Bet: Operator calls settleBet() with TEE signature
  5. 5. Distribute:
    • If win: Mint LP tokens to player (or send tokens if preferred)
    • If loss: Distribute bet amount to pools proportionally

Next Steps