The three formats, and what each one states
#Decimal odds state your total return per unit staked: at 2.50, a 10 stake returns 25, your stake plus 15 profit. Fractional odds state profit relative to stake: 6/4 means 6 profit for every 4 staked, which is decimal 2.50. American odds split into two readings: a positive number, +150, is the profit on a 100 stake, and a negative number, -200, is the stake needed to win 100 profit.
Conversions are mechanical. Fractional a/b becomes decimal a/b + 1. American +A becomes A/100 + 1, and -A becomes 100/A + 1. So 6/4, +150 and 2.50 are literally the same price, and any comparison between them starts by putting everything in decimal.
From odds to implied probability
#A price of 2.50 pays out one time in 2.5 if it is fair, so the probability it implies is 1 divided by 2.50, which is 40%. That single operation, implied probability equals 1 over decimal odds, is the most useful calculation in betting, because it translates every price into the claim it makes about the world.
Odds of 1.25 imply 80%. Odds of 5.00 imply 20%. Odds of 1.01 imply 99%. Reading prices this way makes offers comparable across formats and across bookmakers, and it makes one thing immediately visible: whether the number the bookmaker offers is bigger or smaller than the probability you believe in.
Why the implied probabilities do not add up to 100%
#Convert every outcome of a real market into implied probability and sum them: the total always exceeds 100%. A coin-flip market priced at 1.91 both ways implies 52.4% plus 52.4%, which is 104.7% of probability for an event that can only produce 100%. That excess is the bookmaker's margin, and it has its own page.
The consequence for reading odds is that a bookmaker's price systematically understates the payout a fair price would give. The implied probability of a single price is therefore an overstatement of the true probability by roughly the margin's share, which matters whenever someone treats odds as the market's honest forecast.
What value means, and why it is hard to find
#A bet has value when the probability you can justify is higher than the probability the price implies: believing a team wins 50% of the time and being offered 2.50, implying 40%, is a positive expected value if your 50% is right. Every serious approach to betting reduces to that single comparison.
The honest caveat is the last clause: if your probability is right. Prices are set by companies employing teams and models for exactly this, then moved by the money of everyone else. Beating them consistently means being better informed than that whole apparatus, after the margin. It is not impossible, and for almost everyone it is not the case, which the margin quietly converts into steady loss.
Questions, answered
Which odds format is best?
They encode identical information, so none pays more than another. Decimal is the easiest to compute with, which is why every conversion on this page routes through it. The format worth thinking in is none of the three: it is the implied probability.
Do odds tell me the real probability of an outcome?
Approximately, and always overstated: the sum of a market's implied probabilities exceeds 100% by the bookmaker's margin, so each individual price implies more probability than the outcome truly carries. Odds are a price with a fee inside, not a neutral forecast.
Why do odds change before an event?
Because prices respond to money and information. When news lands or one side attracts heavy staking, the bookmaker moves the price to balance its exposure and re-express probability. Your bet keeps the odds at which it was placed.
Related