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Lazy Sports Betting Tactics
How to beat the bookies in the over-under markets
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How to get an edge in betting
How to test the credibility of a tipster`s record
Kelly criterion method
How to use Kelly Criterion for betting
How Weather Affects Sports Betting
Increase Your Chances of Winning Long Term Betting on Sports
Intermediate and Advanced Sports Betting
Common sportsbetting myths
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Choosing a staking method based on your betting profile
Betting staking plans
Value betting explained
Sports-betting- a game of numbers
Market movement in betting
Types of odds explained
European types of bets explained
American types of bets explained
Martingale Considerations in Sports Betting
In-play betting
Accumulator betting
Mobile betting
A Crash Course in Horse Racing
A Crash Course In Sports Betting
American odds versus decimal odds
Bankroll management
Money management in sportsbetting- odds, edge and variance
Basic bet types explained
Paying for Picks
Betting on winning streaks
Betting psychology- a crash course about aspiring professional bettors
Popular Sports Betting Beliefs
Do you make these 9 sportsbetting mistakes?
Does intuition have a place in sportsbetting?
Exchange betting
Randomness in sportsbetting
Fractional versus decimal odds
Home team advantage analised
How bad at sportsbetting are you?
Reasons to Keep Betting Records
How bookmakers make money
How bookmakers work
How do betting exchanges work
Should You Bet on Multiple Sports or Specialize?
How do free bets work
How does luck influence short term betting
How good are betting tipsters
Sports Betting for Beginners
How loss aversion impacts performance
How many sports to bet on
How Much Should You Bet On a Sporting Event?
Staking-one method to improve your betting
How much you should risk per bet?
How Sports Betting Has Changed Over the Last 20 Years
How To Avoid A Big Sports Betting Loss
The art of multiple betting
The history of lotteries
The value of information in soccer betting
Three careers ideally suited to betting
Tips for Better Sports Betting Results
Types of Online Sports Betting Bonuses
Understanding and managing your risk of ruin
Understanding Horse Racing Bet Types
Understanding Live Betting
Value betting is an essential skill for bettors
Ways to Increase the Percentage of Sports Bets You Win
What are drawdowns and how to manage them
What are the most common mistakes the bettors make
What are the real chances of winning the lottery?
What distinguishes winning from losing betors
What is a handicap soccer betting?
What is the Fibonacci betting system?
What is the Labouchere betting system
What is the Martingale staking system
Why do we gamble? Irrationality and overconfidence
Why patience is an essential trait for any serious bettor
Poisson Distribution: Predict the score in soccer betting
Fixed Staking vs. Variable Staking
Basketball betting: Bet types explained
7 Sure-Fire Baseball Betting Strategies
How Does In-Play Betting Work?
To Parlay, or Not to Parlay?
Wisdom of the Crowds applied to betting
CASINO ARTICLES
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How to Gamble with Dice – Popular Dice Games and Their Variations
How Online Casinos Helped Me Love Roulette Even More
My Top Three Tips for Getting Comps in Casinos
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5 Gambling Tricks You Can Only Use Online
5 LITTLE-KNOWN FACTS THAT AFFECT YOUR AVERAGE HOURLY LOSS IN A CASINO
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5 Tips to Managing Your Casino Bankroll Effectively
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HOW TO GET YOUR FIRST ONLINE CASINO SIGNUP BONUS
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HOW TO SURVIVE A BLIZZARD AT THE CRAPS TABLE
HOW TO WIN AT ROULETTE
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How to Win Consistently at Craps
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HOW VOLATILITY WORKS IN CASINO GAMBLING
Is It Possible to Play Roulette as a Career (Or Even as a Part Time Gig)?
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MONEY MANAGEMENT STRATEGY FOR YOUR NEXT CASINO TRIP
ONLINE CASINO DISPUTES
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The 5 secret joys of casino gambling
The Benefits of an Online Gambling Environment
The Best Long-Term Strategies for Playing Progressive Jackpot Slots
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How much you should risk per bet?

To win in sports betting you need a betting strategy with a positive expected value, i.e. an estimation of your average winnings per bet. But how much capital should you risk per bet to achieve maximum profits? For this, you need to understand the concept of utility. Read on to find all about it.

Expected value, a concept first explored by French mathematicians Pascal and Fermat in the 17th century when trying to solve the problem of a game of points, shows us how much we can expect to win, on average, from a bet. It doesn’t, however, have very much to say about how much capital a bettor should risk on their bet. Here is where expected utility comes into play. 

Expected value & expected utility explained

Expected value (EV) in betting can be calculated by multiplying your probability of winning (p) with the amount you could win per bet, and subtracting the probability of losing multiplied by the amount lost per bet. Since the probability of losing is equivalent to 1 (or 100%) minus the probability of winning, we arrive at the following simplification:

‘o’ represents the European decimal odds made available by the bookmaker. Expected value is the most important number for any bettor, for it informs them about whether they can expect to make or lose money in the long run.

Once the bettor has found the expected value they must decide how much of their capital to bet. The 18th century mathematician Daniel Bernoulli understood that only the foolhardy make decisions about how much to risk based on the objective expected value without regard to the subjective consequences of the bet, that is to say the desirability of what is to be gained (or lost). This subjective desirability is known as utility.

Utility under uncertainty

We are presented with two chests. The first one contains $10,000 in cash. The second chest contains either $20,000 in cash or nothing; we are unsure which but each option is equally likely. You are now asked to take one of the chests. Which one would you choose? 

This is a classic utility puzzle. Mathematically, both of these chests have the same expected value, that is to say, $10,000. If you could repeat this game over and over again forever, it would make no difference which chest you picked. However, in this game you are only allowed to play once. The law of large numbers does not apply.

If you take the first chest, you are certain to gain $10,000. If you choose the second, what you receive is a matter of chance: be lucky and you’ll be $20,000 richer; unlucky, and you’ll receive nothing. Unsurprisingly, given these sums of money, most people choose the certainty of the first chest.

From a utility perspective, the certainty of $10,000 is surely a lot better than the risk of receiving nothing. People who find greater utility in certainties than in gambles with the same mathematical expectation are demonstrating aversion to risk.

How to calculate the optimal stake amount?

Daniel Bernoulli reasoned that the standard rational behaviour of people when making decisions under uncertainty is risk aversion. He quantified his hypothesis thus: “the utility resulting from any small increase in wealth will be inversely proportionate to the quantity of goods previously possessed.” In other words, the more wealth you already possess, the less utility you will perceive from gaining more. Such a utility function is logarithmic, and more commonly known as the diminishing marginal utility of wealth.

Although using the Kelly Criterion can cause significant volatility in returns, it enables winning bettors to maximize their bankroll over the long run.


One of the more practical applications of Daniel Bernoulli’s theory is a money management plan known to many bettors as the Kelly Criterion. Developed by John Kelly while working at AT&T's Bell Labs in 1956 on solving a problem concerning long distance telephone noise, it was quickly adopted by gamblers and investors as a means of optimising money management and profit growth.

Whilst Kelly’s motivation was entirely different to Bernoulli’s, his criterion was mathematically equivalent to the logarithmic utility function. Practically, it directs a bettor to risk a percentage of his overall wealth on a wager that is both directly proportional to the expected value (EV) and inversely proportional to the probability of success.

Recalling that EV = po – 1 (where p is the ‘true’ probability of success and o the decimal odds for the wager), we can calculate the Kelly stake percentage (K) as follows:


Essentially, the Kelly criterion maximises expected logarithmic utility. One consequence of betting with the Kelly Criterion is a significant volatility in returns, a feature that may not best serve everyone’s utility. Furthermore, its use does require precise estimations of the ‘true’ probabilities of outcomes. 

Nevertheless, Kelly’s approach does technically enable winning bettors to maximise the size of their bankroll over the long term. Of course, to do so a bettor needs a bookmaker that will not be suspicious of specific money management strategies like Kelly and more importantly, will not restrict betting as a consequence of winning.