Convert odds between fractional, decimal and American (moneyline) formats and get the implied probability, worked in exact fractions.
Cập nhật Ví dụ đã kiểm tra: 5
A 1-unit stake at these odds returns 3.5 in total (2.5 profit) if it wins. The odds imply a 28.57% chance; a bet only has positive expected value if the true chance is higher than that, and bookmakers' prices include a margin, so implied chances across all outcomes add up to more than 100%.
Worked as exact fractions, so no rounding creeps in between formats.
Decimal odds d are the total return per 1 staked, stake included. Fractional odds a/b give the profit per stake, so d = 1 + a/b. American odds are +100(d − 1) when d is 2 or more and −100/(d − 1) when d is below 2, and the implied probability is 1/d. Every conversion runs through exact fractions, so 10/11 stays 10/11 instead of becoming 0.909…
The default, 5/2, is decimal 3.5 and American +250: a 1-unit stake returns 3.5 if it wins, 2.5 of it profit, and the price implies a 28.57% chance. A −110 line, common on US point spreads, implies 52.38%, the win rate needed to break even.
Implied probability describes the price, not the true chance. Bookmakers build a margin into their prices, so the implied probabilities of all outcomes in a market add up to more than 100%.
Nguồn đối chiếu: d = 1 + 5/2; p = 2/7 = 28.571%; American +100 × 2.5 (standard conversion tables)
Nguồn đối chiếu: d − 1 = 1/2; American −100/0.5 = −200; p = 1/1.5 = 2/3
Nguồn đối chiếu: d = 1 + 100/110 = 21/11; p = 11/21 = 52.381% (the standard −110 break-even rate)
Nguồn đối chiếu: d = 1/0.25 = 4; 3/1; +300
Divide the first number by the second and add 1: d = a/b + 1. So 5/2 becomes 3.5, 1/2 becomes 1.5 and evens (1/1) becomes 2.0. The 1 is the returned stake: fractional odds quote profit only, while decimal odds quote the total return, so a winning 10-unit bet at 5/2 or 3.5 pays back 35 in both cases.
A plus number is the profit on a 100 stake and a minus number is the stake needed to win 100. At +250, 100 staked wins 250 profit (decimal 3.5); at −150, 150 staked wins 100 (decimal 1.667). +100 and −100 both mean evens, and no American odds exist between −100 and +100.
Divide 1 by the decimal odds: p = 1/d. Decimal 3.5 implies 1/3.5 = 28.57%. For fractional odds a/b the shortcut is b/(a + b), so 5/2 gives 2/7. For American −110 it is 110/(110 + 100) = 52.38%, and for +250 it is 100/(250 + 100) = 28.57%.
The overround is how far the implied probabilities of every outcome in a market add up past 100%. With both sides of a bet priced at −110, the total is 52.38% + 52.38% = 104.76%, an overround of 4.76% and a bookmaker margin (vig) of 1 − 1/1.0476 = 4.55% of stakes. Dividing each implied probability by the total, 52.38/104.76, removes the margin and gives 50%.
Odds-on means the implied probability is above 50%: fractional odds below 1/1, decimal odds below 2.0 and negative American odds. At 1/2 odds-on (1.5, or −200) you stake 2 to win 1, an implied 66.67%. Odds against is the reverse: 5/2 (3.5, or +250) pays more than the stake and implies less than 50%.
Độ chính xác phụ thuộc vào dữ liệu nhập và giả định của phương pháp. Phép tính thập phân dùng 50 chữ số có nghĩa, nhưng ước lượng, phương pháp số và dữ liệu nguồn có thể kém chính xác hơn; làm tròn khi hiển thị không loại bỏ các giới hạn đó. Ví dụ có lời giải đã đối chiếu với nguồn độc lập: 5. Ví dụ, “5/2 (defaults)” được kiểm tra bằng d = 1 + 5/2; p = 2/7 = 28.571%; American +100 × 2.5 (standard conversion tables).
Grinstead & Snell, Introduction to Probability (AMS), §1.2 — odds and probability; UK Gambling Commission — how odds work (fractional and decimal).
Chỉ dùng để lập kế hoạch. Bên cho vay, cơ quan thuế và thị trường áp dụng cách làm tròn, phí và quy tắc riêng; hãy xác nhận số liệu với họ trước khi cam kết.
Công cụ tính này có 5 ví dụ đã giải với đáp án từ các nguồn độc lập. Chúng được chạy trong bộ kiểm thử và bạn cũng có thể chạy tại đây.
Calculate expected value E[X], variance and standard deviation for a bet, game or decision from its outcomes and their probabilities or weights.
Calculate P(A or B), P(A and B) and P(A | B) for two events, or apply Bayes' theorem to a test result, with a probability tree and Venn diagram.
Calculate nCr and nPr exactly: combinations and permutations with or without repetition, for poker hands, lottery odds and PIN codes.
Exact probability of dice sums, coin-flip heads and streaks, drawing special cards from a deck and each 5-card poker hand, as a fraction and 1 in N.
Generate random numbers from a seed: integers in a range, decimals, lottery-style draws without repeats and dice rolls, repeatable with xoshiro256**.