Skip to content
ENExplore Calculators

Bingo Probability Calculator

Work out bingo probability instantly with clear inputs, formula shown and shareable results.

About Bingo Probability Calculator

Each card number has been called with probability calls over pool size, so expected marks are that times the card size; a full house needs every card number among the calls, which is C(called, card) / C(pool, card). Expected marks rise linearly with calls but the full house chance rises far more steeply, which is why games seem to end suddenly after a slow start.

Formulas

Expected marks

expected = card numbers x calls made / pool size

Full card

P(all covered) = C(calls made, card numbers) / C(pool, card numbers)

Worked example

With the default values below, Bingo Probability Calculator returns Squares expected to be marked of 9.600. Change any input above and every figure here is recalculated in your browser.

Inputs used

Numbers in the poolaccepts 2–90
75
Numbers called so farminimum 0
30
Numbers on your cardminimum 1
24

Results

Squares expected to be marked
9.600
Chance any one number has been called
40.000%
Chance your whole card is already covered
0.000000%
Numbers still in the bag
45

Step by step

  1. 1Values used
  2. 2Expected marks
  3. 3Full card
  4. 4Squares expected to be marked= 9.600
  5. 5Chance any one number has been called= 40.000
  6. 6Chance your whole card is already covered= 0.000000
  7. 7Numbers still in the bag= 45

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Bingo Probability figure worked out?

expected = card numbers x calls made / pool size. Each card number has been called with probability calls over pool size, so expected marks are that times the card size; a full house needs every card number among the calls, which is C(called, card) / C(pool, card).

Why does this matter?

Expected marks rise linearly with calls but the full house chance rises far more steeply, which is why games seem to end suddenly after a slow start.

What do I need to enter?

Enter numbers in the pool, numbers called so far, numbers on your card. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.

Related Calculators

Bingo Probability Calculator | Calcrivo