Quantum Slot

Big wins and useful evidence are different

Use BIG, REG and small-win counts to infer a hidden setting from six candidates. Try a few automatic stops, then inspect the posterior below.

Instructions, probabilities and how to read your results

How much can the outcomes tell you about a hidden setting?

The exercise is to separate the number of observations from the strength of your conclusion. The machine selects one of six settings, each with slightly different probabilities for BIG, REG and small wins. Count outcomes, compare the six bars in the posterior, then reveal the answer. This learning game combines a browser probability model with hardware-derived randomness when it is available.

Playing requires JavaScript; this guide and the probability table do not. The game includes sound and flashing effects. Use the sound button above to mute it.

A three-minute first exercise

1. Pull the lever and let the reels stop automatically. You can also press the three STOP buttons. Watch the spin, BIG, REG and electron counts. Pressing the left STOP manually can miss a small win, depending on your timing.
2. Read the randomness source below the result. It identifies IBM, QuTech or local randomness for that spin. A result labelled local should not be treated as a hardware measurement.
3. Compare the six posterior bars. They start at about 16.7% each and change with your observations. The longest bar is the candidate with the strongest relative support within this model, not a guaranteed answer.
4. Write down one reason for your guess, then reveal the setting. Did you use BIG, REG or small wins as evidence? Similar bars after a short session are a useful result too: the observations may be insufficient to distinguish such small differences.

Reading the displays

• COMBINED divides the spin count by the total BIG and REG count. One bonus in 100 spins reads 1/100. This is an observed frequency, not the machine's theoretical probability.
• The slump graph tracks the change from the initial 300 coins. ● marks BIG and ○ marks REG. Mode costs and CZ outcomes also affect your balance, so an upward graph alone does not identify a setting.
• ERROR is a game-model noise rate calculated from the cooling gauge. It is not the current failure rate of a physical device or the accuracy of that spin's hardware measurement.
• The small-win collection rate η accounts for missed observations. The posterior adjusts the small-win probability by η, but does not model every effect of the game's noise.

Worked example: does no BIG in 100 spins imply setting 1?

No. With independent draws, the probability of no BIG in 100 spins is (1 − P(BIG))¹⁰⁰. Using the ideal probabilities below gives about 69.3% for setting 1 and 67.5% for setting 6. That observation is common under both settings and offers little separation.

The information table compares these differences using KL divergence. Small wins pay less per event but occur frequently; they carry more information than BIG in this model. The displayed spin count is the estimate log(100)/KL. Each outcome is treated as a separate binary event, and the summed “all three” row is also an approximation. These are not guaranteed stopping times or a strategy that always identifies the setting.

What changes between quantum and classical modes?

Quantum mode costs three coins per spin, adds modelled noise to the third reel and charges the CZ gauge. Classical mode costs two coins and omits that noise step and the CZ. Both modes use the same route to obtain their initial random draw. Selecting classical mode does not force local randomness. The cost difference is a game-design choice, not a benchmark of real quantum computing speed or expense.

In the CZ, inspect the probability before iterating

When the gauge is full, the CZ lets you explore the probability formula for Grover search with one marked item among eight: P(k) = sin²((2k+1) asin(1/√8)). The browser calculates it; Iterate increases k. The probability is 12.5% at k=0, about 78.1% at k=1, 94.5% at k=2, then 33.0% at k=3. More iterations are not always better. Stop here performs a local random draw using the displayed probability. This feature does not run a search on quantum hardware.

Where hardware data ends and the game model begins

The randomness API uses stored IBM Quantum or QuTech bits when available and falls back to local randomness otherwise. The browser also falls back when data has not arrived or a request fails. Clicking does not launch a new hardware job. Noise, visual effects and the CZ use additional local randomness.

The θ shown when you reveal a setting is calculated from the BIG probability as θ = 2 asin(√P). The game does not send a newly rotated circuit to hardware on each spin. Inferring one of six candidates is an example of statistical estimation, not an implementation of general quantum state tomography.

The hardware-bias table counts the bits left in each pool. The Bell panel displays a separate CHSH measurement returned by the API. A finite sample's bias does not identify the cause of hardware error, and an S value above 2 alone does not establish a loophole-free Bell experiment. Interpretation also requires measurement conditions and statistical uncertainty.

Session state and references

Spin counts, coins and the hidden setting belong to the current page session. Reloading starts a new machine. RP uses a separate mechanism, so it should not be assumed to reset in the same way.

This guide was checked against the public calculation code, randomness and fallback code and interface code on September 23, 2026. For the underlying theory, see IBM Quantum Learning on choosing Grover iterations and entanglement and CHSH.

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