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. Player bets → Places bet with tokens
- 2. Player wins → Receives LP tokens automatically
- 3. LP earns yield → Earns from house edge on all bets
- 4. Bet with LP → Can bet directly with LP tokens
- 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. Place Bet: Player calls
placeBet()with tokens and bet params - 2. Lock Liquidity: Contract calculates pool contributions and locks amounts
- 3. TEE Generates Random: Off-chain TEE creates provably fair random number
- 4. Settle Bet: Operator calls
settleBet()with TEE signature - 5. Distribute:
- If win: Mint LP tokens to player (or send tokens if preferred)
- If loss: Distribute bet amount to pools proportionally