How do I simulate a dice-fairness check?

Open this page and use the live ML Model Trainer tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.

Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.

Can I use my own numbers?

Absolutely — every input is adjustable, and with data import you can drive a dice-fairness check from your own measurements.

Use case · powered by ML Model Trainer

ML Model Trainer for a dice-fairness check

Simulate a dice-fairness check live in your browser. This runs the real ML Model Trainer solver — adjust the inputs, watch it respond instantly, and export the result. No install, no account.

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Neural Net

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Neural Network PlaygroundLive

2-layer MLP · live backprop

Controls

Presets

Hidden neurons

Learning rate

Speed1×

A tiny multilayer perceptron trained by real backpropagation. The background shows its learned decision boundary; dots are the training data, colored by true class.

▶ Run in Python

Data Inspector

Epoch0

Loss0.0000

Architecture2→8→1

Governing equation

a = tanh (W_{1} x + b_{1}), \overset{y}{^} = σ (W_{2} a + b_{2}), L = 0.0000

Reading this result: With 8 hidden units the net bends the boundary into curves — more units capture finer shapes like the spiral, but too many can overfit.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Kmeans

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k-Means ClusteringLive

Lloyd's algorithm · live

Controls

Speed1×

Presets

k (centroids)

True clusters

Lloyd's algorithm: assign each point to its nearest centroid, then move each centroid to the mean of its members. Repeat until stable. Try setting k different from the true cluster count.

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Data Inspector

Iteration0

Inertia0.00e+0

Governing equation

J = k = 1 \sum 4 x \in C_{k} \sum ∥ x - μ_{k} ∥^{2}, μ_{k} = \frac{1}{∣ C _{k} ∣} x \in C_{k} \sum x

Reading this result: k matches the 4 true clusters, so each centroid can settle onto one real group and inertia falls to a clean minimum.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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PCA

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Principal Component AnalysisLive

finding the axes of variation

Controls

Presets

Correlation

Spread (x)

PCA finds the directions along which data varies most. The eigenvectors of the covariance matrix are the principal components (cyan = most variance, green = least), and their eigenvalues are the variances along each. Projecting onto the top components is the basis of dimensionality reduction.

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Data Inspector

Variance PC10.00

Variance PC20.00

PC1 explains0%

PC1 angle0°

Governing equation

C v = λ v, \frac{λ _{1}}{λ _{1} + λ _{2}} = \frac{0.00}{0.00} = 0.00

Reading this result: PC1 explains 0% of the variance here; the stronger the correlation between features, the more PCA concentrates information on that first component.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Gradient Descent

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Gradient Descent StudioLive

optimization on a loss landscape

Controls

Watch gradient descent (with momentum) roll downhill on different loss landscapes. Too high a learning rate overshoots.

Presets

Learning rate

Momentum

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Data Inspector

Surfaceripple

Step0/200

Optimizermomentum GD

Governing equation

x_{k + 1} = x_{k} - η \nabla f (x_{k}), η = 3

Reading this result: A learning rate of 3 is well matched to the curvature here: steps are large enough to make progress yet small enough to avoid overshoot, giving a smooth, roughly quadratic descent toward the minimum.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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About this simulation

The full ML Model Trainer tool models a dice-fairness check with the same numerics engineers and scientists use — running entirely client-side. Change any parameter and the result updates in real time, so you can build intuition, check a design, or teach the concept without spreadsheets or installs.

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Other ways to simulate a dice-fairness check

Optimize + UQ for a dice-fairness check Hypothesis Test for a dice-fairness check Linear Regression for a dice-fairness check Central Limit Theorem for a dice-fairness check Confidence Intervals for a dice-fairness check Bayesian Inference for a dice-fairness check

Frequently asked questions

How do I simulate a dice-fairness check?: Open this page and use the live ML Model Trainer tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.
Is it free?: Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.
Can I use my own numbers?: Absolutely — every input is adjustable, and with data import you can drive a dice-fairness check from your own measurements.