3-way moneyline: how the draw changes the odds math

A 3-way moneyline is a bet on one of three outcomes: home win, draw or away win. Because the draw is its own outcome, backing a team loses if the game is drawn, so 3-way prices for each team are longer than in a market without a draw.^[2] Removing the margin means normalizing across all three prices, not two.

How 3-way moneyline odds work

Check which result counts. One sportsbook's house rules, for example, settle bets on the score at the end of regular time, which for soccer is 90 minutes including injury time but not extra time or penalties.^[1]

Take a match priced at home 2.40 (+140), draw 3.30 (+230) and away 3.10 (+210):

The implied probabilities add up to 104.2%; the extra 4.2% is the overround. Dividing each by 1.042 gives the fair (no-vig) probabilities, the proportional method explained in Implied probability and no-vig odds, explained. Convert the prices with the odds converter.

Converting a 3-way moneyline to draw no bet

Draw no bet refunds your stake on a draw.^[2] Its fair probability is the team's share of the non-draw outcomes:

Fair draw-no-bet probability (home) = 40.0% ÷ (40.0% + 30.9%) = 56.4%, fair decimal odds 1.77.

If a sportsbook offers home draw no bet at a longer price than 1.77, it's +EV against this market's fair prices.

Which devig method?

With three outcomes, devig methods disagree more than with two. Using the power method on the same prices gives home 40.2%, draw 28.9% and away 30.8%, close to the proportional figures here but not identical. On markets with a big favourite, the gap grows. See Why do EV betting tools disagree? Devig methods compared.