Appendix A · A.1
Odds conversion table
Fractional, decimal and American odds against implied probability, from 1/100 out to 500/1.
The two formulas that run this whole book: decimal = a/b + 1, and every price a/b claims a probability of p = b/(a + b) = 1/decimal. American odds convert by +A: decimal = 1 + A/100 and −A: decimal = 1 + 100/A. The table below runs from odds-on to outsiders barely worth a bus fare; the fuller ladder, at every standard bookmaker price increment, is archived on the companion site.
| Fractional | Decimal | American | Implied probability |
|---|---|---|---|
| 1/100 | 1.01 | −10000 | 99.01% |
| 1/50 | 1.02 | −5000 | 98.04% |
| 1/20 | 1.05 | −2000 | 95.24% |
| 1/10 | 1.10 | −1000 | 90.91% |
| 1/5 | 1.20 | −500 | 83.33% |
| 2/5 | 1.40 | −250 | 71.43% |
| 4/6 | 1.6667 | −150 | 60.00% |
| 4/5 | 1.80 | −125 | 55.56% |
| Evens | 2.00 | +100 | 50.00% |
| 6/5 | 2.20 | +120 | 45.45% |
| 6/4 | 2.50 | +150 | 40.00% |
| 2/1 | 3.00 | +200 | 33.33% |
| 5/2 | 3.50 | +250 | 28.57% |
| 3/1 | 4.00 | +300 | 25.00% |
| 4/1 | 5.00 | +400 | 20.00% |
| 5/1 | 6.00 | +500 | 16.67% |
| 6/1 | 7.00 | +600 | 14.29% |
| 8/1 | 9.00 | +800 | 11.11% |
| 10/1 | 11.00 | +1000 | 9.09% |
| 12/1 | 13.00 | +1200 | 7.69% |
| 14/1 | 15.00 | +1400 | 6.67% |
| 16/1 | 17.00 | +1600 | 5.88% |
| 20/1 | 21.00 | +2000 | 4.76% |
| 25/1 | 26.00 | +2500 | 3.85% |
| 33/1 | 34.00 | +3300 | 2.94% |
| 50/1 | 51.00 | +5000 | 1.96% |
| 100/1 | 101.00 | +10000 | 0.99% |
| 150/1 | 151.00 | +15000 | 0.66% |
| 200/1 | 201.00 | +20000 | 0.50% |
| 250/1 | 251.00 | +25000 | 0.40% |
| 500/1 | 501.00 | +50000 | 0.20% |
Read the right-hand column as the break-even ladder in its own right: it is the probability the price needs you to be wrong about before it turns a profit for the firm, from 99.01 per cent at 1/100 down to one chance in five hundred at the foot. The longer the price, the smaller the claim it has to beat, which is precisely the terrain Chapter 5's favourite-longshot bias makes its home.
This is reference lifted from the book. The chapters are where the arithmetic gets built and argued for.
Out now · free to read on Kindle Unlimited