How to Determine Money Amount to be Staked?

In order to earn money at sports betting, you need apply a betting strategy featuring a positive mathematical expectation that is represented by evaluation of average winnings per bet. Nonetheless, it can be quite difficult to determine a sum of money that should be staked in order to obtain the highest benefits. For this, you need understand the concept of utility.

Having been developed in the 17th century, the mathematical expectation (or expected value) shows us average winnings that can be obtained from a single wager. The given concept, however, does not determine a sum of money to be staked by a bettor. That is why ordinary gamblers should be familiar with the expected utility phenomenon.

Mathematical Expectation & Expected Utility

The expected value for betting can be calculated according to the following formula:

EV = po – 1,

where p is winning probability and o is decimal odds offered by bookmakers. The expected value is the most significant indicator to predict possibilities for future benefits or losses of money.

The expected value being established, a bettor should decide how much money he will stake. The 18th century witnessed as Bernoulli concluded that only adventurers decide on how much to risk on the basis of objective mathematical expectation without regard to subjective consequences. The given subjective desirability of what is to be earned or lost is known as utility.

Utility under Uncertain Conditions

You are offered with two chests. The first one contains $5 000, while the second one contains either $10 000 or nothing, with each variant having the same probability level. Now, you have to choose only one chest.

If you choose the first chest, you will obligatory obtain $5 000. If you choose the second one, the consequence will depend upon accident: you will become either $10 000 richer or you will be back in square one. Given such amounts of money, it is not a surprise that most people prefer the reliable first variant.

As for utility, a complete confidence to win $5 000 is obviously better than to risk and stay with nothing. People who prefer certainty, rather than risk under the same expected value rate show the risk aversion.

Optimal Stake Amount

Bernoulli`s method found its continuation in 1956 when John Kelly developed his own way to optimize money management systems and increase benefits (Kelly` Criterion). Criterion practically prescribes gamblers to stake a percentage of their total bankroll. Thus, Kelly Criterion looks as follows:

K = (po – 1) / (o – 1)

So, you can see that it is a slightly advanced variation of the expected value formula.

In fact, Kelly Criterion maximizes the expected logarithmic utility. The main peculiarity of betting under Kelly Criterion is represented by a significant profits variability that is not suitable for all the gamblers from the point of view of utility. Besides, the given criterion makes bettors precisely calculate true probability levels.

Notwithstanding, Kelly Criterion technically lets successful punters maximally increase the amount of their future bankroll. Of course, it can be performed only if they avoid suspicious bookmakers blocking money management strategies. Finally, it is quite important to find a bookmaker that will not limit stakes after several wins in a row.