How many bets does it take to know you can beat the sportsbook?
Thousands. Over a few hundred bets luck is bigger than any realistic edge: a bettor with no skill often shows a profit, and a bettor with a real edge often shows a loss.
With flat stakes at −110: after 100 bets a bettor with no edge is ahead 30.9% of the time and a bettor who really wins 55% is behind 30.7% of the time. After 1,000 bets those chances are 6.9% and 4.6%. A bettor with no edge wins 55 or more of 100 bets 18.4% of the time.
Simulate 100 bets by a 55% bettorThe house edge of every sports bet
How often the record points the wrong way
| Bets | A 50% bettor is ahead | A 53% bettor is behind | A 55% bettor is behind |
|---|---|---|---|
| 100 | 30.9% | 45.9% | 30.7% |
| 250 | 24.3% | 40.0% | 18.7% |
| 500 | 15.2% | 37.7% | 11.3% |
| 1,000 | 6.9% | 34.0% | 4.6% |
| 2,500 | 0.9% | 26.7% | 0.4% |
| 5,000 | 0.0% | 19.4% | 0.0% |
| 10,000 | 0.0% | 10.9% | 0.0% |
Exact, from the binomial distribution, for flat stakes on bets that are independent of each other.
Why
Results swing with the square root of the number of bets, while an edge adds up in proportion to it. After 100 bets the number of wins typically lands within about five of its average either way, and a 55% bettor expects only five more wins than a coin flip, so luck can hide the whole edge. After 2,500 bets the swing is about 25 wins and the same edge is worth 125. Until then a good record and a lucky one look the same.