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Binary Market Fees

For standard two-outcome markets (Team A vs Team B), SportToken charges a fee that is mathematically equivalent to the optimal Kelly criterion bet sizing.

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The Key Result

The fee percentage F we charge equals the optimal Kelly fraction f* of vault capital to risk. 
f* = F
This means our fee structure is mathematically optimal for bankroll management.

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Full Mathematical Proof

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Goal

We want to show that the fee percentage F we charge on a bet is equal to the optimal percentage f* of our bankroll that we should wager according to the Kelly criterion.

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Step 1: The Kelly Criterion

The Kelly criterion is given by: f∗=p−qbf^* = \frac{p - q}{b} Where:
  • p = probability of winning
  • q = 1 - p (probability of losing)
  • b = profit multiplier for the odds offered
Example: If offered odds of 0.4, then b = 0.6/0.4 = 1.5 In general, if offered odds x: b=1−xxb = \frac{1 - x}{x}

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Step 2: Setup

Suppose we charge a fee of F, where we claim F = f*. Let the user’s gross bet amount be G. Then: Actual bet amount (after fee)=(1−F)G\text{Actual bet amount (after fee)} = (1 - F)G
  • If we (the vault) win: we gain G
  • If we lose: we must pay out (1−F)G(1+b)(1 - F)G(1 + b)

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Step 3: Implied Odds Calculation

We calculate implied odds based on risk vs potential win: Implied odds=risked amounttotal win\text{Implied odds} = \frac{\text{risked amount}}{\text{total win}} The amount we risk: (1−F)G(1+b)−G(1 - F)G(1 + b) - G The total win: (1−F)G(1+b)(1 - F)G(1 + b) Thus: (1−F)G(1+b)−G(1−F)G(1+b)=(1−F)(1+b)−1(1−F)(1+b)=b−F(1+b)(1−F)(1+b)\frac{(1 - F)G(1 + b) - G}{(1 - F)G(1 + b)} = \frac{(1 - F)(1 + b) - 1}{(1 - F)(1 + b)} = \frac{b - F(1 + b)}{(1 - F)(1 + b)}

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Step 4: Implied Probabilities

Let p* be our implied probability of winning and q* be implied probability of losing. From the above: p∗=b−F(1+b)(1−F)(1+b)p^* = \frac{b - F(1 + b)}{(1 - F)(1 + b)} q∗=1(1−F)(1+b)q^* = \frac{1}{(1 - F)(1 + b)} The implied odds multiplier becomes: b∗=q∗p∗=1b−F(1+b)b^* = \frac{q^*}{p^*} = \frac{1}{b - F(1 + b)}

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Step 5: Applying Kelly Criterion

Returning to Kelly: f∗=p−qb∗f^* = \frac{p - q}{b^*} Since b = p/q, we substitute: f∗=p−q1b−F(1+b)f^* = \frac{p - q}{\frac{1}{b - F(1 + b)}} f∗=(p−q)[b−F(1+b)]f^* = (p - q)[b - F(1 + b)] f∗=(p−q)[pq−F(1+pq)]f^* = (p - q)\left[\frac{p}{q} - F\left(1 + \frac{p}{q}\right)\right] f∗=p−(p−Fp−Fq)=Ff^* = p - \left(p - Fp - Fq\right) = F

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Conclusion

f∗=F\boxed{f^* = F} The fee percentage F we charge is exactly the optimal Kelly fraction f* of our bankroll to risk per game.

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What This Means in Practice

  1. Optimal Risk Management - The vault never over-exposes itself on any single bet
  2. Fair Pricing - Users pay fees proportional to the actual risk their bet creates
  3. Long-term Profitability - Kelly sizing maximizes long-term growth while avoiding ruin
  4. Dynamic Adjustment - As vault exposure changes, fees automatically adjust to maintain optimal sizing

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Rebates: When You Help the Vault

The same Kelly logic works in reverse. When your bet reduces vault risk, you earn a rebate instead of paying a fee.

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How Rebates Work

If the vault is exposed on Side A and you bet on Side B:
  • Your bet offsets existing risk
  • The vault’s expected loss decreases
  • You receive a rebate proportional to the risk reduction

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Rebate Calculation

Rebate Rate = (Exposure Before - Exposure After) / Vault Assets
The rebate uses the same linear averaging as fees:
  • Start rate: Current imbalance / Vault
  • End rate: New imbalance / Vault
  • Your rebate = Bet Amount × (Start + End) / 2

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Example: Earning a Rebate

Setup:
  • Vault: $100,000
  • Current exposure: $2,000 on Team A (2% imbalance)
  • You bet $1,000 on Team B at +150 odds
Calculation:
  • Your to-win: $1,500
  • This offsets $1,500 of Team A exposure
  • New imbalance: $500 (0.5%)
  • Average rebate rate: (2% + 0.5%) / 2 = 1.25%
  • Your rebate: 1,000×1.251,000 × 1.25% = 12.50
Your net fee = System fee (0.3%) - Rebate = 3.00−3.00 - 12.50 = -$9.50 (you earn money!)

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Rebate Scenarios

Market StateYour BetResult
Heavy on ABet on APay fee (adding risk)
Heavy on ABet on BEarn rebate (reducing risk)
BalancedEither sideSmall fee (minimal imbalance change)
Heavy on BBet on AEarn rebate
Heavy on BBet on BPay fee

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Why Rebates Matter

  1. Better odds than sportsbooks - When you take the underbet side, your effective odds improve
  2. Market efficiency - Rebates incentivize balanced betting, reducing vault risk
  3. Transparent value - You see exactly how much you’re earning for helping the vault