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Prize distribution simulator: when do your prizes run out?

Enter your prizes, odds and expected plays. The simulator plays the whole campaign a thousand times in your browser and shows when each prize runs out.

All numbers below are examples. Replace them with your own expected plays and prizes.

Rising: the last day has three times the plays of the first. Weekend peaks: Saturdays and Sundays have twice the plays of a weekday, and day 1 is a Monday. The total number of plays stays the same.

How prizes are given out

Every play has the same chance of winning each prize until it runs out. If more people play than expected, the prizes run out sooner.

Prize 1
Prize 2
Prize 3

How the simulation works

  • Each run plays the whole campaign once, day by day. The result is the spread over all runs, not one guess.
  • Plays per day = your average × the pattern. With variation on, the actual plays each day are drawn at random around that number (a Poisson distribution).
  • Fixed chance: each play draws one random number. It wins prize 1 if the number is below its chance, prize 2 if it falls in the next slice, and so on. A prize that has run out wins nothing.
  • Spread evenly: by the end of day d, quantity × d ÷ days prizes (rounded down) are released. Each play's chance is the prizes left today ÷ the plays expected for the rest of the day.
  • Run-out day is the day the last prize of a kind is won. The median is the middle run; the 10–90% range leaves out the 10% earliest and the 10% latest runs.
  • Check by hand: the chance that a single prize is won within n plays at chance p is 1 − (1 − p)ⁿ. One prize at 1% with 100 plays a day goes on day 1 in about 63% of runs.

A simulation shows what can happen with the numbers you enter, not what will happen. The random numbers come from your browser and nothing is sent anywhere. To work out the chance per play from your prizes, use the prize odds calculator. In Scratcher, you set the quantity and odds of each prize and choose when prizes can be won.

Why simulate an instant-win campaign

In an instant-win game, people see right away if they have won. Each prize has a quantity and a chance per play. The average is easy to work out: plays × chance = expected wins. But the average hides the spread. With 3 main prizes and 7 expected wins, the prizes do not run out on the same day every time. Sometimes they go on day 2, sometimes on day 9.

A simulation plays the campaign many times with random numbers, as real players would. It then shows the spread: the day a prize runs out in a typical run, how early it can go, and how often some are left at the end.

Fixed chance or spread over the days

With a fixed chance, every play has the same odds until the prize runs out. It is simple and fair for each player. The risk is timing: if more people play than you expect, or the chance is a little too high, the best prizes are gone in the first days. People who play later can only win the small prizes.

When prizes are spread over the days, each day has its own share. The chance per play adjusts to the prizes left that day and the plays still expected. The prizes last the whole campaign, which suits advent calendars and campaigns that run for weeks.

How to read the results

  1. Runs out (median): in half of the runs, the prize is gone by this day.
  2. 10–90% of runs: the range that covers most runs. A wide range means the timing is mostly luck.
  3. Runs with prizes left: how often some of the prize is never won. That can be fine for discount codes, but not for a main prize you have promised.
  4. The chart: the median share of each prize left after each day, with a band for most runs.

If the main prize runs out early in most runs, lower its chance. A good starting point is quantity ÷ total expected plays, which the advice under the results works out for you. Read more about the choice between the two mechanics in instant win or prize draw.

Set prizes and odds in Scratcher

In Scratcher, you set the quantity and the chance of each instant-win prize, and choose when prizes can be won. See prizes and winners. To work out the odds from the number of prizes and plays, use the prize odds calculator.

Questions

Questions about simulating prizes

Book a meeting

  • It plays your instant-win campaign many times with random numbers, using your prizes, odds and expected plays. It then shows when each prize typically runs out and how much that varies.

  • The average is the middle of a spread. With a fixed chance, luck can bring several wins close together. The 10–90% range shows how early a prize can go in an unlucky run.

  • 1,000 runs give stable medians and ranges for most campaigns. Run 10,000 if the numbers change noticeably between two runs, for example with very rare prizes.

  • Lower its chance, so the expected wins over the whole campaign match the quantity: chance = quantity ÷ total expected plays. Or spread the prizes over the days, so only a share can be won each day.

  • No. The simulation runs in your browser, and nothing you enter leaves your device.