Recently, I participated in several discussions about betting on low-odds events, which I believe can offer positive expected value (+EV), and this gave me the idea to explore the concept of low-odds betting in more detail.
The first instance occurred when I saw an “odds boost” on a bet published by a bookmaker on Twitter and asked the somewhat rhetorical question: “Boosted to roughly fair odds?” I thought the boosted odds were slightly favorable to the bettor, while others in the space believed it was clearly a strong +EV bet. The bet was on Kai Havertz to have a shot on target for Arsenal against Bournemouth in the English Premier League.
CONDITIONAL PROBABILITIES CAN CHANGE THE LIKELIHOOD OF EVENTS
The original odds were data-driven, set at 1.44*, boosted to 2.00*. The odds indicated a probability of around 70%, and when I checked the data, I saw that Havertz averaged 0.7 shots on target per game in the 2023/24 season. The key point here is that this was a “per game” statistic, not per 90 minutes.
The “conditional” probability for this scenario considers the specific match (home against Bournemouth) and the current form of both Havertz and Arsenal, who were on a winning streak and contending for the title. These variables shift the likelihood of events when considered in isolation.
Looking back, it was likely a high +EV bet, and while the outcome doesn’t prove much due to the small sample size, Havertz did have two shots on target in that match. We must also consider that shots on target will not be evenly distributed across matches, and subjectively evaluate how one shot might correlate with two or more in a single game. I thought the bet on 2+ shots on target could have been even more valuable. I saw odds up to 3.75*, and this shows that it’s not as simple as just multiplying odds to find true value.
(Note: Using Pinnacle’s odds calculator, you can see that -225 in American odds corresponds to 1.444 in decimal.)
EXPECTED VALUE (EV)
Expected value (EV) is a concept that shows how much you’ll win or lose on average in the long term if you place the same bet many times. There are several ways to calculate EV, but we use the following formula: (Probability of winning * potential profit) – (Probability of losing * stake)
Let’s assume that the true odds for the bet would be somewhere in the middle, around 1.66*, and we’re getting 2.00*. In this case, the EV for the bet would be about 20% if those theoretical true odds are correct. Your expected value (EV) here would equal your return on investment (ROI) over time. Later, we’ll look at how much to bet to optimize the value.
The same concept surfaced on Twitter later that week. There was a discussion about whether to take a bet at 1.66* if you can bet at 1.33*—a very similar situation to what was mentioned above. I added my thoughts to that conversation and will now expand on both the theory and math here.
Simple odds math shows that -300 odds imply a 75% chance of winning (300 / (300 + 100) * 100). To calculate the implied probability of American odds, use the following steps: if the odds are positive, use the formula: 100 / (odds + 100) * 100. If the odds are negative, use the formula: odds / (odds + 100) * 100.
(Note: Using Pinnacle’s odds calculator, the math is done for you. We see that -300 in American odds corresponds to an implied probability of 75%.)
When the odds are -150, it implies that the probability of the event happening is 60%. The EV for this bet, using the same formula and method as above, is 25%. The publication was interesting and useful! Would you like to get predictions for a football match? Follow the link https://odds2win.bet/predictions/football and check out the latest analysis for upcoming football matches. Bet wisely!
KELLY FORMULA AND VARIANCE
I mentioned optimizing value, and there’s a formula known as the Kelly Criterion, which helps with this.
Kelly betting formula: F = bp – q / b, where:
- F is the fraction of your bankroll you’re advised to bet.
- b is the net fractional odds received on the bet (e.g., 0.66),
- p is the probability of winning,
- q is the probability of losing, which is 1 – p.
If we use this formula for the bet, it suggests a bet size of 37% (0.37) of your bankroll. Experts prefer to use a fractional Kelly method, often betting 30% of Kelly. Using 30% of Kelly, we get a recommendation to bet around 11% of our bankroll, which seems more reasonable for a bet with a 75% chance of winning. This helps manage variance and bankroll volatility.
VARIANCE—THE DIFFERENCE BETWEEN SHORT-TERM AND LONG-TERM RESULTS
Variance is the difference between short-term and long-term results. We need to consider how often we can find such bets and if the bet size is sufficient to justify the edge.
For smaller bettors, it might not be feasible to take full advantage of this edge. However, for larger bettors, it becomes profitable in the long run. By the way, if you’d like to test your sports knowledge and analytical skills, we recommend visiting the bookmaker rankings via this link: https://odds2win.bet/bonuses/pakistan and claim a personal bonus for your first deposit from one of the reliable sports betting sites.
HOW TO IDENTIFY IF YOU HAVE AN EDGE IN BETTING
We need to assess the difference between the implied probabilities in the odds and the true odds. My experience in poker helps in this regard, as table dynamics shift conditional probabilities. In my book Hypnotised by Numbers, I talk a lot about conditional probability.
Conditional probability is defined as the probability of an event occurring given that another event (based on assumptions or evidence) has already occurred. This can be key to unlocking betting markets and becoming a profitable bettor in cross-sports.
RISK ANALYSIS—THE ABILITY TO ASSESS PROBABILITIES ACCURATELY
Risk analysis is the ability to assess probabilities accurately. It’s a process where some people can process all the variable information in their minds, like a computer iterating, and turn it into probabilities.
This betting approach is known as bottom-up analysis.
CLOSING LINE VALUE (CLV)
In betting, there’s a concept known as closing line value (CLV). We can use Pinnacle’s closing line to improve our skills in evaluating the value of bets and the accuracy of market prices with this concept.
The better we become at evaluating line movement, the closer our CLV should correlate with our expected value and ROI in the long term if our assessments of true odds are correct (assuming no commission). A simple way to remove the vig from an odds line is to divide the implied probability by the bookmaker’s total percentage and multiply by 100.
We can use this formula (with decimal odds) to calculate CLV: (X-Y) / Y * 100, where:
X = the decimal odds you bet at
Y = the closing line decimal odds
To convert American odds to decimal, just divide 1 by the implied probability of the American odds. Pinnacle’s odds calculator can do this for you.
In the U.S., this approach is called top-down betting.
CONCLUSION
The lower the odds and the higher the implied probability of winning, the faster you realize your profits and reduce variance. This is why professional bettors like good +EV bets at low odds.
The moral of the story is that, in theory, getting 1.66* on an event you rate at 1.33* (or similar) is a golden opportunity for large professional sports bettors. The challenge is finding enough of these bets to make money on them.