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Reading the maths
An average is not a session forecast
Expected value describes a mathematical average. It does not describe the money a particular person will finish with.
The average over possibilities
An expected value weights possible outcomes by their probabilities. For example, a hypothetical event paying £2 with probability one quarter and £0 otherwise has an expected gross payout of 50p. If each attempt costs £1, the expected net result is a loss of 50p per attempt. Neither possible gross payout is actually 50p.
Describe the whole model
Write down whether a payout includes the returned stake, what each attempt costs and whether the probabilities remain fixed. These details change the calculation. A precise-looking number is unhelpful if readers cannot reproduce its assumptions.
Use the distinction
A negative expected result is not proof that every short sequence loses. Equally, a favourable short sequence does not change the underlying model. Casino mathematics is useful for recognising uncertainty and cost; it cannot make gambling income dependable. Our examples are educational calculations, not estimates for an identified operator or game.
Methods & sources
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A longer casino session changes more than the average loss
A fixed-stake experiment separates expected loss, cash swings and the chance of finishing ahead. More trials do not turn any of those into a personal forecast.
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One or more is not certainty: the sum, worked in pounds
Over ten independent trials at a fixed 10% chance, the chance of one or more occurrences is 65.13%. Here is the sum, the assumption it rests on, and where it breaks.
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A casino streak looks rarer when you hide the search that found it
Six matching results in a chosen window and six matching results somewhere in a longer record are different events. Count the windows before judging the streak.
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What is the house edge in blackjack: the sum, worked in pounds
The house edge in blackjack is the operator’s share of each £1 staked over a very large number of hands: about 0.28% under liberal rules with basic strategy, and 1.36 points more when blackjack pays 6 to 5. The working, with £10 put through it.
Read What is the house edge in blackjack: the sum, worked in pounds
What is casino house edge and how does it work?
Casino house edge is the share of each £1 staked that the operator keeps on average. It comes from the gap between true odds and paid odds: £10 on red at a single-zero wheel costs 27p, or 2.70%.
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How do you read online casino probabilities without confusing the question?
Separate the chance of an event, the expected count and the value of a payout, with worked examples and an offline probability worksheet.
Read How do you read online casino probabilities without confusing the question?
Continue reading
A longer casino session changes more than the average loss
A fixed-stake experiment separates expected loss, cash swings and the chance of finishing ahead. More trials do not turn any of those into a personal forecast.
Read A longer casino session changes more than the average lossWhat is the house edge in blackjack: the sum, worked in pounds
The house edge in blackjack is the operator’s share of each £1 staked over a very large number of hands: about 0.28% under liberal rules with basic strategy, and 1.36 points more when blackjack pays 6 to 5. The working, with £10 put through it.
Read What is the house edge in blackjack: the sum, worked in poundsA casino streak looks rarer when you hide the search that found it
Six matching results in a chosen window and six matching results somewhere in a longer record are different events. Count the windows before judging the streak.
Read A casino streak looks rarer when you hide the search that found itAt least one: the probability lab
One or more is not certainty: the sum, worked in pounds
What is casino house edge and how does it work?
A casino streak looks rarer when you hide the search that found it
How do you read online casino probabilities without confusing the question?
A longer casino session changes more than the average loss
What is the house edge in blackjack: the sum, worked in pounds