What Are the Chances of Hitting a 10-Fold Accumulator Bet?
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Accumulators have become very popular in the UK, with success stories popping up once in a while. In 2011, Steve Whiteley won £1.45 million on an accumulator with a £2 bet. In 2008, Fred Craggs won £1,000,000 with a 50p bet. But what are the chances of these bets winning? Let’s do a detailed analysis.
The Probability of Landing a 10-Fold Accumulator: A Direct Calculation
A 10-fold accumulator, or acca, is a bet of 10 individual selections. All selections must win for you to get a payout. So what are the chances of that happening? The probability of winning such a bet is the product of the probabilities of each individual selection.
For simplicity, let’s say each selection has the same odds. For 1/1 odds (50% chance of winning), the combined probability is:
P(10-fold win) = 0.510 = 0.000976562 or 0.0977%, where P is the probability.
Why Hitting 10 Bets Is So Unlikely: The Multiplicative Risk Model
Each additional leg reduces the chances of a payout. Remember, each leg must win for the bet to pay out. So it’s all or nothing.
Some think that legs with higher probabilities mean better odds for the acca. Higher odds are better, but the chances are still low. Here’s an example:
For 10 selections, each with an 80% winning chance (0.8), the combined probability will be 0.810 ≈ 0.1074 = 10.74% down from 80%.
Let’s compare long-term stability vs short-term volatility in acca bets.
| Concept | Description | Impact |
|---|---|---|
| Law of Large Numbers | If you repeat a random event enough times, the average result will eventually come to the expected value. | Works for low-variance bets (e.g. singles), not 10-leg acca bets |
| Short-Term Volatility | Fluctuations from one or a few bets | More fluctuations in accas, especially 10-folds. |
| Example | 75% win chance single bet over 1,000 trials | Stabilises near 75% success rate |
| 10-Fold Acca | 0.056 chance per bet; over 100 trials = 5–6 wins | Most bets will fail, and the payout doesn’t cover the variance |
From this risk assessment, 10-folds don’t beat the math, and hitting all ten selections is unlikely.
Empirical Analysis: Historical Success Rates of 10-Fold Accumulators
For the conclusions we made, we used real-world data. For instance, a £1 stake on a 10-fold accumulator with average odds can yield returns exceeding £8,500, but such wins are rare. Bookies promote these bets because they have high profit margins, and most of them fail.
The exact stats on 10-fold accumulator placements are hard to find, but the win frequency is low. Looking at the last 20 years, there are barely 10 stories of big wins from 10 fold accumulator bets. Don’t get it wrong. Some bettors are very lucky, and below are some examples:
- A Greek player won €435,887 for a €220 stake on a 16-leg accumulator
- In 2012, a 19-fold acca paid out £570,000 for Glen Johnson at William Hill
- A Paddy Power customer turned £1 into €206,000 using a 17-fold accumulator bet in football.
These are great achievements, but don’t let them hide the true success rate of acca bets.
Conditional Probability: Does Past Success Improve Future Legs?
In accumulators, each leg is an independent event. The outcome of previous selections doesn’t influence the probability of subsequent ones. This is a common misconception known as the gambler’s fallacy.
Believing that a streak of wins increases the chance of continued success is statistically not true. Conditional probability doesn’t work in acca bets. That means even if 9 legs win, the 10th remains independent and can lose to void the whole accumulator.
How Bookmaker Odds Distort True Probability
Bookmakers incorporate a margin, known as the overround, into their odds to ensure profitability. What you see are inverted probabilities.
Implied Probability = 1/Decimal Odds
E.g. 1/2 = 0.5 = 50%
If an event has a 50% chance of occurring in the match, the fair odds would be 2.00. However, a bookmaker may offer odds of 1.90, and now the implied probability becomes 52.63% while the margin becomes 2.63%.
These margins compound in accumulators. A 10-fold accumulator can result in a bookmaker’s profit margin of up to 50%, significantly reducing the bettor’s expected value.
Expected Value and Variance of a 10-Fold Bet
To better understand how accumulator bets work, take it this way – a selection pays out, and you bet those winnings in the next one. So, if you bet £1 on different football teams to win (assuming the odds are 2.00), it will look like this:
- £1 on Manchester United = £2 return
- £2 return on Arsenal = £4 return
- £4 return on Newcastle = £8 return
- £80 return on Manchester City = £16 return
To get the expected value (EV) of an acca bet, use the following formula:
EV = (Probability of Win X Profit) − (Probability of Loss X Stake)
Because of the low probability of winning a 10-fold accumulator and the compounded bookmaker margins, the EV is usually negative. Also, the variance is high, so outcomes are unpredictable and can deviate significantly from the expected value.
Resources Used for Study
- https://www.bbc.com/news/av/uk-12687610
- https://www.aceodds.com/what-is-an-accumulator-bet.html
- https://sports.yahoo.com/blogs/soccer-dirty-tackle/man-wins-680-000-one-euro-football-accumulator-193352030.html?guccounter=1
- https://sbcnews.co.uk/sportsbook/2015/02/26/irish-punter-turns-paddy-power-e1-accumulator-into-e206000-win/
