Odds Converter and Break-Even Probability

Why three different odds formats exist

American odds anchor on a $100 reference stake. Positive numbers report profit on a $100 wager (+200 wins $200); negative numbers report the stake needed to win $100 (-200 stakes $200). Decimal odds replace that asymmetric convention with a single multiplier per unit staked, including the stake itself — 3.00 means a $1 wager returns $3 total ($2 profit). Fractional odds report net profit per unit staked as a ratio — 5/2 means $5 profit on $2 staked.

Implied probability: the math behind every price

Every price compresses into one number: the implied win rate the book is offering. For negative American odds, implied probability is -N / (-N + 100) — a -150 line implies 60.00%. For positive American odds, implied probability is 100 / (N + 100) — a +150 line implies 40.00%. Decimal odds convert through 1 / decimal; a 2.50 line implies 40.00% as well.

Worked example: -110, +100, and 5/2 side-by-side

A standard NFL spread at -110 carries an implied probability of 110 / 210 = 52.38%, decimal 1.9091, fractional 10/11. A pickem priced at +100 (even money) is 100 / 200 = 50.00%, decimal 2.000, fractional 1/1. A 5/2 horseracing price is 2 / 7 = 28.57%, decimal 3.500, American +250. Every row of the ladder below was generated with the same three formulas.

American / decimal / fractional / probability reference

American	Decimal	Fractional	Implied prob
-400	1.250	1/4	80.00%
-300	1.333	1/3	75.00%
-250	1.400	2/5	71.43%
-200	1.500	1/2	66.67%
-180	1.556	5/9	64.29%
-150	1.667	2/3	60.00%
-130	1.769	10/13	56.52%
-120	1.833	5/6	54.55%
-110	1.909	10/11	52.38%
-105	1.952	20/21	51.22%
+100	2.000	1/1	50.00%
+105	2.050	21/20	48.78%
+110	2.100	11/10	47.62%
+120	2.200	6/5	45.45%
+130	2.300	13/10	43.48%
+150	2.500	3/2	40.00%
+180	2.800	9/5	35.71%
+200	3.000	2/1	33.33%
+250	3.500	5/2	28.57%
+300	4.000	3/1	25.00%
+400	5.000	4/1	20.00%

FAQ

What are American, decimal, and fractional odds? +

Three regional formats for the same number. American odds (used in the US) show how much you win on $100 stake when positive (e.g. +150 wins $150) or how much you must stake to win $100 when negative (e.g. -200 stakes $200 to win $100). Decimal odds (Europe, Australia, Canada) show the total return per unit staked including stake — 2.50 means a $1 stake returns $2.50. Fractional odds (UK, horse racing) show net winnings per unit staked — 3/2 means win $3 profit on $2 staked. All three encode the same implied probability.

Why do bookmakers use different formats in different regions? +

Historical convention more than mathematical preference. American odds emerged from football pools and parlay cards where bettors thought in terms of fixed $100 units. Decimal odds spread from continental Europe where they pair naturally with currency calculations. Fractional odds come from British racecourse tradition where bookmakers shouted price-per-stake ratios like "five-to-two." Modern bettors typically pick the format their books use natively; sharper bettors mentally convert to implied probability because that is the only format you can compare against your own model.

How does implied probability relate to fair price? +

Implied probability is the break-even win rate a bet requires given the offered price. A -110 line implies 52.38% — you must win that share of bets just to break even net of the vig. The fair price (no-vig price) strips out the bookmaker margin so both sides sum to exactly 100% implied probability. Comparing your model's true probability against the implied probability tells you whether the bet is +EV; comparing your model against the fair price tells you the edge net of vig.

When should I use decimal odds instead of fractional in modeling? +

Decimal odds are far easier to manipulate algebraically. Parlay payouts are simply the product of decimal odds. Kelly-fraction math expects decimal-odds inputs (b in the formula is decimal-odds minus 1). Devig calculations sum implied probabilities and divide — trivial with decimal. Fractional odds (3/2, 7/4, 11/10) are great for shouting on a racecourse but turn ugly in spreadsheets. Convert to decimal for any quantitative work and convert back to American or fractional only for display.