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Fix the driver behind crashes, sound loss and screen glitchesFind Drivers →Clear out junk files and repair common Windows errorsFree Scan →A run of bad rolls or doubles is not enough to show that a backgammon app is cheating. The defensible approach is to preserve the app’s complete roll record, test each die against the one-in-six expectation, examine pairs and sequence dependence, and then check how the app’s random-number generator is implemented and audited.
Statistics can identify an anomaly, but they cannot by themselves prove deliberate manipulation, cryptographic unpredictability, or that the server did not selectively alter outcomes. Without the app name, version, raw rolls and technical documentation, no honest conclusion about a particular app’s fairness is possible.
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What “biased dice” can mean
“Bias” is often used for several different allegations. Keep them separate because each requires different evidence:
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- Dependence between dice: the first die changes the distribution of the second, so some pairs occur too often or too rarely.
- Dependence over time: a roll is related to previous rolls, a player, a score, a position or another condition.
- Unpredictability failure: an attacker could forecast future output even though the long-run frequencies look normal.
- Selective handling: the app generates a value but discards, rerolls or substitutes it under particular conditions.
- Mapping or scaling error: a uniformly generated number is converted to faces in a way that gives some faces extra probability.
A frequency test addresses only the first question, and perhaps part of the second. It does not establish the others. Treat every statistical result as evidence about a defined hypothesis, not as a universal verdict on the app.
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Start with a complete, unfiltered record
The quality of the data matters more than the sophistication of the test. Use an export, downloadable match history or complete log whenever the app offers one. Do not build a dataset from screenshots or from games you remember because the rolls felt unlucky; that is selection bias.
Preserve the context with every roll
Keep the original record unchanged and make a working copy for analysis. For each roll, retain:
- Both die values and their order, if the app exposes an order.
- A timestamp, match or game identifier and turn number.
- The app version, operating system and platform (web, iOS, Android or desktop).
- The player or account associated with the roll, where relevant.
- Whether it was an opening roll, a normal turn, a resignation sequence or another special event.
- Any score, position or game-state fields supplied by the export.
Opening-roll procedures can differ from normal turns. Keep them as a separate category unless the app documents that they use the same generation path. Record the date and time you downloaded the data so a later app update cannot silently change what the file represents.
Know what an aggregate histogram cannot tell you
If the app displays only six totals in a profile histogram, you cannot independently inspect order, die pairing, timestamps or whether the displayed values cover every game. You may compare the published totals with one-sixth expectations, but state clearly that sequence and completeness could not be checked.
Count each die, not just the combined total
For a fair six-sided die, each face has probability 1/6. Count the first and second die separately whenever the raw data allow it. Counting only sums hides information: for example, a total of seven can be made by six different ordered pairs, while a double has only one pair for each face.
A simple frequency table
For each die, let N be the number of recorded rolls. The expected count for every face is N / 6. Report the observed count and the difference from that expectation rather than relying on a visual impression.
| Face | Expected probability | Expected count | Observed count | Difference |
|---|---|---|---|---|
| 1 | 1/6 | N / 6 |
Count from die 1 or die 2 | Observed minus expected |
| 2 | 1/6 | N / 6 |
Count from die 1 or die 2 | Observed minus expected |
| 3 | 1/6 | N / 6 |
Count from die 1 or die 2 | Observed minus expected |
| 4 | 1/6 | N / 6 |
Count from die 1 or die 2 | Observed minus expected |
| 5 | 1/6 | N / 6 |
Count from die 1 or die 2 | Observed minus expected |
| 6 | 1/6 | N / 6 |
Count from die 1 or die 2 | Observed minus expected |
Analyze the two dice in separate tables first. Combining them can conceal a problem affecting only one die or a difference in how the app generates the two values.
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Do not invent a universal roll threshold
There is no single number of rolls that guarantees detection of every meaningful bias. Required sample size depends on how large the suspected deviation is, the test’s chosen error rate and the completeness and independence of the observations. A small deviation may need far more data than a dramatic one. Collect the full record available and report its exact size instead of claiming that a particular threshold proves fairness.
Examine pairs and the order of rolls
Ordered and unordered dice pairs
If the export identifies die one and die two, examine the 36 ordered pairs. Under independent fair dice, each ordered pair has probability 1/36. If the app records only an unordered combination, use the probabilities for that representation: a double has one possible ordered arrangement, while a non-double has two. Do not treat an unordered log as if it contained ordered data.
Compare pair counts only after checking that the app does not apply a documented rule that changes how opening rolls or special turns are represented. A pair anomaly can arise from dependence between dice, from a recording error or from a biased face mapping; it is not automatically evidence of intentional cheating.
Check for serial and conditional patterns
Look at whether a result appears related to the previous result. Runs tests and serial-correlation checks address aspects of ordering and dependence. You can also stratify by player, match phase, score or position when those fields exist, but decide those comparisons before looking for a pattern. Searching dozens of slices after seeing an unusual result creates a high chance of finding a random “significant” result.
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Keep the primary analysis separate from exploratory checks. If you test many conditions, disclose how many you tested and treat an isolated finding as a lead for new data, not as confirmation.
Use statistical tests with their limits stated
Chi-square goodness-of-fit
A chi-square goodness-of-fit test compares the six observed face counts with the six equal expected probabilities. It evaluates the hypothesis that the recorded observations follow that distribution under the test assumptions. A statistically significant result means the counts are unusually far from expectation for that model; it does not identify the cause.
Before running the test, specify which die, records and time period are included and which significance rule you will use. If you change those choices after seeing the counts, the reported probability no longer describes a pre-planned test. Check that the data are complete enough and that repeated entries, missing rolls or duplicated exports have not distorted the counts.
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Runs and serial-correlation checks
Frequency tests ignore order. A runs test can ask whether a sequence of categories is arranged more regularly or erratically than expected. Serial-correlation checks examine whether one value is related to earlier values. These tests still depend on how you encode categories and on assumptions about independence; a pass does not prove a secure random-number generator.
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- Non-significant result: the data did not provide enough evidence against the tested model. It is not proof that the app is fair, unpredictable or free of selective handling.
- Significant result: investigate the data extraction, special-roll rules, app version, multiple comparisons and implementation before alleging manipulation.
- Short streak: conspicuous sequences occur in random data and are weak evidence by themselves.
In the United States, 25 CFR §547.14 is a concrete technical example that lists chi-square, runs and serial-correlation tests and discusses unpredictability and unbiased scaling. Its scope is the Class II gaming-system context described by that regulation; it is not a blanket rule for every casual backgammon app.
Separate fairness from unpredictability and tamper resistance
An app can produce face counts close to one-sixth while still exposing a predictable generator, using a flawed conversion from random bytes to faces or allowing an operator to replace results. Conversely, a short sample from a sound generator can look uneven. Ask four separate questions:
- Do the observed face frequencies match the theoretical distribution?
- Are the two dice and successive rolls behaving as the documented model requires?
- Is the underlying generator resistant to prediction?
- Is there evidence that the system cannot selectively discard or alter outcomes?
Outcome statistics mainly address the first two questions. The last two require technical documentation, source or system review and a trustworthy audit trail.
Request implementation and audit evidence
Ask the operator for evidence that applies to the exact client and server versions you use. Useful documentation identifies:
- The random-number generator algorithm, library and version.
- How raw generator output is mapped to faces, including the scaling method.
- Whether rejection sampling or another method avoids modulo bias when converting bytes to six values.
- The test date, test-house identity, certificate or report reference and the platforms and channels covered.
- The statistical tests performed on raw and scaled output, their data scope and their results.
- Whether source-code or configuration review covered the live service rather than only a laboratory build.
- How updates are assessed and whether the documented version matches the one currently installed.
The UK Gambling Commission’s RTS 7 says that “Random number generation and game results must be ‘acceptably random’.” It describes demonstrating randomness to a high degree of confidence through generally accepted statistical analysis and says output should be uniform over its range, match theoretical probabilities, remain unpredictable, avoid repeated streams and use scaling that preserves those properties. RTS 7 was last updated 7 May 2024. It also says adaptive behavior is not permitted under that standard. Whether RTS 7 legally governs a particular backgammon app depends on the app’s jurisdiction and circumstances.
A report that names only a company or says “certified” is incomplete for comparison. Its date, platform, version, scope and actual results determine what the report can support.
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Look for independently verifiable rolls
The strongest player-facing design is independently reproducible. In a commit-reveal system, the service commits to information before play, later reveals the required values and gives the verifier enough material to recompute each roll. The verifier should be able to confirm that the revealed data match the earlier commitment and that the face-mapping rule was applied exactly as documented.
An open-source backgammon dice project documents one example and uses rejection sampling so converting random bytes to six faces does not introduce modulo bias. That project demonstrates a method; it does not show that another app uses the same method. Look for a published protocol, source code or reproducible verifier rather than an unsupported claim that rolls are “provably fair.”
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How to weigh operator statements
Operator disclosures are useful leads, but they are not independent findings unless the underlying report and scope can be checked.
- Backgammon Galaxy’s help material, marked modified 20 May 2025, says it uses a cryptographically secure random-number generator and provides profile dice statistics. Treat those as the operator’s statements; the profile totals still need a complete-data and method assessment.
- backgammon.com says Gaming Laboratories International tested its random-number generator in July 2026 and that the World Backgammon Federation conducted due diligence in August 2026. Those dates and claims are published by the site; without examining the certificate or due-diligence materials, they do not independently establish what versions, channels or tests were covered.
Ask for the report itself, the covered version and the result details. A current client using a different server build may not be covered by an older test.
Compare apps on evidence, not on streak anecdotes
When comparing more than one service, score the evidence on the same axes. A statistical histogram and a technical audit answer different questions.
| Evidence axis | Stronger evidence | What remains unknown when absent |
|---|---|---|
| Complete roll history | Exportable, timestamped records containing both dice and version context | Whether displayed totals omit games, special rolls or selected periods |
| RNG and mapping disclosure | Named algorithm and version, documented scaling and handling of raw output | Whether a frequency match reflects a secure and unbiased implementation |
| Independent testing | Report with test house, date, certificate reference, platform, scope, methods and results | Which build and channels were actually examined |
| Player reproducibility | Commit-reveal or another verifier that recomputes individual rolls | Whether a server can replace a result after generation |
Do not convert missing evidence into a claim that an app is biased. State precisely that the relevant property could not be verified.
Troubleshoot a suspicious result
You saw a long run of bad rolls
Save the match identifier and complete history, but do not treat the run as proof. Add it to the pre-existing dataset and test the full record. A memorable subset is the least reliable sample.
One face is unusually common
Check both dice separately, confirm that opening rolls and normal turns were not mixed improperly, remove duplicate or missing records, and repeat the analysis on an independently exported copy. If the anomaly remains, request the mapping and audit details and collect additional complete data without changing the test rule.
The app provides only a histogram
Record the displayed date, version and totals, then report that order, pair dependence and completeness could not be inspected. Ask whether a raw export or match-history download is available.
A test is significant
Check for multiple testing, app updates, special-turn rules, data corruption and dependence between observations. Report the exact test, dataset and assumptions. A significant result is a reason to investigate implementation and obtain independent evidence, not a finding of intent.
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The app changed versions
Split the data at the update boundary and identify the server and client versions if possible. Do not combine versions and call the result a single implementation test.
Write a reproducible fairness report
A useful report lets another person repeat your work. Include:
- The app, platform, client and server versions known to you, and the collection dates.
- Where the data came from, how completeness was assessed and how many rolls were included.
- Whether opening rolls, normal turns and other special cases were separated.
- Separate face counts for each die, plus pair and sequence analyses when available.
- The hypotheses, test choices, significance rule and every exploratory comparison.
- Data-quality problems, missing fields, duplicate handling and any limits imposed by an aggregate-only display.
- The operator’s RNG, mapping and audit documents, including their dates and stated scope.
- A conclusion limited to what the evidence supports: no detected anomaly in this dataset, an anomaly requiring investigation, or insufficient data to assess.
The most defensible conclusion is usually narrower than “the dice are fair.” For example: “In the complete 12,400-roll export for version X, neither die showed a statistically significant face-frequency departure under the pre-specified test; no conclusion was possible about unpredictability or selective handling because the RNG implementation and server logs were unavailable.”
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