Odds to probability converter: decimal and American odds

What the converter does

Give the tool a decimal price above 1.00, or an American price at most -100 or at least +100, and it returns the break-even probability implied by that price. Give it a percentage strictly between 0 and 100 and it returns the matching decimal and American prices. The arithmetic is exact and the input bounds are enforced: decimals of 1.00 or below, American values between -100 and +100, and the percentage endpoints 0 and 100 have no valid inverse and are rejected.

A decimal price is the total return per unit staked, stake included, so the break-even probability is 1 divided by the price. Decimal 2.00 gives 1 / 2.00 = 0.50, or 50%. American prices use a different convention: +200 means a 200 unit profit on a 100 unit stake, so the probability is 100 / (200 + 100) = 0.3333, about 33.33%. The negative form works the other way: -200 means you stake 200 to win 100, so the probability is 200 / (200 + 100) = 0.6667, about 66.67%.

The percentage input exists so you can work backwards. Enter 50% and you get decimal 2.00, American +100. Enter 33.33% and you are near American +200. Passing the endpoints is not allowed because 0% implies an unbounded decimal price, while 100% gives decimal 1.00, which the tool rejects because it requires decimal odds above 1.00.

Worked example: 2 decimal 1.80 prices

Take a 2-way book showing decimal 1.80 on both sides. Each side implies 1 / 1.80 = 0.555555..., or about 55.5556%. You can calculate the 2-way overround by hand: add the 2 converted probabilities and subtract 1. The sum is 1.111111..., which as a percentage is 111.1111%, or 11.1111 percentage points above 100. That excess is the overround, the margin the price setter has built in. The tool itself converts one input at a time, so the 2-way sum is a manual step.

Suppose you must judge whether these 2 1.80 prices are internally consistent. You compute the sum and get 1.111111. The book is coherent but carries an 11.1111 point margin. If you later find a third price for one of the outcomes at another venue, you cannot compare it directly to 1.80 without accounting for that margin, because the 2 prices embed different amounts of vigorish. Illustrative numbers, not an observed market.

The overround alone does not give you a true probability. To move from implied probabilities to a margin-free split you have to assume something, for example scaling both sides down proportionally. That assumption is yours, not the tool's. The converter stops at the break-even figure and leaves the true-probability estimate to you.

If you want to carry the conversion further into a model, you can feed the same numbers into an Elo rating system once you have built ratings from results, or into an expected value calculator to compare your own probability estimate against the price. Both need your estimate as an input.

Illustrative conversions

The table below shows the implied probability of each side priced at decimal 1.80 and their combined overround. Every figure is arithmetic on the stated input; none of it is a claim about any real market.

Bookmaker margin is not a Polymarket share price

On Polymarket, the displayed price is usually the midpoint of the best bid and best ask, and when the spread exceeds 0.10 the platform shows the last trade instead. Midpoints are reference points, not executable guarantees. Depth, the observation date and the size you intend to trade all matter, and a market order can eat through several price levels and incur slippage. That is a different mechanism from a bookmaker's 2-way decimal or American book, where the margin is baked into the quoted prices.

A share price of 0.5556 on a prediction market is not the same object as a 1.80 decimal price, even though both imply roughly 55.56% at face value. The share price floats with the order book, the decimal price carries a bookmaker margin, and neither is automatically the true probability. Translate odds with the converter, then examine executable quotes and depth separately for whatever you intend to act on.

The same caution applies when you invert a percentage. If you convert 55.56% into a decimal and compare it to a live order book, you may be comparing a theoretical quote to a midpoint that nobody will actually fill at. Note the timestamp and the source of every price you feed in.

Where the implied probability falls short

Break-even is not a forecast. Betting decimal 2.00 breaks even when the true chance is exactly 50%, assuming no commission, no limits and no other costs. If the true chance is lower, that side loses on average. The losing case is the ordinary one whenever you convert a price and treat the output as a fair chance: the number tells you what the price requires, not what will happen.

Prices move. A bookmaker line can shift within minutes, and a prediction market midpoint moves with the order book. A conversion recorded from a stale quote may describe a market that no longer exists. When the spread is wide, the displayed price is a weak proxy for what you can execute, and the converter cannot repair a bad input.

Treat any stored conversion as a snapshot tied to a time and a source. Recompute before you act.

A quick decision rule

Convert both sides of a 2-way book and sum the implied probabilities. If the sum sits at 1.000000 exactly, there is no margin at the quoted prices, under the arithmetic assumptions. If the sum is above 1, the gap in percentage points is the overround you are paying, and a fairer split requires an assumption you make yourself. If the sum is below 1, the quoted prices are inconsistent in your favour on paper, so check quote timing, costs and execution before drawing a conclusion.

Keep the converter in its lane. It turns a price into a break-even probability and back. The tool converts one quote at a time; to calculate a 2-way overround, add the 2 converted probabilities and subtract 1. It does not estimate true probabilities, does not recommend trades and does not know whether a price is executable. Where you need a probability to compare against, build it separately, for instance with a documented forecasting method, and bring it back here only for the arithmetic.

To test numeric assumptions, see the expected-value calculator.