What Is Certainty Equivalent
By now, you understand how to calculate expected value (EV), determine fair odds, and use the Kelly Criterion to size bets optimally. That knowledge tells you whether a wager has a mathematical edge, and how much to stake. However, it does not tell you whether a particular +EV bet is worth taking over the guaranteed profit from matched betting.
That’s where Certainty Equivalent (CE) comes in.
CE is the missing link between raw +EV math and real-world decision-making. It takes into account:
- Your bankroll size
- Your risk tolerance
- The variance of the bet’s outcome
For new bettors, CE is essential because bankrolls are often small and signup offers are some of the largest promotions available. A significant early loss can slow bankroll growth significantly, even if the bet was +EV. CE helps you avoid that by quantifying the trade-off between guaranteed profit and risk.
Key Takeaways
What Is Certainty Equivalent?
The Certainty Equivalent (CE) of a bet is the amount of guaranteed profit that would make you indifferent between taking the bet and locking in the sure thing.
- EV is the long-run average outcome if you could take the same bet infinitely.
- CE adjusts EV for risk, using your bankroll size and risk aversion (derived from your Kelly fraction).
If CE is higher than the guaranteed option (e.g., matched betting a free bet at 70% conversion), you should ride the bet. If CE is lower, you should take the guaranteed profit.
CE uses the same Constant Relative Risk Aversion (CRRA) model that underlies the Kelly Criterion. Full Kelly higher risk and fractional Kelly results in less risk.
Factors That Go Into Certainty Equivalent
When calculating CE, DarkHorse Odds considers:
- Bankroll size: Larger bankrolls can absorb variance better, so CE stays closer to EV.
- Kelly Fraction: Lower fractions mean more risk aversion, which reduces CE for high-variance bets.
- Fair Win Probability: Derived from your fair odds calculation, reflects the true chance of winning.
- Profit On A Win: This is normal betting profits plus any bonuses/promotions.
- Loss On A Losing Bet: This could be the bet amount, but it also considers any bonuses and promotions that come on a loss.
- Outcome Volatility: The difference between the win and loss outcomes, in dollars, drives the risk penalty.
- Matched Betting Conversion Amount: The guaranteed amount you could profit.
The result is a single dollar amount, certainty equivalent, which you can directly compare to your matched betting profit option.
Applying Certainty Equivalent to Promotions
Once CE is calculated, the decision is straightforward:
- If the certainty equivalent is greater than your matched betting conversion, you should consider placing the +EV bet.
- If it’s less than your matched betting conversion, you should consider placing the matched bet and take the guaranteed profit.
DarkHorse Odds performs this comparison automatically when your "Matched Bet Comparison Method" is set to "Certainty Equivalent".
If your "Matched Bet Comparison Method" is set to "Expected Value", CE is ignored and the sort order in the Bet Finder results uses the matched betting profit and the +EV profit. There is no consideration for CE in this case.
Examples: Bonus Bet
One of the most common promotions is a Bonus Bet, where you keep only the winnings if the bet wins, not the original stake. In these situations, CE considers the bet size, the odds offered by the sportsbook, your calculated fair odds, your bankroll, and your Kelly fraction. It then compares the certainty equivalent to the matched betting conversion.
Example 1 – Small Bankroll, 0.25 Kelly
- Promotion: $100 Bonus Bet
- Bankroll: $2,000
- Kell Fraction: 0.25
For a bettor with a $2,000 bankroll and 0.25 Kelly Fraction the first +EV result has a CE of $57.02, despite having an EV of $69.67. The lower CE is due to a small bankroll being more subject to variance from a $100 Bonus Bet, and the lower risk tolerance of 0.25 Kelly. This bettor should take the guaranteed money from matched betting and convert it at ~70%, as shown by a CE of $57.02 compared to the +EV of $69.67.
Example 2 – Large Bankroll, Full Kelly
- Promotion: $100 Bonus Bet
- Bankroll: $20,000
- Kell Fraction: 1
A bettor with a $20,000 bankroll has the bankroll to sustain the variance from a $100 Bonus Bet at +302 (24.9%) fair odds. Also, they have their Kelly Fraction set to 1, which means they are willing to take larger risks. The combination of a larger bankroll and aggressive Kelly Fraction results in a CE of $69.30 which is nearly the same as the EV of $69.67. Taking the EV bet is arealistic option for this bettor, unlike the first bettor with the smaller bankroll.
The same bet, Rams moneyline, is the top +EV result in both examples. However the CE, and therefore the sort order, is very different. For the bettor with a smaller bankroll the sort order is 142, compared to 2 for the bettor with a large bankroll.
Practical Tips
- Early on, protect your roll. Large signup offers can be tempting to ride, but a large loss hurts far more when you’re starting.
- Split large promos when allowed — reduces variance and raises CE.
- Balance odds and variance. Longer odds often improve EV for SNR bets but increase variance; CE will show you when the trade-off is worth it.
Summary
Certainty Equivalent turns the abstract math of +EV into a practical decision that accounts for bankroll, risk tolerance, and variance. The DarkHorse Odds Bet Finders calculate CE and compare it to matched betting conversion rates, so you can confidently choose between risk and guaranteed profit.
