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Expected value

A bet’s average mathematical result over the long run. In casino games the expected value is negative for the player due to the house edge.

Also: expected value · EV · mathematical expectation

Definition

Expected value (EV) is the amount a bet on average wins or loses if the same decision is repeated very many times. It’s calculated as the weighted average of all possible outcomes and their probabilities.

In casino games a player’s expected value is always negative by exactly the house edge — that’s the casino’s business model. Understanding expected value helps you compare games, assess the real value of bonuses and view wins and losses realistically.

Related and sources

See also house edge, RTP and bonus hunting. Source: Expected value (Wikipedia).

Quick facts

Negative for the playerIn casino games
EV = RTP − 100%Relation to RTP
−2.7% of the betIn European roulette

Example: a €1 bet on red in European roulette wins with probability 18/37 and loses 19/37. The expected value is (18/37 × €1) − (19/37 × €1) ≈ −€0.027, i.e. −2.7% of the bet — exactly the house edge.

How to use expected value?

1

Comparing games

A game with a higher RTP means a smaller negative expected value — on average you lose less.

2

Comparing bet types

Within one game bets can differ: in roulette the EV of all standard bets is the same, in baccarat the banker bet is best.

3

Assessing bonuses

A bonus can improve expected value if the terms are mild; with harsh terms it stays clearly negative.

4

Setting expectations

A negative EV means the casino is ahead in the long run — play for entertainment, not earnings.

Frequently asked questions

If expected value is negative, why does anyone win at all?

EV describes the average over the long run. In a short session chance and variance rule — individual players can win a lot even though the average across all players is negative.

Does any casino game have a positive expected value?

Normally no — the house edge is always present. Exceptions arise only from special offers, for example bonuses with very mild terms, and even those are limited by the casino.

Guide

Expected Value (Ootusväärtus): the number behind every casino bet

Expected value is one of the most important metrics for understanding how gambling really works over time. In plain terms, it tells you the average result of a given bet across the long run: how much a player will win or, in the case of casino games, how much they will typically lose for every unit they stake. It is calculated conceptually by multiplying each possible outcome by the probability that it occurs and then adding all of those figures together. The number you get is not a prediction of any single round – it is the value that the actual result gradually converges toward as the number of bets grows, regardless of whether the current session feels lucky or unlucky.

In casino games the expected value for the player is almost always negative, and the reason is the house edge – the mathematical advantage built into every game so that, on average, a portion of the money staked stays with the operator. This is easiest to see through the return-to-player figure, or RTP. If a game has an RTP of 96%, then for every euro wagered the average return is 96 cents, which means the expected value is minus four cents per euro. That does not mean you lose exactly four cents on each spin – a single round can deliver a large win or a total loss. It means that across thousands or millions of bets, the real outcome settles close to that theoretical value.

For players in Estonia, grasping expected value is a genuinely practical skill for informed play. It explains why no betting strategy can turn a negative expectation into a positive one as long as the underlying game math stays the same. Systems such as doubling your stake after a loss do not improve the expected value of any individual bet; they merely reshape the distribution of outcomes, trading many small wins against rare but larger losses. The same logic helps you judge bonus offers realistically: wagering requirements and bet caps directly affect an offer's true expected value, and an eye-catching headline number does not automatically make a promotion good for the player.

A common misconception is that after a long losing streak a win is somehow "due", or that a machine must be about to pay out. In reality each spin is produced by a random number generator and carries no memory of previous rounds, so the expected value applies freshly and identically to every play. It is precisely this independence between rounds that makes a negative expectation so relentlessly consistent over the long term.

Freespin.ee is an independent comparison portal, not a casino operator, and our aim is to help you assess gambling risk realistically. Play only at casinos licensed by the EMTA, remember that gambling in Estonia is permitted from the age of 21, and treat it as entertainment rather than a way to earn money. If you feel your play is slipping out of control, set firm time and money limits and reach out to a support helpline.