People wait hours in the cold for the northern lights because they are rare. The rarity is exactly what makes seeing them memorable. The same psychology operates in betting: a small stake at long odds feels more appealing than a safe small win, even when the expected value is worse.
This article covers what a long price actually means, how to convert it into a probability, and why a run of long shots looks like a losing strategy for a long time even when the bet was reasonably priced.
Odds are probability written differently
Decimal odds convert straight into an implied probability by dividing one by the price:
| Odds | Implied probability | How often it lands on average |
|---|---|---|
| 1.50 | 66.7% | Twice in three |
| 3.00 | 33.3% | Once in three |
| 10.00 | 10% | Once in ten |
| 50.00 | 2% | Once in fifty |
| 101.00 | 0.99% | Once in a hundred |
A 100/1 bet is therefore not "almost impossible, but when it hits, it hits". It is a bet that loses on average 99 times out of 100. Place ten of them and the most likely outcome is ten losses in a row.
Why a losing run feels like evidence
Ten consecutive losses on a 2% bet say nothing about whether the bet was sound. The probability that none of ten 2% bets lands is about 82% – which makes it the ordinary result, not the exception. The rarity of the outcome means you cannot judge from a handful of bets.
The same applies in the other direction: one long shot landing does not prove the estimate was right. A 2% event happens, and when it does, it is not a sign of anything.
The bookmaker's margin
The probabilities implied by a set of odds always add up to more than one hundred percent. The excess is the bookmaker's cut. In a two-way market priced 1.90 and 1.90 the sum is 52.6% + 52.6% = 105.2%, so one hundred is exceeded by 5.2 percentage points. The larger the excess, the worse the price for the player – and on long shots the excess is typically larger than on close markets.
The practical conclusion is simple: a long price is neither good nor bad in itself. It is a price, and whether the price is reasonable is only settled by comparing it with your own estimate of the probability.
The Finnish Meteorological Institute tracks aurora activity and the solar cycle at ilmatieteenlaitos.fi. The odds formats are explained in our glossary, and living with variance is covered in emotional control in poker.
Questions and answers
How do you convert odds into a probability?
Divide one by the decimal odds. Odds of 4.00 mean an implied probability of 1 / 4.00 = 25 percent.
Is it worth betting long odds?
Odds are neither good nor bad in themselves – they are a price. A long price is worth taking only if your own estimate of the probability is higher than the one implied. The bookmaker's cut is typically larger on long shots.
What does the bookmaker's margin mean?
The probabilities implied by the odds add up to more than one hundred percent, and the excess is the bookmaker's cut. At 1.90 and 1.90 the sum is 105.2 percent, exceeding one hundred by 5.2 percentage points.
Do ten consecutive losses show the strategy is bad?
No. On 2% bets, the probability that none of ten lands is about 82 percent. With rare events you cannot judge from a handful of bets.
