Random Lot Picker

A uniform integer interval

The picker samples one integer from 1 through n, inclusive. For n lots, P(selected lot = j) = 1/n for every permitted j. It assumes the numbering is continuous, every number represents one eligible item, and no number carries a hidden extra chance.

A numbered ticket example

With 20 lots, ticket 13 has probability 1/20 = 5% of being selected. If a second prize is drawn after ticket 13 is removed, there are 19 remaining tickets and each remaining ticket has probability 1/19 for that second prize. Leaving 13 in the pool instead would allow the same ticket to win twice.

Numbering is part of the model

The tool does not know whether lot 7 represents one apartment, ten raffle entries, or a missing ticket. If a participant owns three tickets, give that participant three separate numbers deliberately; do not assume a single number somehow represents three chances.

Avoid rejection after the fact

A common failure is to redraw because the selected number looks inconvenient. That changes a fair selection into a conditional process. If some numbers are ineligible, exclude them before the draw or renumber the eligible set so the published range matches the actual pool.

What this picker cannot express

A single integer draw cannot choose a weighted option, make a ranked order, or distribute several non-identical prizes. Use a weighted selector when chances differ and a shuffle when each ticket must be ordered without repeats. This page is intentionally limited to one equal-probability numbered selection.

A pool check

Count the physical tickets or eligible records against the upper limit. If the sheet has lots 101 through 120, either map the displayed 1 through 20 result to that range beforehand or relabel the tickets. Treating a number as self-explanatory is how an otherwise uniform selection is misapplied. A signed ticket list also makes it possible to demonstrate that no eligible number was silently omitted. Keep that list with the selection record. Where ticket numbers are not consecutive, make a lookup table rather than drawing an integer and skipping a rejected number: skipping changes the process and can make the published upper limit misleading.

A number needs a published meaning

A draw result such as 13 has no practical effect until the ticket register says what 13 represents. In a raffle it might identify an entry; in a warehouse it might identify a shelf; in a housing allocation it might be only a queue position. Keep the mapping stable between the published pool and the result. Changing it afterwards is not a correction to the random number; it changes the allocation.

Sampling one label from a documented frame

A numbered lot is a finite sampling frame: the complete list from which a selection may be made. NIST describes simple random sampling as giving every response an equal chance of observation; the same discipline applies here. A range of 1 through 20 represents twenty possible labels only if the register actually contains those twenty eligible entries. Missing lot 8 or adding a second owner behind lot 14 changes the frame, not the random-number calculation. Publish the eligible register before drawing, then retain it with the result.

Three prizes require a removal decision

Take a raffle of 20 tickets with prizes worth $100, $50, and $25. If ticket 13 wins the first prize and is removed, each of the other 19 tickets has a 1/19 chance of the second prize. A remaining ticket such as 7 has probability (1/20)(1/19)(1/18) of receiving the exact ordered sequence of all three prizes, but it has a 3/20 chance of receiving any prize because three distinct winning positions exist. If repeat winners are allowed, ticket 13 stays in the interval for every draw and may win all three prizes. State that choice before the first number appears.

Intervals are poor proxies for weighted claims

Consecutive numbers are excellent for equally eligible tickets, queue positions, or uniquely numbered records. They are misleading when an entry has a different entitlement. A donor with five valid entries needs five separately recorded ticket numbers; putting their name beside one number silently turns five chances into one. Conversely, giving someone five arbitrary numbers because they are a friend is a weighting rule and should be visible to everyone. This picker cannot audit the fairness of the register, verify identity, or decide eligibility after a dispute. Those controls belong around the draw, not inside an integer result.

Handle void numbers before selection

If lots 4 and 17 were withdrawn from a numbered run of 1 through 20, do not draw from twenty and reroll when either appears. The transparent approach is to build the eligible list of eighteen labels and select one position from that list. A reroll can be fair if it is announced and repeated consistently, but viewers no longer see a one-step 1-to-18 procedure, and an operator must record every rejected result. Renumbering or a published lookup table is easier to audit.

Record the selected label exactly

Write “lot 13” rather than only the winner’s name. The label connects the public result to the published register and makes later checking possible even if two entries have similar names. That precision costs nothing and avoids an avoidable identity dispute.

Map labels before using a numbered interval

A uniform integer picker is reliable only when the mapping from numbers to eligible entries is fixed. Suppose a raffle sheet lists tickets 101 through 120. A displayed 1 can mean ticket 101 by the rule “add 100,” and a displayed 20 can mean ticket 120; each physical ticket then has probability 1/20. If ticket 114 was voided, drawing from 1 through 20 and simply skipping 14 is not the same process. One response may cause a redraw, so the final probabilities and the audit record depend on how that redraw is handled.

Questions about this selection

Other chance methods

All coins and lots tools · Draw Straws · Rock Paper Scissors