What this calculator works out
This calculator works out the expected value of entering a prize draw — the prize multiplied by your chance of winning it — and compares that against what the entries cost.
Expected value is what a very large number of identical entries would average out to. For almost every commercial draw it is negative, and the page explains why that is the design rather than a flaw.
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Before you read the result
- Prize value should be what the prize is worth to you, not its advertised retail price. A holiday you would not otherwise take is worth less than its ticket price.
- The calculation assumes a single prize and equally likely entries.
- A negative expected value is normal. The gap funds the prize, the promoter and, for charity draws, the cause.
- Expected value describes an average over many repetitions, not what will happen to you.
An expected value of −£0.50 does not mean you will lose 50p. It means that across a very large number of identical entries, the average outcome would be a 50p loss per entry. Any individual entry either wins the prize or wins nothing. The figure is a way of comparing offers, not a forecast.
How this calculator works
Probability times prize, against the cost:
Probability = your entries ÷ total entries
Expected value = prize × probability
Spend = cost per entry × your entries
Net = expected value − spendWhere a promotion offers several prizes, the expected value is the sum of each prize multiplied by the chance of winning it — a calculation this tool does not perform, so it will understate the value of a multi-prize draw.
Free entry routes, which many UK promotions must offer, have a spend of zero and therefore a positive expected value however small the chance.
Worked example: a £500 prize
Using the default figures — a £500 prize, 1,000 total entries, £1 per entry, buying 1:
- Chance of winning: 0.1%
- Expected value: £0.50
- Spend: £1.00
- Net: −£0.50
Half the ticket price comes back as expected value; the other half funds whatever the draw exists to fund. That ratio is typical and is not a criticism — a charity raffle returning 50% as prizes is doing exactly what it says. What the figure does is let you compare draws consistently, and notice when one returns far less than that.
Common mistakes
- Reading expected value as a prediction. It is a long-run average, not your outcome.
- Using the advertised prize value. Use what it is worth to you.
- Expecting a positive result. Paid draws are designed to return less than they take.
- Ignoring the free entry route. Where one exists, it changes the arithmetic entirely.
- Buying more entries to improve the expected value. It scales the loss as well as the chance.
Frequently asked questions
Why is the expected value always negative?
Because the draw has to fund something. A commercial promotion funds marketing and profit; a charity draw funds the cause; a lottery funds prizes, good causes, duty and operating costs. If the expected value were positive, the promoter would lose money on every entry. This is a structural feature, not evidence of anything improper.
What about free entry routes?
Many UK promotions must offer a free way to enter, usually by post, to stay outside lottery licensing rules. A free entry has no cost, so its expected value is positive however small the chance. Promoters are required to treat postal entries equally, and the free route is frequently under-used.
Does this apply to premium rate entry?
Yes, and it is worth calculating. Entry by premium rate call or text carries a cost that should go into the spend figure, including any additional network charges. Those costs are often larger than they appear and are a common reason a draw's expected value is far below its headline.
How should I think about buying entries?
As entertainment or as a donation, with a budget set in advance, rather than as an investment. If you would be unhappy to lose the money, the expected value tells you that losing it is the most likely outcome. If gambling is causing difficulty for you or someone you know, the National Gambling Helpline is free and confidential on 0808 8020 133, and GambleAware provides advice and support.
Is what I enter stored?
No. Figures are processed in your browser and never transmitted or retained.
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References
- Gambling Commission — rules on prize draws, free entry routes and lotteries
- GambleAware — free confidential advice and support on gambling harm
Sources are checked at publication and can change — how I choose and check references.