Start with the Core Problem
You’re staring at a spreadsheet, numbers flashing, and you wonder: “What’s the expected value of this round robin bet?” Here’s the deal: EV isn’t magic, it’s arithmetic dressed in probability.
Break Down the Round Robin Structure
First, remember a round robin is just a collection of parlays. If you have three selections — A, B, C — a 2-way round robin spits out three two-leg combos: A&B, A&C, B&C. Add a 3-way, you get the full three-leg parlay.
Count Your Units
Identify how many individual bets you’re making. Formula: n choose k. For n picks and k-leg combos, total bets = n! / (k! · (n-k)!). Quick mental math saves time.
Calculate Individual Parlay EV
Each combo’s EV = (Probability of winning × Payout) − (Probability of losing × Stake). Probability is the product of each leg’s win chance. Multiply the odds, convert to implied probability, then invert.
Example: Leg A at -150 (66.7% implied), Leg B at +200 (33.3%). Two-leg combo win prob = 0.667 × 0.333 ≈ 22.2%.
Payout Computation
Take the decimal odds for each leg, multiply, then subtract 1 to get net profit multiplier. Stake is usually one unit per combo.
Aggregate the EVs
Sum the EV of every combo, then subtract the total stake across all combos. That net figure is your round robin EV. If it’s positive, you’ve found a profitable edge; if negative, you’re in the red.
Speed Hack
Instead of looping through each combo, use the formula: EV_total = C × (∏(odds) × ∏(probabilities) − 1) where C is the number of combos. It collapses the math into a single line.
Adjust for Real-World Factors
Bookmaker margins, juice, and correlation between selections skew raw probabilities. Knock down the win chances by 5-10% to simulate overround. Re-run the EV, and you’ll see the true picture.
Quick Check
Plug your numbers into a calculator, verify the EV is not a phantom. A negative EV by even 0.02 can wipe out a bankroll over time.
Final Piece of Actionable Advice
Run the EV calculation before you place any round robin — if the result isn’t positive after adjusting for juice, scrap the bet. And for a deeper dive, check out this guide on how to calculate round robin EV.