This page’s goal is to educate readers about expected value (EV) and its connection to casino deposit bonuses. While there is no shortage of sites that list the latest bonuses, I’ve yet to come across one that explains the EV of bonuses.

Knowing the expected value (EV) of gaming bonuses is helpful since it indicates whether or not the bonus is a good bargain. You’re leaving money on the table if you blindly accept deposit bonuses without analyzing their expected value.

If I ever mention the EV next to a bonus description on the blog, you’ll know exactly what I’m talking about now that you’ve read this article.

## Expected Value: A Very Short Introduction

In probability theory, the idea of expected value is used to characterize the typical result of a random occurrence. Expected value is used to estimate the long-term success of a bet or situation in a gambling context.

If the anticipated value of a gamble is positive (+EV), then the gamble is lucrative over the long run. The expected value of any gambling game can be determined with only two pieces of data:

probabilities of each possible result

Possible Payouts for Each Outcome

That data will tell you whether or not a particular gambling game, bet, or bonus is worth your time and money. What’s more, you can calculate the exact return on investment for that game.

## Assume a coin flip.

Let’s use the analogy of a coin toss to illustrate. Let’s pretend I’m making you a bet on a coin toss. If it comes up heads, you get $1 from me, and vice versa if it comes up tails. You can probably see right from the off that this is a game of equal odds, in which you face no distinct advantages or disadvantages.

In any case, let’s spend a moment on the math to show how expected value is computed and how to read the results.

We are aware of the probabilities associated with each of the two outcomes in this game. The monetary value of each possible result is also known to us. So now we know everything we need to.

Outcome Probability Payout Heads 1/2 $1 Tails 1/2 -$1

Next, we total up all of the probabilities by multiplying them by their respective payouts:

(1/2)*1 = .5

+

(1/2)*-1 = -.5

Total: 0

The game has no intended value. That means you can hope to finish even with the game in the long run. Keep in mind that a coin flip can never result in a loss of zero dollars. It’s always a $1 victory or a $1 loss. In a similar vein, it’s unlikely that you’ll come out ahead after 10 tosses of the coin. Varying conditions lead to unpredictable outcomes in the short term.

However, if we play this game many times, your actual results will converge on zero.

Don’t be put off by how wordy this straightforward example is. I have a propensity for wordiness. There is no complicated arithmetic involved in the idea itself.

The Use of Expected Value in Gambling

For those who enjoy gambling, this is the fun part. The anticipated value of each casino game may be calculated with a little bit of math. Two things are absolutely crucial for you to understand:

The sum of all bets you intend to make

The inherent casino advantage

Multiplying your expected stake by the house edge gives you the expected value of each casino game. Assume, for the sake of argument, that you are playing a slot machine with an identical 5% house advantage. Also, let’s assume you’ve set aside $1,000 to wager on 1,000 spins of the slot machine.

You’re prepared to risk a total of $1,000 on your bets. Add 5% to that:

$1,000 x 0.05 = $50

This game has a negative expected value of $50. In the long run, if you put $1,000 into this slot machine, you will lose $50.

It blows my mind how easy this computation is. Every casino game’s house edge can be found on various websites. To calculate the expected return, simply find the house edge for the game you want to play and multiply it by the entire amount you plan to risk.

How you play can change the house advantage in various games. The house edge in blackjack, for instance, is very sensitive to player strategy. The house edge in blackjack can be lowered to as low as 0.5% with skilled play. The house edge in blackjack skyrockets if you play poorly.

Implications for Pay Raise Plans

This means that if you have the following data, you can calculate the value of any casino bonus:

The minimum and maximum bets

Gambling house edge on the game you plan to play Bonus size

Always check the wagering requirements before accepting a casino bonus. Calculate the precise amount of wagering required to release the bonus. The next step is to research the house edge of the game you intend to use to earn the bonus.

Then, simply multiply the required wager amount by the house edge of the game in question. If you want to play a game with a 2.7% house advantage but you can’t risk less than $60,000, here’s what you do.

$60,000 x .027 = $1620

In order to earn the bonus, you’ll need to spend $1620. While your individual results may vary significantly, this is the estimated price tag in the long run.

Think of that sum in relation to the potential bonus payout. If the incentive is $2,000, you would take the $1,620 you lost and apply it toward the remaining $1,800, for a total of $380.

## This bonus is worth an estimated $380.

The bonus in this case is rather reasonable. Hooray! Bonuses aren’t often as large, though. For this reason, it’s instructive to be familiar with the connection between bonuses and expected value.

For a more in-depth discussion of how to determine the EV of bonuses, please refer to this blog post.

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