BigBunny Expected Value: What Each Peso You Stake Costs

Expected value is the average result of a bet: take every outcome, multiply it by its probability, and add the products. A positive number would mean the bet pays you over time and a negative one means it costs you, and casino games sit below zero by design. A few lines of arithmetic show how much, which is the number behind every decision in the know when to stop rules.

The formula for expected value

Expected value is the sum of outcome times probability for every outcome. Two outcomes make a short sum, for example: win a stake or lose it.

1. List every outcome and what it pays or costs.
2. Write the probability of each, so that they add to 1.
3. Multiply each outcome by its probability.
4. Add the products together.

The result is the average per bet over a very long run, not what the next bet will do. Why a short run strays from it is in the page on the law of large numbers.

A worked example: even-money roulette

A single-zero wheel has 37 pockets, numbered 0 to 36. An even-money bet such as red covers 18 of them and pays 1 to 1. This is an example on a ₱100 bet with the working shown.

The sum is 100 × 18/37 minus 100 × 19/37, which is -100/37, about -₱2.70 per ₱100 bet. On average the wheel keeps ₱2.70 of every ₱100, because the zero pocket belongs to neither side. On the very next spin you will either win ₱100 or lose ₱100, and the -₱2.70 never actually happens.

The rules and bet types for the wheel are on the roulette page; the term for this built-in gap is explained under house edge meaning.

From a published RTP to a loss per peso

A return to player figure already is an expected value in disguise. The RTP meaning entry says what it measures, and the conversion is one subtraction.

Gates of Olympus by Pragmatic Play shows 96.50% in this site’s game data, and the game has its own page for Gates of Olympus. Here is the example.

1. Expected return per ₱1 staked: ₱0.9650.
2. Expected loss per ₱1 staked: 1 - 0.9650 = ₱0.0350.
3. On a ₱10 spin: ₱0.35 expected loss.
4. On 500 spins of ₱10, which is ₱5,000 staked: ₱175 expected loss.

Your own 500 spins can finish with a bigger loss or a profit. The ₱175 is the centre of a wide spread, and a very volatile game widens the spread further.

What to do with an expected value

Use it to price an evening before it starts. If you plan ₱5,000 of stakes, an RTP of 96.50% prices the evening at about ₱175, and you can decide whether that is worth the entertainment.

• Compare games by RTP and by volatility, not by the look of the reels.
• Stop treating an earlier loss as something a later bet can repair, which is the trap described under the sunk cost fallacy in a losing session.
• Remember a near miss changes none of these figures.
• If the arithmetic stops feeling like a reason to stop, take a cooling off period.

For any table game, open the table’s own info screen and read the payouts before you work out your own sum.