Bingo

How to play 75-ball bingo

A card is a 5×5 grid. The B column holds five numbers from 1–15, I from 16–30, N from 31–45, G from 46–60 and O from 61–75. The centre square is free and starts daubed, so a card carries 24 numbers, not 25.

Balls are drawn one at a time and called by letter and number — B 7, O 64. If a called number is on your card, daub it. When your daubed marks complete the pattern that was called for the game, call bingo. In this hall a winning card in the room is held until the next ball would be drawn, so you always get the whole of a ball's interval to spot your own and call it first — but the moment a card in the room completes the pattern, the room calls, and a bingo you had and did not say is theirs.

Two small mercies, both deliberate. The current ball is yours to find; anything older that you have missed is ringed in red on your card, so the board can never tell you that you are one away while your card visibly disagrees with it. And if you would rather not scan at all, auto-daub is a checkbox in the rail — marking a called number is data entry, not a decision, and we are not going to pretend otherwise in order to invent a skill this game does not have.

Is online bingo rigged? The only answer worth giving

Every online bingo room on earth gets accused of steering the balls — of holding the jackpot until the room fills, of letting the house card get there first. And every one of them answers "our RNG is certified", which is a claim about an audit you did not see, of software you cannot read. It is not checkable, so it is not an answer.

Here is what this page does instead. Before the first ball we generate a server seed and publish its SHA-256 hash. You supply a client seed — anything you like — and because our commitment is already locked, we cannot go shopping for a server seed that suits us. The entire 75-ball order is then a pure function of those two seeds: not of how many cards are in the room, not of how you are doing, not of whose card the house is holding. It is fixed before ball one. When the game ends we reveal the server seed, and you can hash it, check it against the commitment you were shown, and re-derive all 75 balls on our verifier page. Change one ball and the seeds stop reproducing it.

One technical honesty note, because we would rather state it than have someone find it. The ball order is drawn from the same die stream fair.html verifies, using rejection sampling rather than a modulo shortcut — 6ⁿ is never a multiple of 75, so die % 75 would make low numbers come out first slightly more often, which is precisely what the accusations are about. A consequence is that the published die log is not a minimal encoding: a die that fed a rejected sample decides nothing, and changing it would leave the 75 balls identical. That is not a hole, because the proof runs the other way — the balls you were called are a deterministic function of the committed seed, and altering one is always caught.

The number every bingo site hides: your actual odds

Your share of the win is exactly the number of cards you hold divided by the number of cards in the room, with ties split. Two cards in a thirty-card room is 6.7%. There is no strategy term in that expression, no dauber-speed term and no lucky-card term, and this board prints it on screen the whole time you are playing.

It follows from a symmetry that is worth spelling out, because the folklore says otherwise. The expected time for a card to reach a pattern depends only on the shape of that pattern, never on which numbers are printed on the card: the draw is a uniform random permutation of 1–75, and any card's numbers can be mapped onto any other card's by a permutation that preserves the column ranges. Every card in the hall has the identical win-time distribution. Tippett's theory — prefer numbers near the middle in a long game — is a statement about which card to buy and it does not survive contact with a uniform draw. Our test suite asserts this rather than arguing it.

The three rules people argue about

1. The free space counts toward a line. It is already daubed, so the middle row, the N column and both diagonals need only four called numbers. In our engine that is structural, not a special case: a card's marks are a 25-bit mask whose centre bit is permanently on. The measurable consequence — of the 10,626 four-number subsets of a card, exactly four are a bingo, and they are exactly the four lines through the centre. And a blackout needs 24 numbers, not 25.

2. Four corners is not a line. It is a separate declared pattern and it never touches the free space at all, so it needs four called numbers of its own. In a plain "any line" game, a player holding the four corners has nothing. It is also much slower: 60.8 balls on average against 41.37 for any line.

3. Two cards can bingo on the same ball. The order is fixed in advance and shared by every card in the room, so simultaneous wins are ordinary rather than exotic — with a handful of cards in play they happen constantly. Our engine returns a list of winners and flags the tie instead of silently picking one, because nothing in the rules entitles it to choose. Splitting the pot, or awarding it to the first shout, is a house policy decision, and an engine that quietly picked a winner would be hiding a payout.

What the board tells you that no other bingo screen does

A hall player tracks one thing in their head all game: how close am I, and to what. Every online bingo product refuses to do that arithmetic for you, and there is no reason for it beyond habit. This board prints the answer above your cards and updates it on every ball: "1 TO GO — B 7 · N 38 · O 64 wins · 3 of the 41 balls left", with those cells lit on the card itself. When you have the pattern, it says so and the call button lights up.

It also shows what a hall cannot: how many cards in the room are one away. That is the pressure you are actually under, and hiding it would not be more realistic, only less honest.

Strategy, and why there is none

There is no decision to make in bingo. You do not choose your numbers, you do not choose when to stop, and marking a number that was called is data entry, not a choice. Whether you win was settled the moment the balls were shuffled. The only lever that exists is how many cards you hold, and that is not skill — it is buying more tickets, and it scales your share linearly and no faster.

So the only thing you can get wrong on this page is not noticing you had it. That is attention, not strategy, which is why the board shouts when you are one away and auto-daub is one click away in the rail. A page that turned a lottery into a reflex test and called the result skill would be lying twice.

Questions people ask

Is online bingo rigged?

On almost every site you cannot tell, and that is the honest answer — "our RNG is certified" is not something a player can check. This one is committed before the first ball and verifiable afterwards from seeds you half-supplied. That is a different claim, and it is the only one we are willing to make.

Does the free space count?

Yes — any line through the centre needs only four called numbers, and a blackout needs 24 rather than 25.

Are some cards luckier than others?

No, and it is provable. Every card in the hall has the identical win-time distribution, because the draw is a uniform permutation and the columns are interchangeable within their ranges. Tippett's theory is folklore.

How many balls to a bingo?

On one card, any line: exactly 8491934/205275 = 41.3685738643… balls on average. Four corners, exactly 60.8. Blackout, exactly 72.96.

How many bingo cards exist?

111,007,923,832,370,565 counting each column as a set — C(15,5)⁴ × C(15,4), the N column taking only four numbers because the centre is free. Counting the order within a column as well gives 552,446,474,061,128,648,601,600,000.

Can two people win at once?

Yes, constantly. Our engine reports every winner and flags the tie rather than choosing.

Is this free?

Yes. No signup, no ads, no video between games, no daily limit, no coin economy, no power-ups and nothing to buy — and no leaderboard either, because a bingo high score ranks luck.

The honest small print

The draw is commit-reveal over the same die stream fair.html verifies, so no new trusted code stands between the seeds and the balls; if fairdice.js fails to load, the game still runs from a seeded generator and the rail is labelled unverified rather than showing a badge we cannot back. The other cards in the room are ours, dealt from the same shuffle as yours, and they are cards rather than opponents — there is no bot here because there is nothing for a bot to decide. Win counts are kept in your own browser only. Published figures on this page — the card count, the exact expected-ball rationals and the four-subsets-that-are-a-bingo result — are derived from scratch in bingo-engine.js and asserted in tools/bingo_test.mjs, not quoted on trust; the chi-square check on the draw is proved to bite by sabotaging the sampler with a modulo shortcut and watching the gate fire.