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.

How is this different from the No Vig calculator and the Implied Odds calculator? +

This Odds Converter translates a single price between four formats. The Implied Odds Calculator focuses on the probability and break-even percentage of a single side. The No Vig Calculator takes BOTH sides of a market (or N sides), strips the bookmaker margin, and returns each outcome's fair probability. Use the converter for format translation, the implied-odds page for single-side break-even, and the no-vig page when you have a complete market and want the fair price.