Skip to main content

​
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.

​
The Key Result

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

​
Full Mathematical Proof

​
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.

​
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}

​
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)

​
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)}

​
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)}

​
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

​
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.

​
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

​
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.

​
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

​
Rebate Calculation

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

​
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!)

​
Rebate Scenarios

​
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