Beer Pong Calculator (cups in the rack, expected throws & chance to clear)

Understanding the beer pong calculator — concept and principle

This calculator works out how many cups are in a triangular rack, how many throws you can expect to need to clear it at your hit rate, and the chance of clearing it within a given number of throws. It is a fun way to see probability in action.

Triangle of cups: with the default inputs the result is 19.7% (≥ 10 hits in 30 throws).

How it is calculated

Cups c = r × (r + 1) ÷ 2 for r rows

Expected throws = c ÷ p, where p is the hit rate

Chance to clear within N throws = Σ (k = c…N) C(N, k) × p^k × (1 − p)^(N − k)

Expected cups hit in N throws = N × p

The principle

A triangle of r rows holds a triangular number of cups. If every throw hits with the same probability and each hit removes one cup, the number of throws to clear the rack follows a negative binomial distribution with mean c ÷ p. Clearing within N throws means getting at least c hits in N independent tries, which is a binomial probability.

Worked example

Default inputs: 4 rows, 25% hit rate, 30 throws.

Cups = 4 × 5 ÷ 2 = 10.
Expected throws = 10 ÷ 0.25 = 40; expected turns (2 throws each) = 20.
Expected hits in 30 throws = 30 × 0.25 = 7.5.
Chance of at least 10 hits in 30 throws = 19.7%.

Each point is the calculator re-run with only “Your hit rate per throw (%)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Your hit rate per throw (%)	Expected throws to clear all cups
6.25	160
12.5	80
18.8	53.3
25	40
31.2	32
37.5	26.7
50	20

How to read the result

Because 30 throws is fewer than the 40 expected, clearing the rack is unlikely, about one chance in five. Small changes in hit rate make a big difference. House rules such as re-racks, bounce shots and balls back are ignored.

Common mistakes

Assuming a constant hit rate when players tire or improve.
Forgetting that the other team's defence changes outcomes.
Confusing expected throws with guaranteed throws.

Keep in mind: Play with water if anyone is under the legal drinking age or will be driving. Drink responsibly.

Frequently asked questions

How many cups in a standard rack?

Ten, in four rows.

Why is the expected number of throws c ÷ p?

Each cup takes on average 1 ÷ p throws to hit.

Does the order of hits matter?

Not for this calculation; only the number of hits counts.

Sources: Ross SM, A First Course in Probability, Pearson (binomial and negative binomial distributions)

Checked 9 Nov 2026. Triangular numbers for the rack; binomial and negative binomial distributions (standard probability). The hit rate, number of throws and fill are example values.

Your numbers