How fair go Turns Betting Maths into a Step-by-Step Process for Australians
Probability theory tells us that every wager has an expected value, and that number is the single most honest description of any bet you will ever place. The brand fair go is built around this idea, and anyone who wants to understand what it actually offers should start with the arithmetic rather than the advertising. The service at https://pradaphonebylg.com/ presents markets, odds and account tools in Australian dollars, which makes the following calculations directly comparable to your own bank balance. This article works through the mathematics step by step, so you can see exactly where value exists and where it does not.
Step 1 – Reading fair go Odds as Probabilities
Decimal odds are a compact way of writing an implied probability. The conversion is simple: implied probability equals one divided by the decimal odds. If fair go lists a head-to-head market at 2.00, the implied chance is 1 / 2.00 = 0.50, or 50 percent. At 1.50, it is 1 / 1.50 = 0.6667, or about 66.67 percent. This single division is the foundation of everything that follows, and it takes less than a second per market once you are used to it.
The sum of all implied probabilities in a market is called the overround. Suppose a two-outcome market is priced at 1.90 and 1.90. Each side implies 1 / 1.90 = 0.5263. The total is 0.5263 + 0.5263 = 1.0526, so the overround is 5.26 percent. That figure is the operator’s theoretical margin, and it is the number to compare whenever you look at different markets inside fair go.
Step 2 – Calculating Expected Value on fair go Markets
Expected value, usually shortened to EV, measures the average result of a bet if it were repeated many times. The formula is EV equals the probability of winning multiplied by the net profit, minus the probability of losing multiplied by the stake. A worked example makes the logic concrete.
Assume you stake 100 AUD at odds of 2.50, and your own analysis says the true probability of winning is 45 percent. The net profit on a win is 100 times 1.50, which equals 150 AUD. The loss on a defeat is 100 AUD. So EV equals 0.45 times 150 minus 0.55 times 100. That is 67.50 minus 55.00, giving positive 12.50 AUD. Over 100 identical bets, the expected return is 1,250 AUD above break-even, though individual results will vary widely around that mean.
Now change the true probability to 35 percent. EV equals 0.35 times 150 minus 0.65 times 100, which is 52.50 minus 65.00, giving negative 12.50 AUD. The same odds produce a losing proposition once your estimate of the true chance drops. This is why fair go cannot be judged by odds alone; the arithmetic depends entirely on the accuracy of your probability estimate.
Step 3 – Building a fair go Bankroll Model with the Kelly Criterion
The Kelly criterion answers a precise question: what fraction of your bankroll should you stake to maximise long-run growth? For decimal odds, the formula is f equals the edge divided by the odds minus one, where the edge is your estimated probability multiplied by the odds, minus one.
Take odds of 2.50 and an estimated probability of 45 percent. The edge is 0.45 times 2.50 minus 1, which equals 0.125. The denominator is 2.50 minus 1, which equals 1.50. So f equals 0.125 / 1.50, which is 0.0833, or 8.33 percent of your bankroll. On a 1,000 AUD bankroll, that is an 83.30 AUD stake. Many analysts recommend half-Kelly, which would be 41.65 AUD, to reduce variance at the cost of slightly slower growth.
The table below summarises how the recommended stake changes as your probability estimate shifts, holding the odds at 2.50 and the bankroll at 1,000 AUD.
| Estimated probability | Edge | Full Kelly fraction | Stake on 1,000 AUD |
|---|---|---|---|
| 40 percent | 0.000 | 0.00 percent | 0.00 AUD |
| 42 percent | 0.050 | 3.33 percent | 33.30 AUD |
| 44 percent | 0.100 | 6.67 percent | 66.70 AUD |
| 45 percent | 0.125 | 8.33 percent | 83.30 AUD |
| 48 percent | 0.200 | 13.33 percent | 133.30 AUD |
| 50 percent | 0.250 | 16.67 percent | 166.70 AUD |
Step 4 – Understanding Variance and Sample Size on fair go
Variance quantifies how far results scatter around the expected value. For a bet with two outcomes, the variance is p times 1 minus p times the squared payout difference, where p is the win probability. With a 45 percent chance and payouts of 150 AUD profit versus 100 AUD loss, the difference is 250 AUD. Variance equals 0.45 times 0.55 times 250 squared, which is 0.2475 times 62,500, or 15,468.75. The standard deviation is the square root of that, roughly 124.37 AUD per bet.
Standard deviation matters because it determines how large a sample you need before results resemble the expected value. A common rule of thumb is that you need at least 100 bets, and often several hundred, before the average result stabilises. After 100 bets with an EV of positive 12.50 AUD, the expected total is 1,250 AUD, but the standard deviation of that total is 124.37 times the square root of 100, which is 1,243.70 AUD. So a perfectly normal run of 100 bets could finish anywhere from roughly break-even to well above 2,400 AUD without contradicting the model.
- Track every stake in Australian dollars to compute your actual EV over time.
- Record the odds at the moment you place each bet, not the odds later shown.
- Log your own probability estimate before the result is known, so you can score your accuracy.
- Compare your realised return against the EV formula after at least 200 bets.
- Recompute your Kelly fraction whenever your bankroll changes by more than 20 percent.
- Separate markets by sport or type, because calibration differs between them.
Step 5 – Calibrating Your Own Probabilities Using fair go Data
Calibration is the degree to which your stated probabilities match reality. If you say 60 percent on twenty different bets and exactly twelve win, your calibration is exact at that level. The calculation is observed wins divided by predicted wins, and the closer that ratio is to 1.00, the better your model. A ratio of 0.80 means you are overconfident; a ratio of 1.20 means you are underconfident and probably leaving value on the table.
Working through fair go markets with this discipline turns guesswork into measurement. You can compute a Brier score, which is the average of the squared difference between your predicted probability and the actual outcome coded as one or zero. Lower scores are better, and a score below 0.25 generally indicates useful forecasting skill. Because every market settles in Australian dollars, your records convert directly into profit and loss without currency adjustment.
Step 6 – A Practical Weekly Routine for fair go Users
A repeatable process beats intuition, and the steps below can be completed in under an hour each week. The sequence is designed so that each stage feeds the next with numbers rather than impressions.
- Export your transaction history and total the stakes and returns in AUD.
- Compute your realised EV by dividing net profit by total stakes, then compare it with your predicted EV.
- List every market where your predicted probability differed from the implied probability by more than five percentage points.
- Recalculate the overround on three markets you intend to use next week.
- Apply the Kelly formula to each selection and cap any stake at five percent of your bankroll.
- Set a weekly loss limit in dollars and stop when it is reached, regardless of the mathematics.
- Review your calibration ratio monthly and adjust your probability estimates accordingly.
Each of these steps produces a number you can audit. Over a year of weekly reviews, you accumulate enough data to distinguish genuine skill from luck, which is the only reliable way to judge any betting activity.
Step 7 – Common Arithmetic Errors to Avoid with fair go
Most costly mistakes are not about picking losers; they are about arithmetic. Converting odds incorrectly, forgetting the overround, or staking a fixed amount regardless of edge will erode a bankroll even when your selections are sound. The list below covers the errors that appear most often in practice.
- Treating implied probability as the true probability instead of adding your own estimate.
- Ignoring the overround when comparing two markets with different margins.
- Using full Kelly stakes without accounting for estimation error in your probabilities.
- Judging performance after fewer than 100 bets, where variance dominates.
- Mixing currencies without converting, which distorts every EV calculation.
- Chasing losses by increasing stakes after a losing run, which raises variance without raising EV.
- Recording odds after the event rather than at the moment of the bet.
Correcting these habits costs nothing and improves the accuracy of every subsequent calculation. The mathematics of fair go does not promise profit, but it does promise clarity, and clarity is the prerequisite for any rational decision about where to place your money in Australian dollars.